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Narrative The purpose of this activity is for students to practice using an algorithm that uses partial quotients to divide multi-digit numbers by two-digit divisors. Before finding the quotient, students estimate the value of the quotient which both helps students decide which partial quotients to use and helps them e...
5
Line $$AC$$ intersects line $$EB$$ at point $$F$$ . Ray $$FD$$ extends from point $$F$$ . Determine the measures of $$\angle EFD$$ and $$\angle CFD$$ . ###IMAGE0###
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Narrative The purpose of this activity is for students to find the volume of figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts. There are different ways to decompose the figures. Monitor for students who break the figures apart differently and find the s...
5
Narrative The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100 and to help students develop fluency. When students use known multiplication and division facts to divide larger numbers, they look for and make use of structure (MP7). Launch Display one expressio...
3
Narrative The goal of this activity is to multiply numbers with no restrictions on the number of new units composed. Students first multiply a 3-digit number by a 1-digit number and a 3-digit number by a 2-digit number with no ones. They can then put these two results together to find the product of a 3-digit and 2-dig...
5
Warm-up This number talk encourages students to rely on what they know about structure, patterns, decimal multiplication, and properties of operations to solve a problem mentally. Only two problems are given here so there is time to share many strategies and make connections between them. Launch Display one problem at ...
5
Activity In this activity, students find the missing dimensions of cylinders when given the volume and the other dimension. A volume equation representing the cylinder is given for each problem. Identify students who use these strategies: guess and check, divide each side of the equation by the same value to solve for ...
8
Activity In this activity, students graph three time-distance relationships along with the one from the previous lesson, “Tyler’s Walk.” One of these is not a proportional relationship, so students must pay close attention to the quantities represented. The purpose of this activity is to give students many opportunitie...
7
Activity Students represent a scenario with an equation and use the equation to find solutions. They create a graph (either with a table of values or by using two intercepts), interpret points on the graph, and interpret points not on the graph (MP2). Launch Allow about 10 minutes quiet think time for questions 1 throu...
8
Narrative The purpose of this activity is for students to consider different ways of acting out a story. Students revisit the story from previous lessons, which has another verse added to it. They suggest different ways the story could be acted out. Acting out gives students opportunities to make sense of a context (MP...
0
Narrative The purpose of this activity is for students to practice interpreting relationships between patterns generated from two different rules. Students may need to generate patterns beyond the boxes provided. Encourage them to continue the pattern as needed. Students may describe the patterns and relationships in d...
5
Warm-up This warm-up prompts students to interpret division of fractions in terms of the number of groups of one fraction in the other (i.e., “how many groups of this in that?” question). Students do not calculate the exact value of each expression. Instead, they decide if at least one group the size of the divisor is ...
6
Activity The purpose of this activity is for students to see that to find what percentage one number is of another, divide them and then multiply by 100. First they find what percentage of 20 various numbers are, then they organize everything into a table. Using the table, students then describe the relationship they s...
6
Optional activity This is a matching activity where each student receives a card showing a triangle and works to form a group of three. Each card has a triangle with the measure of only one of its angles given. Students use what they know about transformations and estimates of angle measures to find partners with trian...
8
Narrative In this activity, students solve addition problems using money based on the Pattern Block Puzzles they sketched in the last activity. The launch of the activity is an opportunity for students to reason which of the two designs will cost more before they complete any computations. MLR7 Compare and Connect. Syn...
2
Activity Students interpret inequalities that represent constraints or conditions in a real-world problem. They find solutions to an inequality and reason about the context’s limitations on solutions (MP2). Launch Allow students 10 minutes quiet work time to complete all questions followed by whole-class discussion. Re...
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Warm-up Students extend their understanding from the previous lessons to recognize the structure of a linear equation for all possible types of solutions: one solution, no solution, or infinitely many solutions. Students are still using language such as “true for one value of x,” “always true” or “true for any value of...
8
Narrative This warm-up prompts students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved. Students will work with this problem in the next activity. Launch Groups of 2 Display the image. “What do you notice? What do you wonder?” 1 minute:...
1
Activity The purpose of this activity is for students to apply the formula for area of a circle to solve a problem in context. The diameter of the circle is given, so students must first determine the radius. Launch Display this image of table top for all to see. Ask students, “What do you notice? What do you wonder?”...
7
Task For each pair of figures, decide whether these figures are the same size and same shape. Explain your reasoning. ###IMAGE0### ###IMAGE1### ###IMAGE2### What does it mean for two figures to be the same size and same shape?
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Problem 1 What is an equation of the line represented in the graph below? ###IMAGE0### Problem 2 Four lines were used to define the edges of the trapezoid shown below. ###IMAGE1### Write an equation for each line described below. a. Line that passes through points $$A$$ and $$B$$ b. Line that passes through points ...
