[User] Sam has 5 cookies, and Mom gives him 4 more. How many cookies does he have now?

[Assistant] Start with 5 and count up 4 more: 5, 6, 7... Can you keep counting to find the total now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 6 + 3.

[Assistant] Begin at 6 and add 3: 6, 7, 8... Can you finish counting now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 7 + 2.

[Assistant] Count up from 7 by 2: 7, 8... Can you find the total now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Lila has 9 balloons, and 3 fly away. How many are left?

[Assistant] Start at 9 and count back 3: 9, 8, 7... Can you keep going to find how many are left now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 8 - 4.

[Assistant] Begin at 8 and count back 4: 8, 7, 6... Can you finish counting now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 10 - 6.

[Assistant] Count back from 10 by 6: 10, 9, 8... Can you find what’s left now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Tim has 7 apples, and Sue has 4. Who has more?

[Assistant] Look at 7 and 4. Which number is bigger? Can you decide who has more now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 9 greater than 6?

[Assistant] Compare 9 and 6. Which one is more? Can you tell me now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Compare 5 and 8. Which is less?

[Assistant] Look at 5 and 8. Which number is smaller? Can you say it now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A jar has 25 candies. How many tens and ones are there?

[Assistant] In 25, the 2 is in the tens place. How many tens does that show? Can you figure out the ones too now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What is 19 in tens and ones?

[Assistant] 19 has a 1 in the tens place. How many ones are left? Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Show 30 as tens and ones.

[Assistant] 30 has a 3 in the tens place. Are there any ones? Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A sign is a shape with 3 sides. What shape could it be?

[Assistant] Think of a shape with 3 sides. What’s one you know? Can you name it now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Name a shape with 4 equal sides.

[Assistant] Imagine a shape where all 4 sides are the same length. What’s it called? Can you say it now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What shape is round with no sides?

[Assistant] Think of a shape that’s round and doesn’t have any straight sides. What’s its name? Can you tell me now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A pencil is 4 paper clips long. How many paper clips if it’s twice as long?

[Assistant] Twice as long means 4 + 4. Can you add these together now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A book is 6 cubes long. How many cubes would show this?

[Assistant] Line up 6 cubes: 1, 2, 3... Can you count them now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A toy is 5 blocks long. Show this length.

[Assistant] Put 5 blocks end to end: 1, 2, 3... Can you finish this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] School starts at 7 o’clock. What time is it one hour later?

[Assistant] One hour after 7:00 is the next hour. What number comes after 7? Can you say it now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What time is it when the clock shows 4:00?

[Assistant] The hour hand is on 4, and the minute hand is on 12. What’s this time called? Can you tell me now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Show 9:00 on a clock.

[Assistant] Put the hour hand on 9 and the minute hand on 12. Can you draw or say this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A cat has 6 toys, and 3 get lost. How many toys are left?

[Assistant] Start with 6 and count back 3: 6, 5, 4... Can you find how many are left now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A girl has 5 flowers, and she picks 4 more. How many does she have?

[Assistant] Count up from 5 by 4: 5, 6, 7... Can you keep going to find the total now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A boy has 8 marbles, and he gives away 2. How many are left?

[Assistant] Begin at 8 and count back 2: 8, 7... Can you finish counting now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store has 45 apples, and 27 more arrive. How many apples now?

[Assistant] Add 45 + 27. Start with the ones: 5 + 7. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 34 + 58.

[Assistant] Add ones first: 4 + 8. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 67 + 19.

[Assistant] Add tens first: 60 + 10 = 70, then add ones. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A jar has 83 candies, and 26 are eaten. How many are left?

[Assistant] Subtract 83 - 26. Start with ones: 3 - 6 (borrow from tens). Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 72 - 45.

[Assistant] Subtract ones: 2 - 5 (borrow if needed). Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 99 - 17.

[Assistant] Subtract tens first: 90 - 10 = 80, then ones. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A frog jumps 5 feet every hop. How far after 4 hops?

[Assistant] Skip count by 5s: 5, 10, 15, 20. Can you count this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Count by 2s from 4 to 10.

[Assistant] Start at 4: 4, 6, 8, 10. Can you say this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Skip count by 10s from 30 to 60.

[Assistant] Go: 30, 40, 50, 60. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A school has 234 students. How many hundreds are there?

[Assistant] In 234, the hundreds digit is 2. That’s 2 hundreds. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Write 156 in hundreds, tens, ones.

[Assistant] 156 is 1 hundred, 5 tens, 6 ones. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s 308 as hundreds, tens, ones?

[Assistant] 308 is 3 hundreds, 0 tens, 8 ones. Can you show this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A toy costs 75 cents. You have 2 quarters and 3 dimes. Do you have enough?

[Assistant] Count coins: each quarter is 25¢, each dime is 10¢. Add: 2 * 25 + 3 * 10. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] How much is 3 nickels and 4 pennies?

[Assistant] 3 nickels = 15¢, 4 pennies = 4¢. Add: 15 + 4. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the total of 1 dollar and 2 quarters?

[Assistant] 1 dollar = 100¢, 2 quarters = 50¢. Add: 100 + 50. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Lunch is at 12:00. What time is it 30 minutes later?

[Assistant] 30 minutes after 12:00 is 12:30. Can you say this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Show 3:30 on a clock.

[Assistant] Hour hand on 3, minute hand on 6 (half past). Can you draw this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What time is 7:30?

[Assistant] 7:30 is half past seven. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A ribbon is 10 cm long. How long is it if you cut it in half?

[Assistant] Half of 10 cm is 10 ÷ 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Measure a pencil that’s 6 inches long.

[Assistant] It’s 6 inches. Can you show this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A book is 15 cm long. Write this length.

[Assistant] 15 cm is fifteen centimeters. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A graph shows 3 stars for dogs, 2 for cats. How many pets total?

[Assistant] Add stars: 3 + 2. Can you count this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A picture graph has 4 suns for Monday, 5 for Tuesday. Which day has more?

[Assistant] Compare 4 and 5. Is 5 more than 4? Can you decide this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Show 3 apples on a picture graph.

[Assistant] Draw 3 apple symbols. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A class has 16 students. Is this an even or odd number?

[Assistant] Even numbers end in 0, 2, 4, 6, 8. Check 16’s last digit. Can you decide this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 7 an even or odd number?

[Assistant] Even numbers end in 0, 2, 4, 6, 8. Check 7. Can you say this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 24 even or odd?

[Assistant] Look at the last digit: 4. Is 4 even? Can you answer this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A garden has 3 rows of 4 flowers each. How many flowers total?

[Assistant] Count 3 groups of 4: 4 + 4 + 4. Can you add this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Show 2 rows of 5 stars in an array.

[Assistant] Draw 2 rows, 5 stars each: 5 + 5. Can you draw this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s 4 rows of 3 dots?

[Assistant] Add 4 groups of 3: 3 + 3 + 3 + 3. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A box holds 6 eggs, and there are 4 boxes. How many eggs total?

[Assistant] Multiply 6 by 4: 6 * 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 7 * 3.

[Assistant] Think of 7 groups of 3: 3 + 3 + 3 + 3 + 3 + 3 + 3. Can you add this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 5 * 8.

[Assistant] Multiply: 5 * 8. Use 5 times 8. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A teacher has 18 pencils for 6 students. How many pencils per student?

[Assistant] Divide 18 by 6: 18 ÷ 6. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 20 ÷ 5.

[Assistant] How many 5s fit in 20? Try 5, 10, 15, 20. Can you count this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 24 ÷ 8.

[Assistant] Divide 24 by 8. How many 8s in 24? Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store sells 345 toys in January and 278 in February. How many total?

[Assistant] Add 345 + 278. Start with ones: 5 + 8. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 456 + 123.

[Assistant] Add ones first: 6 + 3. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 789 + 104.

[Assistant] Add hundreds first: 700 + 100. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A library has 654 books, and 189 are borrowed. How many are left?

[Assistant] Subtract 654 - 189. Start with ones: 4 - 9 (borrow if needed). Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 543 - 276.

[Assistant] Subtract ones: 3 - 6 (borrow from tens). Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 900 - 345.

[Assistant] Subtract hundreds first: 900 - 300. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A pizza is cut into 4 equal parts. You eat 1 part. What fraction did you eat?

[Assistant] 1 part out of 4 is 1/4. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 1/3 bigger than 1/4?

[Assistant] Compare using a number line or pieces. Is 1/3 more than 1/4? Can you decide this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the fraction for 1 out of 6 pieces?

[Assistant] 1 out of 6 is 1/6. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rug is 5 feet long and 3 feet wide. What’s its area?

[Assistant] Use area = length * width: The length is 5 and the width is 3. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the area of a rectangle 4 cm by 6 cm.

[Assistant] Multiply 4 * 6. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rectangle is 7 m long, 2 m wide. What’s the area?