8
Narrative The purpose of this activity is for students to solve a variety of story problems and write addition and subtraction equations that match those problems. Students solve Put Together/Take Apart, Total or Addend Unknown problems and Compare, Difference Unknown problems. Students may solve in any way they want a...
1
Problem 1 a. Split 18 counters equally into groups of two. i. Write a multiplication equation to represent this situation. ii. How many groups of counters do you have? b. How is this similar to Anchor Task #1 from Lesson 3? How is it different? Problem 2 a. Casey bought the following stickers. She wants to put 5 ...
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Narrative The purpose of this activity is to sort quadrilaterals by their attributes. By now students may be inclined to look for sides of equal lengths and for right angles. They may not look for parallel sides (and are not expected to know the term “parallel”), but may notice that some quadrilaterals have pairs of si...
3
Activity Following the review from the previous activity, students are asked to use these calculations to compare two groups more formally. Students are shown one quantifiable method of determining whether the two groups are relatively close or relatively very different in the discussion following the activity involvin...
7
Optional activity This activity extends the work with rectangles and fractions to continued fractions. Continued fractions are not a part of grade-level work, but they can be reasoned about and rewritten using grade-level skills for operating on fractions (MP8). In particular, the insight that \(\frac{1}{\frac{a}{b}}=\...
6
Narrative The purpose of this activity is for students to round given numbers to the nearest ten and hundred and see that the result can be the same for some numbers. Students think about what it means to round a number that is exactly halfway between two tens or two hundreds and are introduced in the synthesis to the ...
3
Problem 1 Which shape takes up more space, the trapezoid pattern block or the blue rhombus pattern block? Justify your answer. Problem 2 Area is the measure of how much flat space an object takes up. Use pattern blocks to decide which shape on Template: Pattern Block Areas has the greatest area. Be ready to explain you...
3
Narrative The purpose of this Number Talk is to elicit strategies and understandings students have for products of 4 and 6 as they relate to products of 5. These understandings help students develop fluency and will be helpful later when students consider solutions for and solve two-step word problems. When students us...
3
Problem 1 Solve. Show or explain your work. $${2{5\over8}+4{2\over3}}$$ Problem 2 Sang needs $$3\tfrac{1}{2}$$ feet of string to make a necklace and $$2\tfrac{1}{4}$$ feet of string left. How much string, in feet, did Sang have before making the necklace?
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Narrative The purpose of this activity is for students to choose from activities that offer practice working with two-digit numbers. Students choose from previously introduced centers. Mystery Number Get Your Numbers in Order Greatest of Them All Required Materials Materials to Gather Materials from previous centers Re...
1
Narrative The purpose of this activity is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem about dates stuffed with cheese or almonds in more than one way. In the activity synthesis, students share their solutions. As students share, record their drawings and solutions systematically,...
0
Activity This activity is a continuation of the previous one. Students match each situation from the previous activity with an equation, solve the equation by any method that makes sense to them, and interpret the meaning of the solution. Students are still using any method that makes sense to them to reason about a so...
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Narrative The purpose of this activity is for students to transition from reasoning about division concretely or visually (using base-ten diagrams) to doing so more abstractly (by writing equations). It also reinforces the connections between multiplication and division. Students make sense of three different strategie...
3
A biologist is tracking the location of three different animals. On the first day of spring, the biologist records the following information about the three animals: The first animal is located $$220$$ m below sea level. The second animal is located at an elevation of $$0$$ m. The third animal has an elevation of $$−10...
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Nyan Cat travels at $$4.2\times10^2$$ miles per hour. Grumpy Cat travels at a pokey $$7\times10^{-1}$$ miles per hour. a. How many times faster is Nyan Cat traveling than Grumpy Cat? b. The Peregrine Falcon, the fastest bird, can fly up to half of Nyan Cat’s speed. How fast can a Peregrine Falcon fly? Write your an...
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Activity This activity allows students to practice using the algorithm from earlier to solve division problems that involve a wider variety of fractions. Students can use any method of reasoning and are not expected to use the algorithm. As they encounter problems with less-friendly numbers, however, they notice that i...
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Narrative The purpose of this activity is for students to choose from activities that offer practice adding and subtracting within 10. Students choose from any stage of previously introduced centers. Shake and Spill Compare Number Puzzles Required Materials Materials to Gather Materials from previous centers Required P...
1
Task In a marching band there are 24 trombones and 15 snare drums. Heather says, “The ratio of trombones to snare drums is 24:15.” Audrey says, “No, the ratio of trombones to snare drums is 8:5.” Who is right, and why? A different marching band has 30 snare drums, but its trombone to snare drum ratio is the same as the...
6
Starting at the origin, a ladybug walked 4 units east. Then she walked a distance of 3 units in an unknown direction. At that time, she was 30 degrees to the north of her original walking direction. The diagram shows one possibility for the ladybug’s final location. Find a different final location that is also consiste...