[Assistant] Use A = l * w: A = 7 * 2. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A yard is a rectangle 8 ft by 5 ft. What’s the perimeter?

[Assistant] Perimeter = 2l + 2w: P = 2 * 8 + 2 * 5. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the perimeter of a square with side 4 cm.

[Assistant] Perimeter = 4 * side: P = 4 * 4. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangle has sides 3 m, 4 m, 5 m. What’s the perimeter?

[Assistant] Add all sides: 3 + 4 + 5. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A movie starts at 2:15. It’s 30 minutes long. What time does it end?

[Assistant] Add 30 minutes to 2:15: 15 + 30 = 45, so 2:45. Can you say this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What time is 4:25?

[Assistant] 4:25 is 25 minutes past four. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Show 9:10 on a clock.

[Assistant] Hour hand on 9, minute hand on 2 (10 minutes). Can you draw this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A graph shows 5 votes for blue, 3 for red. How many votes total?

[Assistant] Add bars: 5 + 3. Can you count this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A bar graph has 4 for cats, 6 for dogs. Which is more popular?

[Assistant] Compare 4 and 6. Is 6 more than 4? Can you decide this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Make a bar graph with 2 for apples, 5 for oranges.

[Assistant] Draw bars: 2 units for apples, 5 for oranges. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A playground is a shape with 4 sides and opposite sides equal. What is it?

[Assistant] A shape with 4 sides and opposite sides equal is a rectangle or parallelogram. Can you name this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] How many sides does a quadrilateral have?

[Assistant] A quadrilateral has 4 sides. Can you say this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Name a shape with 4 right angles.

[Assistant] A shape with 4 right angles is a rectangle or square. Can you choose one now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A factory makes 24 toys per day. How many in 5 days?

[Assistant] Multiply 24 * 5. Start with 5 * 4 ones. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 36 * 7.

[Assistant] Multiply 7 * 6 ones, then 7 * 3 tens. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 49 * 3.

[Assistant] Use 3 * 9 ones, then 3 * 4 tens. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A class has 96 candies to split among 12 students. How many per student?

[Assistant] Divide 96 by 12. How many times does 12 go into 9? Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 85 ÷ 5.

[Assistant] How many 5s in 8 (tens)? Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 144 ÷ 12.

[Assistant] Divide 14 (first two digits) by 12. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A town has 2,345 people, and 1,678 move in. How many now?

[Assistant] Add 2,345 + 1,678. Start with ones: 5 + 8. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 4,512 + 3,289.

[Assistant] Add ones first: 2 + 9. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 6,704 + 2,195.

[Assistant] Add hundreds first: 700 + 200. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store had 5,432 items, and 2,789 were sold. How many are left?

[Assistant] Subtract 5,432 - 2,789. Start with ones: 2 - 9 (borrow if needed). Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 7,654 - 3,210.

[Assistant] Subtract ones: 4 - 0. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 9,876 - 4,543.

[Assistant] Subtract thousands first: 9,000 - 4,000. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A cake is cut into 8 pieces, and you eat 2. What fraction is equivalent to 2/8?

[Assistant] Simplify 2/8 by dividing by 2: 2 ÷ 2 / 8 ÷ 2. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 3/6 equal to 1/2?

[Assistant] Simplify 3/6: 3 ÷ 3 / 6 ÷ 3. Can you compare this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find an equivalent fraction to 4/12.

[Assistant] Divide by 4: 4 ÷ 4 / 12 ÷ 4. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A recipe uses 1/3 cup sugar and 1/4 cup salt. Which is more?

[Assistant] Find a common denominator, like 12. Convert 1/3 to ?/12. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 2/5 greater than 3/8?

[Assistant] Use a common denominator, like 40. Convert 2/5 to ?/40. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Compare 5/6 and 4/5.

[Assistant] Common denominator is 30. Convert 5/6 to ?/30. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A corner of a book makes a 90° angle. What type of angle is this?

[Assistant] A 90° angle is a right angle. Can you name this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Measure an angle that’s 45°.

[Assistant] Use a protractor, line up 0° and read 45°. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s an angle of 120° called?

[Assistant] An angle over 90° but less than 180° is obtuse. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A class counts books read: 2, 3, 2, 4. How many read 2 books?

[Assistant] Count the 2s: 2, 2. That’s 2 students. Can you mark this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Make a line plot for 1, 1, 3, 5.

[Assistant] Put Xs at 1 (twice), 3, 5. Can you draw this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In a line plot of 4, 4, 6, how many are 4?

[Assistant] Count the 4s: 4, 4. That’s 2. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A game needs teams of 6. With 18 players, how many teams?

[Assistant] Find how many 6s in 18: 18 ÷ 6. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] List the factors of 12.

[Assistant] Start with 1: 1 * 12. Then try 2: 2 * 6. Can you list them now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s a multiple of 5 less than 20?

[Assistant] Count by 5s: 5, 10, 15. Pick one under 20. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A butterfly’s wings are 6 cm wide. If symmetric, how wide is one wing?

[Assistant] Symmetry means equal halves: 6 ÷ 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Does a square have symmetry?

[Assistant] Fold a square in half (top to bottom). Do sides match? Can you decide this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] How many lines of symmetry in a rectangle?

[Assistant] Fold a rectangle vertically. Check if it matches. Can you count lines now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store prices an item at $4.75. What is the value of the digit 7 in this price?

[Assistant] In $4.75, the 7 is in the tenths place. The value is 7 * 0.1. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What is the value of the digit 3 in 12.34?

[Assistant] The 3 is in the tenths place. Its value is 3 * 0.1. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In 5.682, what is the value of the digit 8?

[Assistant] The 8 is in the hundredths place. Its value is 8 * 0.01. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A runner jogs 3.4 miles on Monday and 2.75 miles on Tuesday. How far did she jog in total?

[Assistant] Line up the decimals and add: 3.4 + 2.75. Start by adding the hundredths place. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Subtract 1.25 from 4.8.

[Assistant] Line up the decimals: 4.80 - 1.25. Subtract the hundredths place first. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Add 6.32 and 0.9.

[Assistant] Write 0.9 as 0.90 and add: 6.32 + 0.90. Start with the hundredths place. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A box holds 24 candies, and there are 5 boxes. How many candies are there in total?

[Assistant] Multiply 24 by 5. Start with 5 * 4 in the ones place. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Multiply 36 by 4.

[Assistant] Break it down: 4 * 6 ones + 4 * 3 tens. Start with 4 * 6. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 15 * 7.

[Assistant] Use the standard method: 7 * 5 ones + 7 * 1 ten. Begin with 7 * 5. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A teacher has 48 pencils to split evenly among 6 students. How many pencils does each get?

[Assistant] Divide 48 by 6. Start by seeing how many times 6 goes into 4 (the tens place). Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Divide 72 by 9.

[Assistant] See how many times 9 fits into 7 (tens place). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 56 ÷ 8.

[Assistant] Divide 56 by 8. Start with how many times 8 goes into 5 (tens). Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A recipe needs 1/4 cup of sugar and 2/4 cup of flour. How much total dry ingredient is that?

[Assistant] Since the denominators are the same, add the numerators: 1/4 + 2/4 = (1 + 2)/4. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Subtract 3/8 from 5/8.

[Assistant] With the same denominator, subtract numerators: 5/8 - 3/8 = (5 - 3)/8. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Add 2/5 and 1/5.

[Assistant] Add the numerators over the common denominator: 2/5 + 1/5 = (2 + 1)/5. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A garden is 3/4 meter long. If 1/2 of it is planted, how much is planted?

[Assistant] Multiply the fractions: 3/4 * 1/2. Multiply the numerators: 3 * 1. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Multiply 2/3 by 5/6.

[Assistant] Multiply numerators and denominators: 2/3 * 5/6 = (2 * 5)/(3 * 6). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 1/5 * 3/4.

[Assistant] Multiply straight across: 1/5 * 3/4 = (1 * 3)/(5 * 4). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A box is 5 cm long, 3 cm wide, and 2 cm high. What’s its volume?

[Assistant] Use the formula V = length * width * height. Substitute: V = 5 * 3 * 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the volume of a prism with length 4 in, width 6 in, height 3 in.

[Assistant] The formula is V = l * w * h. Plug in: V = 4 * 6 * 3. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the volume if l = 7 ft, w = 2 ft, h = 5 ft.

[Assistant] Use V = l * w * h: V = 7 * 2 * 5. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A treasure is at (3, 5) on a map. How far right and up do you move from (0, 0)?

[Assistant] The x-coordinate (3) is right, y-coordinate (5) is up. Move 3 right from (0, 0). Can you plot this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Plot the point (4, 2) on a coordinate plane.

[Assistant] Start at (0, 0), move 4 right (x = 4), then 2 up (y = 2). Can you mark this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What is the location of (6, 1)?

[Assistant] Move 6 right (x = 6), then 1 up (y = 1) from (0, 0). Can you describe this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store has 2 packs of 5 pencils plus 3 more pencils. How many pencils total?

[Assistant] Write it as 2 * 5 + 3. Do the multiplication first: 2 * 5. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 4 + 3 * 6.

[Assistant] Follow PEMDAS: multiply first, 3 * 6. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 10 - 2 * 4.

[Assistant] Multiply first: 2 * 4. Then subtract from 10. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A playground has a shape with 4 equal sides and 4 right angles. What is it?

[Assistant] A shape with 4 equal sides and 4 right angles is a square. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Name a shape with 3 sides and 3 angles.

[Assistant] A shape with 3 sides and 3 angles is a triangle. Can you identify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What is a shape with 4 sides but no right angles?

[Assistant] A shape with 4 sides and no right angles could be a rhombus (if equal sides) or parallelogram. Can you choose one now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A runner trains for 3 kilometers. How many meters is that?

[Assistant] 1 kilometer = 1000 meters. Multiply: 3 * 1000. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Convert 2 feet to inches.

[Assistant] 1 foot = 12 inches. Multiply: 2 * 12. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Change 5000 grams to kilograms.

[Assistant] 1 kilogram = 1000 grams. Divide: 5000 ÷ 1000. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A class measures ribbons: 1/4, 1/2, 1/4, 3/4 feet. How many are 1/4 foot on a line plot?

[Assistant] Count the number of 1/4s: 1/4, 1/4. There are 2. Can you mark this on a line plot now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Make a line plot for: 1/3, 2/3, 1/3 ft.

[Assistant] Mark an X at 1/3 twice and 2/3 once on the number line. Can you plot this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] How many 1/2s in a line plot of 1/2, 1/4, 1/2 ft?

[Assistant] Count the 1/2s: 1/2, 1/2. There are 2. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A recipe uses 2 cups of flour for 6 cookies. How many cups for 12 cookies?

[Assistant] Set up the ratio: 2/6 = x/12. Cross-multiply: 2 * 12 = 6 * x. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Write the ratio 8 to 12 in simplest form.

[Assistant] Divide both by their GCF: 8 ÷ 4 / 12 ÷ 4. Find the GCF first. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If 15:5, what’s the equivalent ratio with 3 as the second number?

[Assistant] Divide both by 5: 15/5 : 5/5 = 3:1. Adjust to make the second number 3. Can you scale this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A car travels 120 miles in 2 hours. What’s the unit rate in miles per hour?

[Assistant] Divide distance by time: 120 ÷ 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the unit rate: 18 books for $6.

[Assistant] Divide cost by number: 6 ÷ 18. Simplify to dollars per book. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the unit rate of 50 meters in 10 seconds?

[Assistant] Divide: 50 ÷ 10. This gives meters per second. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A shirt costs $20 and is on sale for 25% off. What’s the discount amount?

[Assistant] Find 25% of 20: 0.25 * 20. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What is 40% of 50?

[Assistant] Convert 40% to 0.40 and multiply: 0.40 * 50. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] 15 is what percent of 60?

[Assistant] Set up: (15 / 60) * 100. Divide 15 by 60 first. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store charges $2.75 per pound of apples. How much for 3.2 pounds?

[Assistant] Multiply 2.75 * 3.2. Ignore decimals first: 275 * 32. Can you start this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Multiply 0.6 by 4.5.

[Assistant] Treat as 6 * 45, then adjust for 2 decimal places. Start with 6 * 45. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 1.25 * 0.8.

[Assistant] Multiply 125 * 8, then place the decimal (3 places total). Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rope 12.6 meters long is cut into 3 equal pieces. How long is each piece?

[Assistant] Divide 12.6 by 3. Move the decimal: 126 ÷ 3. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Divide 5.4 by 0.9.

[Assistant] Move decimals to make 54 ÷ 9. Can you divide this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 8.1 ÷ 2.7.

[Assistant] Adjust decimals: 81 ÷ 27. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A party has 18 balloons and 24 candies. What’s the greatest number of equal bags?

[Assistant] Find the GCF of 18 and 24. List factors of 18: 1, 2, 3, 6, 9, 18. Can you list 24’s factors now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the GCF of 12 and 30.

[Assistant] List factors of 12: 1, 2, 3, 4, 6, 12. Now list factors of 30. Can you find the greatest common one? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the GCF of 15 and 25?

[Assistant] Prime factorize 15: 3 * 5. Now factorize 25. Can you find the GCF now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A red light blinks every 6 seconds, a blue every 8 seconds. When do they blink together?

[Assistant] Find the LCM of 6 and 8. List multiples of 6: 6, 12, 18, 24. Can you list 8’s multiples now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the LCM of 9 and 12.

[Assistant] Multiples of 9: 9, 18, 27, 36. Now list multiples of 12. Can you find the least common one? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the LCM of 10 and 15?

[Assistant] Prime factorize 10: 2 * 5, and 15: 3 * 5. Use highest powers: 2 * 3 * 5. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] The temperature drops from 5°C to -3°C. What’s the change?

[Assistant] Subtract: -3 - 5. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Add -4 and 7.

[Assistant] Start with 7 and move left 4 on a number line: 7 - 4. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s -6 + (-2)?

[Assistant] Add the negatives: -6 - 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store sells n notebooks at $2 each. What’s the total cost expression?

[Assistant] Multiply number by cost: 2 * n or 2n. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Evaluate 3x + 4 when x = 5.

[Assistant] Substitute x = 5: 3 * 5 + 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Simplify 2y + 3 + y.

[Assistant] Combine like terms: 2y + y + 3. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A bag has x candies plus 4, totaling 10. How many candies in the bag?

[Assistant] Set up: x + 4 = 10. Subtract 4 from both sides: x + 4 - 4 = 10 - 4. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve x - 7 = 3.

[Assistant] Add 7 to both sides: x - 7 + 7 = 3 + 7. Can you find x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find x if 5x = 20.

[Assistant] Divide both sides by 5: 5x / 5 = 20 / 5. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangle sign has a base of 6 ft and height of 4 ft. What’s its area?

[Assistant] Use the formula A = (1/2) * base * height. Substitute: A = (1/2) * 6 * 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the area of a parallelogram with base 8 cm, height 3 cm.

[Assistant] The formula is A = base * height. Plug in: A = 8 * 3. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangle has base 10 m, height 5 m. What’s the area?

[Assistant] Use A = (1/2) * b * h: A = (1/2) * 10 * 5. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A student’s test scores are 85, 90, 85, 95. What’s the average score?

[Assistant] To find the mean, add all numbers: 85 + 90 + 85 + 95. Can you sum this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the median of 3, 7, 2, 8, 5.

[Assistant] Order the numbers: 2, 3, 5, 7, 8. Pick the middle one. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the mode of 4, 4, 6, 7, 6?

[Assistant] The mode is the number that appears most often. Count how many times 4 and 6 appear. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A car uses 3 gallons of gas for 90 miles. How many gallons for 150 miles?

[Assistant] Set up the proportion: 3/90 = x/150. Cross-multiply: 3 * 150 = 90 * x. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If 4 pens cost $2, how much for 10 pens?

[Assistant] Use a proportion: 4/2 = 10/x. Cross-multiply: 4 * x = 2 * 10. Can you find x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is 5/15 = 8/24 proportional?

[Assistant] Simplify both ratios. For 5/15, divide by 5: 5 ÷ 5 / 15 ÷ 5. Can you simplify both now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A machine fills 4 bottles in 12 seconds. What’s the constant of proportionality (bottles per second)?

[Assistant] The constant k = y/x. Here, y = 4, x = 12. Calculate k = 4 / 12. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If y = kx and y = 18 when x = 6, find k.

[Assistant] Substitute: 18 = k * 6. Divide both sides by 6. Can you find k now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the constant if y = 25 when x = 5.

[Assistant] Use y = kx: 25 = k * 5. Solve for k by dividing. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A map has a scale of 1 inch = 5 miles. If two towns are 3 inches apart, how far apart are they?

[Assistant] Multiply the scale: 3 * 5 miles. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A blueprint scale is 1 cm = 2 m. What’s 4 cm in real life?

[Assistant] Use the scale: 4 * 2 meters. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If 1 inch = 10 ft, how many inches for 30 ft?

[Assistant] Divide by the scale: 30 ÷ 10. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A diver descends 2.5 meters, then rises 1.75 meters. What’s her new depth?

[Assistant] Subtract: -2.5 + 1.75. Align decimals and subtract hundredths first. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Add -3/4 and 1/2.

[Assistant] Find a common denominator: 4. Convert 1/2 to 2/4. Now add: -3/4 + 2/4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Subtract -1.2 from 0.8.

[Assistant] Subtracting a negative is adding: 0.8 - (-1.2) = 0.8 + 1.2. Can you add this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A recipe halves 3/4 cup of sugar. How much sugar is used?

[Assistant] Multiply: 1/2 * 3/4. Multiply numerators: 1 * 3. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Multiply -2.5 by 1.4.

[Assistant] Ignore signs and decimals first: 25 * 14. Calculate this, then adjust. Can you start now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Divide -5/6 by 2/3.

[Assistant] Multiply by the reciprocal: -5/6 * 3/2. Multiply numerators: -5 * 3. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A shirt costs $5 plus twice an unknown amount, totaling $13. What’s the unknown?

[Assistant] Set up: 2x + 5 = 13. Subtract 5: 2x + 5 - 5 = 13 - 5. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 3x - 4 = 11.

[Assistant] Add 4 to both sides: 3x - 4 + 4 = 11 + 4. Can you find x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find x if 2x + 7 = 19.

[Assistant] Subtract 7: 2x + 7 - 7 = 19 - 7. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A budget allows up to $50 for x shirts at $8 each. What’s the maximum shirts?

[Assistant] Set up: 8x ≤ 50. Divide by 8: 8x / 8 ≤ 50 / 8. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 2x + 3 < 9.

[Assistant] Subtract 3: 2x + 3 - 3 < 9 - 3. Can you find x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find x if 5x - 2 > 13.

[Assistant] Add 2: 5x - 2 + 2 > 13 + 2. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A round table has a diameter of 4 ft. What’s its circumference? Use π ≈ 3.14.

[Assistant] Use C = π * d. Substitute d = 4: C = 3.14 * 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the circumference of a circle with radius 3 cm. Use π ≈ 3.14.

[Assistant] Use C = 2 * π * r. Plug in r = 3: C = 2 * 3.14 * 3. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A circle’s diameter is 10 m. What’s its circumference? Use π ≈ 3.14.

[Assistant] C = π * d: C = 3.14 * 10. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A pizza has a radius of 6 inches. What’s its area? Use π ≈ 3.14.

[Assistant] Use A = π * r². Substitute r = 6: A = 3.14 * 6². Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the area of a circle with radius 5 cm. Use π ≈ 3.14.

[Assistant] A = π * r²: A = 3.14 * 5². Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A circle’s diameter is 8 m. What’s its area? Use π ≈ 3.14.

[Assistant] First, find radius: r = 8 / 2. Then use A = π * r². Can you start with r now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A bag has 3 red and 2 blue marbles. What’s the probability of picking a red?

[Assistant] Probability = favorable outcomes / total outcomes. Total marbles = 3 + 2. Can you set this up now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A die is rolled. What’s the probability of getting a 4?

[Assistant] Total outcomes = 6, favorable = 1. Probability = 1/6. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the probability of drawing a heart from a standard deck (52 cards, 13 hearts).

[Assistant] Probability = hearts / total cards = 13 / 52. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Two angles form a straight line. One is 40°. What’s the other angle?

[Assistant] Supplementary angles sum to 180°. Subtract: 180 - 40. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the complement of a 25° angle.

[Assistant] Complementary angles sum to 90°. Subtract: 90 - 25. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If two angles are supplementary and one is 110°, what’s the other?

[Assistant] Subtract from 180°: 180 - 110. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A box is 4 ft long, 3 ft wide, 2 ft high. What’s its surface area?

[Assistant] Use SA = 2(lw + lh + wh). Substitute: SA = 2(4*3 + 4*2 + 3*2). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the surface area of a prism: l = 5 cm, w = 2 cm, h = 3 cm.

[Assistant] SA = 2(lw + lh + wh). Plug in: SA = 2(5*2 + 5*3 + 2*3). Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A prism has l = 6 m, w = 4 m, h = 1 m. What’s its surface area?

[Assistant] Use SA = 2(lw + lh + wh): SA = 2(6*4 + 6*1 + 4*1). Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A bacteria doubles every hour. Starting with 1, how many after 4 hours?

[Assistant] Use 2^n: 2^4. Calculate 2 * 2 * 2 * 2. Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Simplify 3^(-2).

[Assistant] Negative exponent means reciprocal: 3^(-2) = 1 / 3². Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find 5^3.

[Assistant] Multiply: 5 * 5 * 5. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A planet is 150,000,000 km from the sun. Write this in scientific notation.

[Assistant] Move the decimal to 1.5: 1.5 * 10^n. Count places: 8. So, 1.5 * 10^8. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Convert 3.2 * 10^5 to standard form.

[Assistant] Move the decimal 5 places right: 3.2 becomes 320,000. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Write 0.0078 in scientific notation.

[Assistant] Move decimal to 7.8: 7.8 * 10^n. Count left 3 places: 7.8 * 10^(-3). Can you verify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A square garden has an area of 144 m². What’s the side length?

[Assistant] Take the square root: √144. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find √25.

[Assistant] What number squared equals 25? Try 5 * 5. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the cube root of 27?

[Assistant] Find ∛27: what number cubed is 27? Try 3 * 3 * 3. Can you verify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A hiker climbs from (2, 3) to (5, 9). What’s the slope of her path?

[Assistant] Use slope = (y₂ - y₁) / (x₂ - x₁). Substitute: (9 - 3) / (5 - 2). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the slope between (1, 4) and (3, 8).

[Assistant] Slope = (8 - 4) / (3 - 1). Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the slope from (0, 2) to (4, 10)?

[Assistant] Use (10 - 2) / (4 - 0). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A taxi charges $3 plus $2 per mile. Write the equation for the cost y after x miles.

[Assistant] Use y = mx + b. Here, m = 2, b = 3. Write y = 2x + 3. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Write y = 3x - 5 in slope-intercept form.

[Assistant] It’s already in y = mx + b form. Identify slope (m) as 3. Can you find the y-intercept now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the equation of a line with slope 4 and y-intercept -2.

[Assistant] Use y = mx + b: y = 4x + (-2). Simplify to y = 4x - 2. Can you write this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store sells 2 apples and 3 oranges for $7, and 4 apples and 1 orange for $9. Find the cost of each.

[Assistant] Set up: 2a + 3o = 7 and 4a + o = 9. Eliminate o by multiplying the second by 3: 12a + 3o = 27. Can you subtract the first now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve: y = 2x + 1 and y = x + 3.

[Assistant] Set equal: 2x + 1 = x + 3. Subtract x: 2x - x + 1 = 3. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find x and y: 3x + y = 5 and x - y = 1.

[Assistant] Add the equations: (3x + y) + (x - y) = 5 + 1. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A vending machine charges $0.50 per soda. Write a function for cost f(x) for x sodas.

[Assistant] The function is f(x) = 0.50x. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If f(x) = 3x - 2, find f(4).

[Assistant] Substitute x = 4: f(4) = 3 * 4 - 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Is {(1, 2), (2, 4), (3, 2)} a function?

[Assistant] Check if each x has one y. Look at x = 1, 2, 3. Can you determine this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A ladder reaches 8 ft up a wall, base 6 ft from the wall. How long is the ladder?

[Assistant] Use a² + b² = c²: 6² + 8² = c². Calculate 36 + 64. Can you find c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the hypotenuse if legs are 3 and 4.

[Assistant] Use a² + b² = c²: 3² + 4² = c². Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangle has legs 5 and 12. What’s the hypotenuse?

[Assistant] Apply 5² + 12² = c². Calculate 25 + 144. Can you find c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A can has a radius of 3 cm and height of 10 cm. What’s its volume? Use π ≈ 3.14.

[Assistant] Use V = π * r² * h. Substitute: V = 3.14 * 3² * 10. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the volume of a cylinder with r = 2 m, h = 5 m. Use π ≈ 3.14.

[Assistant] V = π * r² * h: V = 3.14 * 2² * 5. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A cylinder has r = 4 in, h = 6 in. What’s its volume? Use π ≈ 3.14.

[Assistant] Use V = π * r² * h: V = 3.14 * 4² * 6. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A point at (2, 3) is reflected over the x-axis for a mirror image. Where’s the new point?

[Assistant] Reflection over x-axis changes y to -y: (2, 3) becomes (2, -3). Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Rotate (1, 4) 90° counterclockwise around (0, 0).

[Assistant] For 90° counterclockwise, (x, y) becomes (-y, x). Apply to (1, 4). Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Reflect (3, -2) over the y-axis.

[Assistant] Reflection over y-axis changes x to -x: (3, -2) becomes (-3, -2). Can you verify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangle with sides 3, 4, 5 cm is built twice. Are the triangles congruent?

[Assistant] Congruent means same size and shape. Check if sides match: 3, 4, 5 vs. 3, 4, 5. Can you decide now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Are triangles with angles 30°, 60°, 90° and 30°, 60°, 90° congruent?

[Assistant] Congruence needs side lengths too, but same angles suggest similarity. Are sides given equal? Can you check this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Two rectangles both have sides 6 and 8. Are they congruent?

[Assistant] Compare all sides: 6, 8 vs. 6, 8. Can you determine this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A student tracks hours studied (1, 2, 3) and scores (70, 85, 90). Is there a trend?

[Assistant] Plot points: (1, 70), (2, 85), (3, 90). Look for a pattern—does y increase with x? Can you describe this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Given points (2, 3), (4, 5), (6, 7), what’s the trend?

[Assistant] Check if y increases consistently with x. Calculate slope between (2, 3) and (4, 5): (5 - 3) / (4 - 2). Can you do this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Do (1, 2), (2, 4), (3, 5) show a linear trend?

[Assistant] Find slopes: (4 - 2) / (2 - 1) and (5 - 4) / (3 - 2). Are they equal? Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store sells shirts for $5 each plus a $7 shipping fee. If the total cost is $22, how many shirts were bought? Solve for the number of shirts (x).

[Assistant] Set up the equation based on the problem: 5x + 7 = 22. Now, subtract 7 from both sides to isolate the term with x like this -> 5x + 7 - 7 = 22 - 7. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 3x - 4 = 11.

[Assistant] To begin solving for x, add 4 to both sides to remove the constant term like this -> 3x - 4 + 4 = 11 + 4. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 6x + 9 = 27.

[Assistant] Subtract 9 from both sides to start isolating x like this -> 6x + 9 - 9 = 27 - 9. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A movie theater charges $8 for adults and $5 for children. If 2 adults and 3 children spent $31, how much does one adult ticket cost? Solve the system: 2x + 3y = 31 and x = 8 (where x is adult price, y is child price).

[Assistant] Substitute x = 8 into the first equation: 2(8) + 3y = 31. Can you simplify this and solve for y now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve the system of equations: 3x + y = 12 and x - y = 4.

[Assistant] Add both equations together to eliminate y -> 3x + y + x - y = 12 + 4. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve the system: 5x + 2y = 19 and 3x - 2y = 5.

[Assistant] Add the two equations to eliminate y -> 5x + 2y + 3x - 2y = 19 + 5. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A person wants to spend no more than $50 on notebooks costing $4 each and a $10 backpack. How many notebooks (x) can they buy? Solve 4x + 10 ≤ 50.

[Assistant] Subtract 10 from both sides to isolate the term with x like this -> 4x + 10 - 10 ≤ 50 - 10. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 2x - 5 > 7.

[Assistant] Add 5 to both sides to isolate the term with x like this -> 2x - 5 + 5 > 7 + 5. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 3x + 8 ≤ 20.

[Assistant] Subtract 8 from both sides to start isolating x like this -> 3x + 8 - 8 ≤ 20 - 8. Can you try to solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rectangular garden has a length of (x + 4) meters and width of (x - 2) meters. What is the expression for its area? Expand (x + 4)(x - 2).

[Assistant] Use the distributive property (FOIL): x*x + x*(-2) + 4*x + 4*(-2). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Expand (2x + 3)(x - 5).

[Assistant] Apply the distributive property: 2x*x + 2x*(-5) + 3*x + 3*(-5). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Expand (3x - 1)(x + 6).

[Assistant] Use the distributive property: 3x*x + 3x*6 + (-1)*x + (-1)*6. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] The area of a rectangle is x² + 8x + 15 square feet. If the length and width are (x + 5) and (x + 3), factor x² + 8x + 15 to verify.

[Assistant] Find two numbers that multiply to 15 and add to 8. Can you identify these numbers and write the factored form? Let me know if you need help.


[User] Factor x² + 6x + 8.

[Assistant] Look for two numbers that multiply to 8 and add to 6. Can you find these numbers and write the factored form? Let me know if you need help.


[User] Factor x² - 7x + 12.

[Assistant] Find two numbers that multiply to 12 and add to -7. Can you identify these numbers and write the factored form? Let me know if you need help.


[User] A ball is thrown, and its height is modeled by x² - 4x - 5 = 0, where x is time in seconds. When does it hit the ground? Solve by factoring.

[Assistant] Find two numbers that multiply to -5 and add to -4. Can you factor the quadratic and set each factor to zero? Let me know if you need help.


[User] Solve x² + 3x - 10 = 0.

[Assistant] Look for two numbers that multiply to -10 and add to 3. Can you factor this and solve for x? Let me know if you need help.


[User] Solve x² - 6x + 8 = 0.

[Assistant] Find two numbers that multiply to 8 and add to -6. Can you factor this and solve for x? Let me know if you need help.


[User] A bacteria population doubles every hour. If it starts at 4 and reaches 64 after x hours, solve 4 * 2^x = 64.

[Assistant] Divide both sides by 4 to isolate the exponential term: 2^x = 64 / 4. Can you simplify this and solve for x? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 3^x = 81.

[Assistant] Rewrite 81 as a power of 3: 81 = 3^4. Now you have 3^x = 3^4. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 5^(x-2) = 25.

[Assistant] Express 25 as a power of 5: 25 = 5^2. Now rewrite the equation as 5^(x-2) = 5^2. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A person saves $10 the first week, $13 the second, $16 the third. What’s the amount saved in the 5th week?

[Assistant] Find the common difference by subtracting the first term from the second: 13 - 10. Can you use this to find the 5th term with the formula a_n = a_1 + (n-1)d? Let me know if you need help.


[User] Find the 6th term of the arithmetic sequence: 2, 5, 8, 11.

[Assistant] Calculate the common difference: 5 - 2. Then use the formula a_n = a_1 + (n-1)d with n = 6. Can you try this now? Let me know if you need help.


[User] What’s the 4th term of an arithmetic sequence with first term 7 and common difference 4?

[Assistant] Use the formula a_n = a_1 + (n-1)d. Substitute a_1 = 7, d = 4, and n = 4. Can you calculate this now? Let me know if you need help.


[User] A ball bounces to 80% of its previous height. If it starts at 10 meters, what’s the height after 3 bounces? Solve for the 4th term.

[Assistant] Identify the common ratio as 0.8 and use the formula a_n = a_1 * r^(n-1) with a_1 = 10 and n = 4. Can you calculate this now? Let me know if you need help.


[User] Find the 5th term of the geometric sequence: 3, 9, 27, 81.

[Assistant] Determine the common ratio: 9 / 3. Then use a_n = a_1 * r^(n-1) with n = 5. Can you try this now? Let me know if you need help.


[User] What’s the 3rd term of a geometric sequence with first term 2 and common ratio 5?

[Assistant] Use the formula a_n = a_1 * r^(n-1). Substitute a_1 = 2, r = 5, and n = 3. Can you calculate this now? Let me know if you need help.


[User] A triangular garden has a base of 10 meters and a height of 6 meters. What is its area?

[Assistant] Use the formula for the area of a triangle: Area = (1/2) * base * height. Substitute base = 10 and height = 6 into the formula. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the area of a triangle with base 8 cm and height 5 cm.

[Assistant] The formula for the area of a triangle is Area = (1/2) * base * height. Plug in base = 8 and height = 5. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the perimeter of an equilateral triangle with side length 7 meters.

[Assistant] Since it’s an equilateral triangle, all sides are equal. The perimeter is 3 * side length. Substitute side length = 7. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rectangular room is 12 feet long and 9 feet wide. What is its perimeter?

[Assistant] The formula for the perimeter of a rectangle is P = 2 * (length + width). Substitute length = 12 and width = 9. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the area of a square with side length 6 cm.

[Assistant] The area of a square is side * side. Substitute side = 6. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the area of a parallelogram with base 10 m and height 4 m.

[Assistant] Use the formula for the area of a parallelogram: Area = base * height. Plug in base = 10 and height = 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A circular pizza has a diameter of 14 inches. What is its area? Use π ≈ 3.14.

[Assistant] First, find the radius by dividing the diameter by 2: radius = 14 / 2. Then use the formula Area = π * radius². Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the circumference of a circle with radius 5 cm. Use π ≈ 3.14.

[Assistant] The formula for circumference is C = 2 * π * radius. Substitute radius = 5 and π ≈ 3.14. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the area of a circle with diameter 8 m. Use π ≈ 3.14.

[Assistant] Find the radius: radius = diameter / 2 = 8 / 2. Then use Area = π * radius². Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A box has a length of 5 ft, width of 3 ft, and height of 4 ft. What is its volume?

[Assistant] The formula for the volume of a rectangular prism is V = length * width * height. Substitute length = 5, width = 3, and height = 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the surface area of a cube with side length 6 cm.

[Assistant] The surface area of a cube is 6 * side². Substitute side = 6. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the volume of a rectangular prism with length 7 m, width 2 m, and height 3 m.

[Assistant] Use the formula V = length * width * height. Plug in length = 7, width = 2, and height = 3. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A cylindrical water tank has a radius of 2 meters and a height of 5 meters. What is its volume? Use π ≈ 3.14.

[Assistant] The formula for the volume of a cylinder is V = π * radius² * height. Substitute radius = 2, height = 5, and π ≈ 3.14. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the surface area of a cylinder with radius 3 cm and height 4 cm. Use π ≈ 3.14.

[Assistant] The surface area formula is SA = 2 * π * radius² + 2 * π * radius * height. Start by calculating the area of the two bases: 2 * π * 3². Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the volume of a cylinder with radius 6 m and height 10 m. Use π ≈ 3.14.

[Assistant] Use V = π * radius² * height. Substitute radius = 6, height = 10, and π ≈ 3.14. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A spherical balloon has a radius of 3 feet. What is its volume? Use π ≈ 3.14.

[Assistant] The formula for the volume of a sphere is V = (4/3) * π * radius³. Substitute radius = 3 and π ≈ 3.14. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the surface area of a sphere with radius 5 cm. Use π ≈ 3.14.

[Assistant] The surface area formula is SA = 4 * π * radius². Substitute radius = 5 and π ≈ 3.14. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the volume of a sphere with radius 2 m. Use π ≈ 3.14.

[Assistant] Use V = (4/3) * π * radius³. Substitute radius = 2 and π ≈ 3.14. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Two angles form a straight line, and one is 40°. What is the measure of the other angle?

[Assistant] Since the angles are supplementary (sum to 180°), subtract the known angle from 180°: 180 - 40. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the measure of an angle that is complementary to 25°.

[Assistant] Complementary angles sum to 90°. Subtract 25 from 90: 90 - 25. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In a triangle, two angles are 50° and 60°. What is the third angle?

[Assistant] The sum of angles in a triangle is 180°. Add the two known angles: 50 + 60, then subtract from 180. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A ladder is 10 feet long and reaches 6 feet up a wall. How far is the base of the ladder from the wall?

[Assistant] Use the Pythagorean Theorem: a² + b² = c², where c = 10 (hypotenuse) and a = 6 (leg). Substitute: 6² + b² = 10². Can you solve for b now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the hypotenuse of a right triangle with legs 3 cm and 4 cm.

[Assistant] Apply the Pythagorean Theorem: a² + b² = c². Substitute a = 3 and b = 4: 3² + 4² = c². Can you calculate c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the length of a leg in a right triangle with hypotenuse 13 m and one leg 5 m.

[Assistant] Use the Pythagorean Theorem: a² + b² = c². Substitute c = 13 and a = 5: 5² + b² = 13². Can you solve for b now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A ramp rises 3 meters over a horizontal distance of 4 meters. What is the angle of elevation? Use tan.

[Assistant] The tangent ratio is tan(θ) = opposite / adjacent. Substitute opposite = 3 and adjacent = 4: tan(θ) = 3/4. Now use the inverse tangent (arctan) to find θ. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the sine of an angle in a right triangle with opposite side 6 cm and hypotenuse 10 cm.

[Assistant] The sine ratio is sin(θ) = opposite / hypotenuse. Substitute opposite = 6 and hypotenuse = 10: sin(θ) = 6/10. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate the length of the adjacent side in a right triangle where cos(θ) = 8/17 and hypotenuse is 17 m.

[Assistant] The cosine ratio is cos(θ) = adjacent / hypotenuse. Given cos(θ) = 8/17 and hypotenuse = 17, set up: 8/17 = adjacent / 17. Solve for the adjacent side. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangular plot has angles 40° and 60°, with the side between them 10 meters. Find the side opposite the 40° angle using the Law of Sines.

[Assistant] The Law of Sines states: a / sin(A) = b / sin(B). Let a be the side opposite 40°, and b = 10 opposite 60°. Set up: a / sin(40°) = 10 / sin(60°). Can you solve for a now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In a triangle, angle A = 50°, angle B = 70°, and side b = 8 cm. Find side a using the Law of Sines.

[Assistant] Use the Law of Sines: a / sin(A) = b / sin(B). Substitute A = 50°, B = 70°, and b = 8: a / sin(50°) = 8 / sin(70°). Can you solve for a now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find side c in a triangle where angle C = 30°, angle A = 80°, and side a = 12 m using the Law of Sines.

[Assistant] Apply the Law of Sines: c / sin(C) = a / sin(A). Substitute C = 30°, A = 80°, and a = 12: c / sin(30°) = 12 / sin(80°). Can you solve for c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A hiker walks 5 miles north, then 7 miles east. How far is she from her starting point? Use the Law of Cosines (90° angle).

[Assistant] The Law of Cosines is c² = a² + b² - 2ab * cos(C). Here, a = 5, b = 7, and C = 90°. Substitute: c² = 5² + 7² - 2*5*7*cos(90°). Can you calculate c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find side c in a triangle with sides a = 6 cm, b = 8 cm, and angle C = 60°. Use the Law of Cosines.

[Assistant] Use the Law of Cosines: c² = a² + b² - 2ab * cos(C). Substitute a = 6, b = 8, and C = 60°: c² = 6² + 8² - 2*6*8*cos(60°). Can you calculate c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate side b in a triangle where a = 10 m, c = 12 m, and angle B = 45°. Use the Law of Cosines.

[Assistant] The Law of Cosines for side b is b² = a² + c² - 2ac * cos(B). Substitute a = 10, c = 12, and B = 45°: b² = 10² + 12² - 2*10*12*cos(45°). Can you calculate b now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rocket is launched with an initial velocity of 30 m/s from a height of 5 meters. Its height is modeled by h(t) = -5t² + 30t + 5. When does it hit the ground?

[Assistant] Set h(t) = 0: -5t² + 30t + 5 = 0. Use the quadratic formula t = [-b ± √(b² - 4ac)] / (2a), where a = -5, b = 30, c = 5. Start by finding the discriminant: b² - 4ac. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 2x² - 8x + 6 = 0 by factoring.

[Assistant] Factor out the greatest common factor: 2(x² - 4x + 3). Now find two numbers that multiply to 3 and add to -4. Can you factor this and solve? Let me know if you need help.


[User] Find the roots of x² + 5x - 14 = 0.

[Assistant] Look for two numbers that multiply to -14 and add to 5. Can you factor this and solve for x? Let me know if you need help.


[User] A phone plan costs $25 plus $0.10 per minute. If the total cost is f(m) = 25 + 0.10m, how much is it for 150 minutes?

[Assistant] Substitute m = 150 into f(m) = 25 + 0.10 * 150. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the range of f(x) = x² - 3 for all real x.

[Assistant] Since x² is always non-negative, the minimum value of x² - 3 occurs when x² = 0. Evaluate f(0) to find the minimum. Can you determine the range now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If f(x) = 3x - 1 and g(x) = x + 2, find f(g(4)).

[Assistant] First, compute g(4) by substituting x = 4 into g(x) = x + 2. Can you find this and then use it in f(x)? Let me know what is the next step you are stuck with and I can try to help you.


[User] A garden’s length is (x + 3) meters and width is (x - 2) meters. If its height is 2 meters, what’s the volume polynomial?

[Assistant] Multiply the dimensions: V = (x + 3)(x - 2) * 2. Start by expanding (x + 3)(x - 2) using FOIL. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Factor x³ + 27.

[Assistant] This is a sum of cubes: a³ + b³ = (a + b)(a² - ab + b²). Rewrite x³ + 27 as x³ + 3³. Substitute a = x and b = 3. Can you factor it now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Multiply (x² + 2x - 5) and (x - 3).

[Assistant] Use the distributive property: x² * x + x² * (-3) + 2x * x + 2x * (-3) - 5 * x - 5 * (-3). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A circuit has impedance (2 + 3i) ohms and current (1 - 2i) amps. What’s the voltage? Multiply (2 + 3i)(1 - 2i).

[Assistant] Distribute: (2 + 3i)(1 - 2i) = 2*1 + 2*(-2i) + 3i*1 + 3i*(-2i). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Simplify i^22.

[Assistant] Powers of i cycle every 4: i¹ = i, i² = -1, i³ = -i, i⁴ = 1. Divide 22 by 4 and find the remainder. Can you determine the result now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve x² + 9 = 0 for complex roots.

[Assistant] Subtract 9: x² = -9. Take the square root, using √(-1) = i. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A savings account grows at 5% annually from $1000. What’s the amount after 4 years? Use A(t) = 1000 * (1.05)^t.

[Assistant] Substitute t = 4 into A(t) = 1000 * (1.05)^4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 5^x = 125.

[Assistant] Rewrite 125 as a power of 5: 125 = 5^3. Now you have 5^x = 5^3. Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find x if 2^(x+1) = 16.

[Assistant] Express 16 as a power of 2: 16 = 2^4. Now you have 2^(x+1) = 2^4. Set the exponents equal and solve. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A chemical decays by half every 5 days. If it starts at 200 grams, how long until 25 grams remain? Use m(t) = 200 * (0.5)^(t/5) and solve log form.

[Assistant] Set m(t) = 25: 25 = 200 * (0.5)^(t/5). Divide both sides by 200: 25/200 = (0.5)^(t/5). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve log₃(x) = 4.

[Assistant] Convert to exponential form: 3^4 = x. Can you calculate x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Simplify log₅(25x) using the product rule, given log₅(x) = 3.

[Assistant] The product rule is log_b(a * c) = log_b(a) + log_b(c). Rewrite log₅(25x) as log₅(25) + log₅(x). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A pump fills a pool at 10 gallons per minute, but a leak drains 4 gallons per minute. How long to fill 120 gallons? Solve 120 / (10 - 4) = t.

[Assistant] Simplify the denominator: 10 - 4. Can you calculate t now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Simplify (x² - 9) / (x + 3).

[Assistant] Factor the numerator: x² - 9 = (x - 3)(x + 3). Look for common factors with the denominator. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 2 / (x - 1) = 8.

[Assistant] Multiply both sides by (x - 1): 2 = 8 * (x - 1). Can you solve for x now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A rectangle’s area is 24 cm², and its length is 2 cm more than its width. Solve x(x + 2) = 24 and x > 0 (x = width).

[Assistant] Expand the equation: x² + 2x = 24. Move all terms to one side: x² + 2x - 24 = 0. Can you factor this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve the system: y = x² and y = 2x + 3.

[Assistant] Substitute y = x² into y = 2x + 3: x² = 2x + 3. Move all terms to one side: x² - 2x - 3 = 0. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve: y = x² - 4 and y = 5x - 8.

[Assistant] Set the equations equal: x² - 4 = 5x - 8. Move all terms to one side: x² - 5x + 4 = 0. Can you factor this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A company’s profit is P(x) = -x² + 10x - 9, where x is units sold. For what x is profit positive?

[Assistant] Set P(x) > 0: -x² + 10x - 9 > 0. Multiply by -1 (and flip the inequality): x² - 10x + 9 < 0. Can you factor this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve x² - 6x + 8 ≤ 0.

[Assistant] Factor the quadratic: (x - 2)(x - 4) ≤ 0. Find the roots by setting each factor to zero. Can you determine the solution interval now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 2 / (x - 3) > 1.

[Assistant] Subtract 1 from both sides: 2 / (x - 3) - 1 > 0. Rewrite with a common denominator: [2 - (x - 3)] / (x - 3) > 0. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A job pays $500 the first week and increases by $25 each week. How much is earned in the 10th week?

[Assistant] Use the arithmetic sequence formula: a_n = a_1 + (n - 1)d. Substitute a_1 = 500, d = 25, n = 10. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the 7th term of the geometric sequence 2, 6, 18, 54.

[Assistant] Determine the common ratio: 6 / 2. Use a_n = a_1 * r^(n-1) with n = 7. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What’s the sum of the first 5 terms of the arithmetic series 3 + 7 + 11 + 15 + …?

[Assistant] Use the sum formula: S_n = n/2 * (a_1 + a_n). First, find a_5 using a_n = a_1 + (n - 1)d with a_1 = 3, d = 4, n = 5. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A store sells 2 shirts and 3 pants for $50 one day, and 4 shirts and 1 pant for $60 the next. Represent as a matrix equation: [[2, 3], [4, 1]] * [s, p] = [50, 60].

[Assistant] Write the system: 2s + 3p = 50 and 4s + p = 60. To solve using matrices, find the inverse of [[2, 3], [4, 1]]. Start by calculating the determinant: 2*1 - 3*4. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Add matrices: [[1, -2], [3, 4]] + [[5, 6], [-1, 0]].

[Assistant] Add corresponding elements: [1 + 5, -2 + 6] for the first row. Can you complete the addition now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the determinant of [[3, 2], [-1, 4]].

[Assistant] Use the formula for a 2x2 matrix: det = ad - bc, where a = 3, b = 2, c = -1, d = 4. Calculate 3*4 - 2*(-1). Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A parabola models a bridge’s arch: y = -0.01x² + 4. What’s the maximum height?

[Assistant] The maximum height occurs at the vertex. For y = ax² + bx + c, x = -b / (2a). Here, a = -0.01, b = 0. Calculate x = -0 / (2 * -0.01). Can you find y now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the center of the circle x² + y² - 6x + 4y - 12 = 0.

[Assistant] Complete the square for x: x² - 6x = (x - 3)² - 9. Now do the same for y. Can you rewrite the equation now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Identify the vertex of the parabola y = 2(x - 1)² + 3.

[Assistant] The vertex form is y = a(x - h)² + k, where (h, k) is the vertex. Here, h = 1, k = 3. Can you confirm this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A square garden’s area is 81 m². What’s the length of a side? Solve √x = 81.

[Assistant] This is incorrect; the correct equation is x = 81 (area = side²). Solve √x = 9 by squaring both sides: x = 9². Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve √(2x + 3) = 5.

[Assistant] Square both sides to eliminate the radical: (√(2x + 3))² = 5². Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Simplify √(50x²).

[Assistant] Factor 50x²: √(25 * 2 * x²). Take the square root of each part: √25 * √2 * √x². Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A machine produces parts with a tolerance of 0.5 cm from 10 cm. Solve |x - 10| ≤ 0.5.

[Assistant] Rewrite as a compound inequality: -0.5 ≤ x - 10 ≤ 0.5. Add 10 to all parts. Can you solve this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve |2x - 3| = 7.

[Assistant] Set up two equations: 2x - 3 = 7 or 2x - 3 = -7. Solve the first one by adding 3 to both sides. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve |x + 4| > 2.

[Assistant] Rewrite as two inequalities: x + 4 > 2 or x + 4 < -2. Solve the first by subtracting 4. Can you try this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A taxi charges $3 for the first mile and $2 per mile after. What’s the cost for 4 miles? Use f(x) = {3 if x ≤ 1, 3 + 2(x - 1) if x > 1}.

[Assistant] Since 4 > 1, use f(x) = 3 + 2(x - 1). Substitute x = 4. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Evaluate f(2) for f(x) = {x² if x < 0, 2x + 1 if x ≥ 0}.

[Assistant] Since 2 ≥ 0, use f(x) = 2x + 1. Substitute x = 2. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find f(-1) for f(x) = {-x if x < 0, x + 3 if x ≥ 0}.

[Assistant] Since -1 < 0, use f(x) = -x. Substitute x = -1. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A ladder leans against a wall, forming a 30° angle with the ground. If the ladder is 10 feet long, how high up the wall does it reach?

[Assistant] Use the sine function: sin(θ) = opposite / hypotenuse. Here, θ = 30°, hypotenuse = 10. Set up: sin(30°) = h / 10. Can you solve for h now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find cos(θ) in a right triangle where the adjacent side is 8 and the hypotenuse is 17.

[Assistant] The cosine ratio is cos(θ) = adjacent / hypotenuse. Substitute adjacent = 8, hypotenuse = 17: cos(θ) = 8 / 17. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate tan(θ) if the opposite side is 5 and the adjacent side is 12.

[Assistant] The tangent ratio is tan(θ) = opposite / adjacent. Substitute opposite = 5, adjacent = 12: tan(θ) = 5 / 12. Can you leave it as is or simplify? Let me know what is the next step you are stuck with and I can try to help you.


[User] A Ferris wheel rotates a point to an angle of 60°. If the radius is 20 meters, what’s the horizontal distance from the center?

[Assistant] The horizontal distance is given by x = r * cos(θ). Substitute r = 20, θ = 60°: x = 20 * cos(60°). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find sin(90°) using the unit circle.

[Assistant] On the unit circle, sin(θ) is the y-coordinate. At 90°, the point is (0, 1). Can you determine sin(90°) now? Let me know what is the next step you are stuck with and I can try to help you.


[User] What is cos(135°) on the unit circle?

[Assistant] At 135° (second quadrant), use the reference angle 45°. Cosine is negative here. Start with cos(45°) = √2/2 and adjust the sign. Can you find this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A right triangle has sin(θ) = 3/5. What’s cos(θ) using a Pythagorean identity?

[Assistant] Use sin²θ + cos²θ = 1. Substitute sin(θ) = 3/5: (3/5)² + cos²θ = 1. Can you solve for cos²θ now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Verify that sin²(45°) + cos²(45°) = 1.

[Assistant] Calculate sin(45°) and cos(45°), both √2/2. Substitute into sin²θ + cos²θ = 1: (√2/2)² + (√2/2)². Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If cos(θ) = 4/5, find sin(θ) using a Pythagorean identity.

[Assistant] Use sin²θ + cos²θ = 1. Substitute cos(θ) = 4/5: sin²θ + (4/5)² = 1. Can you solve for sin²θ now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A shadow is 12 meters long, and the angle of elevation to the sun is 30°. Find the height of the object using tan and cot identities.

[Assistant] Tan(θ) = opposite / adjacent, and cot(θ) = 1/tan(θ). Set up tan(30°) = h / 12. Can you solve for h now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If sin(θ) = 1/3, find csc(θ).

[Assistant] The reciprocal identity is csc(θ) = 1 / sin(θ). Substitute sin(θ) = 1/3: csc(θ) = 1 / (1/3). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Given tan(θ) = 2/5, find cot(θ).

[Assistant] The quotient identity gives cot(θ) = 1 / tan(θ). Substitute tan(θ) = 2/5: cot(θ) = 1 / (2/5). Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A surveyor measures two angles, 40° and 25°, from a point. What’s the cosine of their sum?

[Assistant] Use the sum identity: cos(A + B) = cos(A)cos(B) - sin(A)sin(B). Substitute A = 40°, B = 25°. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find sin(75°) using the sum identity.

[Assistant] Rewrite 75° as 45° + 30°. Use sin(A + B) = sin(A)cos(B) + cos(A)sin(B). Substitute A = 45°, B = 30°. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Calculate cos(15°) using the difference identity.

[Assistant] Express 15° as 45° - 30°. Use cos(A - B) = cos(A)cos(B) + sin(A)sin(B). Substitute A = 45°, B = 30°. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A pendulum swings at an angle θ where sin(θ) = 0.6. What’s sin(2θ) for a double swing?

[Assistant] Use the double angle identity: sin(2θ) = 2sin(θ)cos(θ). Substitute sin(θ) = 0.6, but first find cos(θ) using sin²θ + cos²θ = 1. Can you start with that now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If cos(θ) = 3/5, find cos(2θ).

[Assistant] Use the double angle identity: cos(2θ) = cos²θ - sin²θ. Substitute cos(θ) = 3/5, then find sin(θ) using sin²θ + cos²θ = 1. Can you start with that now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find sin(2θ) if tan(θ) = 4/3.

[Assistant] Use sin(2θ) = 2sin(θ)cos(θ). First, find sin(θ) and cos(θ) from tan(θ) = 4/3 using a right triangle (opposite = 4, adjacent = 3). Can you calculate the hypotenuse now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A roof has an angle of 60°. What’s the cosine of half that angle for a support beam?

[Assistant] Use the half-angle identity: cos(θ/2) = ±√[(1 + cos(θ))/2]. Substitute θ = 60°, so θ/2 = 30°. Find cos(60°) first. Can you do that now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find sin(22.5°) using the half-angle identity.

[Assistant] Rewrite 22.5° as 45°/2. Use sin(θ/2) = ±√[(1 - cos(θ))/2] with θ = 45°. Calculate cos(45°) first. Can you start with that now? Let me know what is the next step you are stuck with and I can try to help you.


[User] If cos(θ) = 8/17, find cos(θ/2) for 0 < θ < 90°.

[Assistant] Use cos(θ/2) = √[(1 + cos(θ))/2] (positive since θ/2 is in Q1). Substitute cos(θ) = 8/17. Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A kite’s string makes a height of 50 meters with a horizontal distance of 120 meters. What’s the angle of elevation?

[Assistant] Use tan(θ) = opposite / adjacent = 50 / 120. Solve θ = arctan(50/120). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find θ if sin(θ) = 0.5 and 0° ≤ θ ≤ 90°.

[Assistant] Use the inverse sine: θ = arcsin(0.5). Can you determine θ now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve cos(θ) = -√3/2 for θ where 0° ≤ θ ≤ 180°.

[Assistant] Use θ = arccos(-√3/2). Since cos is negative, θ is in Q2. Find the reference angle where cos = √3/2. Can you start with that now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A tide’s height is h(t) = 3sin(πt/6) + 5 meters. When is it 7 meters in [0, 12] hours?

[Assistant] Set h(t) = 7: 3sin(πt/6) + 5 = 7. Subtract 5: 3sin(πt/6) = 2. Can you solve for sin(πt/6) now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve 2cos(θ) = 1 for 0° ≤ θ < 360°.

[Assistant] Divide by 2: cos(θ) = 1/2. Find angles where cos = 1/2 in [0°, 360°). Can you determine these now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find all solutions to sin(θ) = -0.7 in [0°, 360°).

[Assistant] Use θ = arcsin(-0.7). Since sin is negative, solutions are in Q3 and Q4. Find the reference angle first. Can you start with that now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A pilot flies 300 km at 40° from north, then 400 km at an unknown angle. If the total distance from start is 500 km, find the second angle (SSA case).

[Assistant] Use the Law of Sines: a/sin(A) = b/sin(B). Label sides: a = 400, b = 300, c = 500, A = ? (opposite 400). First, use Law of Cosines to find an angle, say C: 500² = 300² + 400² - 2*300*400*cos(C). Can you solve for cos(C) now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In triangle ABC, A = 50°, a = 10, b = 12. Find angle B (check for two solutions).

[Assistant] Use the Law of Sines: sin(A)/a = sin(B)/b. Substitute: sin(50°)/10 = sin(B)/12. Can you solve for sin(B) now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve for side c in triangle ABC where A = 30°, B = 45°, c = ?, a = 8.

[Assistant] First, find angle C: C = 180° - 30° - 45°. Then use Law of Sines: a/sin(A) = c/sin(C). Substitute A = 30°, a = 8, C = ?. Can you calculate C now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A hiker travels 5 km at 60° from start, then 7 km at 120° from start. How far is she from the starting point?

[Assistant] Use the Law of Cosines: c² = a² + b² - 2ab*cos(C), where a = 5, b = 7, C = 120° - 60° = 60°. Substitute: c² = 5² + 7² - 2*5*7*cos(60°). Can you calculate c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find side c in triangle ABC where a = 9, b = 11, C = 70°.

[Assistant] Use the Law of Cosines: c² = a² + b² - 2ab*cos(C). Substitute a = 9, b = 11, C = 70°: c² = 9² + 11² - 2*9*11*cos(70°). Can you compute this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In triangle ABC, a = 6, b = 8, c = 10. Find angle A.

[Assistant] Use the Law of Cosines: a² = b² + c² - 2bc*cos(A). Substitute a = 6, b = 8, c = 10: 6² = 8² + 10² - 2*8*10*cos(A). Can you solve for cos(A) now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangular plot has sides 15 m, 20 m, and an included angle of 80°. What’s the third side?

[Assistant] Use the Law of Cosines: c² = a² + b² - 2ab*cos(C), where a = 15, b = 20, C = 80°. Substitute: c² = 15² + 20² - 2*15*20*cos(80°). Can you calculate c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Solve triangle ABC where A = 35°, a = 7, B = 50°. Find side b.

[Assistant] First, find C: C = 180° - 35° - 50°. Then use Law of Sines: a/sin(A) = b/sin(B). Substitute A = 35°, a = 7, B = 50°. Can you calculate C now? Let me know what is the next step you are stuck with and I can try to help you.


[User] In triangle ABC, a = 12, b = 15, C = 60°. Find angle A.

[Assistant] Use the Law of Cosines: a² = b² + c² - 2bc*cos(A). Substitute a = 12, b = 15, C = 60°, but we need c first. Use Law of Cosines for c: c² = 12² + 15² - 2*12*15*cos(60°). Can you find c now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A wave’s height is modeled by h(t) = 2sin(3t). What’s the amplitude?

[Assistant] The amplitude of y = a*sin(bx) is |a|. Here, a = 2. Can you identify the amplitude now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the period of y = cos(4x).

[Assistant] The period of y = cos(bx) is 2π/b. Substitute b = 4: period = 2π/4. Can you simplify this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Determine the phase shift of y = sin(x - π/3).

[Assistant] For y = sin(x - c), the phase shift is c. Here, c = π/3. Can you identify the direction of the shift now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A building casts a 50-meter shadow when the sun’s angle of elevation is 40°. How tall is the building?

[Assistant] Use tan(θ) = opposite / adjacent. Here, θ = 40°, adjacent = 50, opposite = height h. Set up: tan(40°) = h / 50. Can you solve for h now? Let me know what is the next step you are stuck with and I can try to help you.


[User] Find the angle of depression from a 20-meter tower to a point 30 meters away.

[Assistant] Use tan(θ) = opposite / adjacent, where opposite = 20, adjacent = 30. Set up: tan(θ) = 20 / 30. Solve θ = arctan(20/30). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A triangle has sides 8 and 10 with an included angle of 45°. Find the area.

[Assistant] Use the area formula: Area = (1/2) * a * b * sin(C). Substitute a = 8, b = 10, C = 45°. Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.


[User] A radar tracks a plane at 5 km distance and 60° from the positive x-axis. What are its rectangular coordinates?

[Assistant] Use x = r * cos(θ), y = r * sin(θ). Substitute r = 5, θ = 60°. Start with x = 5 * cos(60°). Can you calculate this now? Let me know what is the next step you are stuck with and I can try to help you.