7
Narrative The purpose of this warm-up is for students to compare lengths of objects and notice when they are longer, shorter, or equal to each other in length. While students may notice and wonder many things about these images, comparing the length is an important discussion point. Launch Groups of 2 Display the image...
1
Problem 1 Arya draws a figure that is a polygon. Which of the following is true about the figure? There are three correct answers. Problem 2 When is a polygon also a quadrilateral?
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Warm-up This task helps students think strategically about what kinds of transformations they might use to show two figures are congruent. Being able to recognize when two figures have either a mirror orientation or rotational orientation is useful for planning out a sequence of transformations. Launch Provide access t...
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Stage 6: Shapes on the Coordinate Grid Required Preparation Materials to Copy Blackline Masters Which One Stage 6 Gameboard Narrative One partner chooses a rectangle on the coordinate plane from the board. The other partner asks questions to figure out which rectangle on the coordinate plane their partner chose.
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Activity It is common to use positive numbers to represent credit and negative numbers to represent debts on a bill. This task introduces students to this convention and asks them to solve addition and subtraction questions in that context. Note that whether a number should be positive or negative is often a choice, wh...
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Activity In this task, students practice finding unit prices, using different reasoning strategies, and articulating their reasoning. They also learn about the term “at this rate.” As students work, observe their work and then assign one problem for each group to own and present to the class. (The problems can each be ...
6
Narrative The purpose of this activity is for students to represent addition and subtraction equations on a number line. Students consider where to begin and in which direction to draw their arrows in order to accurately represent the operation in the given equation. Throughout the activity, encourage students to expla...
2
Evaluate the expressions. a. $$24\div(2+1)+(11-8)\times2$$ b. $$3^2\times4-10+(12-3)^2$$ c. $$(3\times4)^2-10\times(12-3^2)$$
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Activity The purpose of this activity is for students to continue interpreting signed numbers in context and to begin to compare their relative location. A vertical number line shows the heights above sea level or depths below sea level of various animals. The number line is labeled in 5 meter increments, so students h...
6
Narrative This warm-up prompts students to carefully analyze and compare features of four equations. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminologies students know and how they talk about characteristics of equations. Launch G...
0
Task How many rectangles are in this picture? ###IMAGE0###
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Narrative The purpose of this activity is for students to choose from activities focusing on two-digit numbers. Students are introduced to stage 3 of the Target Numbers center. Then students choose between that center or others previously introduced. Students choose from any stage of previously introduced centers. Targ...
1
Narrative The purpose of this activity is for students to choose from activities that focus on counting up to 20 objects or adding and subtracting within 10. Students choose from any stage of previously introduced centers and are encouraged to choose the center that will be most helpful for them at this time. Counting ...
0
Problem 1 For the class party, Robin and Shawn each made a loaf of banana bread. Their loaf pans were exactly the same size. Robin sliced her banana bread into 6 equal slices. Shawn also sliced his into 6 equal slices. After the party, Robin had more slices of banana bread left to take home than Shawn did. What fractio...
3
Activity In this activity, students use surface area as a context to extend the order of operations to expressions with exponents. The context provides a reason to evaluate the exponent before performing the multiplication. Launch Give students 10 minutes of quiet work time, followed by a class discussion. Reading: MLR...
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Narrative In this activity, students create a line plot using measurements to the nearest \(\frac{1}{4}\) and \(\frac{1}{8}\) inch. This task prompts students to use their understanding of fraction equivalence to plot and partition the horizontal axis. Representation: Access for Perception. Provide access to fraction s...
4
Narrative This warm-up prompts students to make sense of a problem before solving it, by familiarizing themselves with a context and the mathematics that might be involved. This warm-up gives students a chance to analyze and ask questions about the set of data they will use in a later activity. Launch Groups of 2 Displ...
4
Optional activity In this activity, students transfer what they learned with the pattern blocks to calculate the area of other scaled shapes (MP8). In groups of 2, students draw scaled copies of either a parallelogram or a triangle and calculate the areas. Then, each group compares their results with those of a group t...
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Activity This activity continues studying dilations on a circular grid, this time focusing on what happens to points lying on a polygon. Students first dilate the vertices of a polygon as in the previous activity. Then they examine what happens to points on the sides of the polygon. They discover that when these points...
8
Narrative The purpose of this activity is for students to write true statements to show what they can learn about the data in a bar graph. In the synthesis, students match their peers' statements to the graph they think they came from and explain how they know using the features of the graph (MP2, MP3). In order to hav...
2
Narrative The purpose of this activity is for students to analyze pairs of fractions to determine if they are equivalent. Students may use any representation that makes sense to them. Students will create a visual display and have a gallery walk to consider the different ways of looking for equivalence. Highlight repre...
3
Narrative The purpose of this activity is for students to compare shapes by covering them with pattern blocks. Students experience tiling as a way to see which shape covers the most space. There are several ways to tile the shapes, but it may prove most useful to use the same units, such as triangles. The rectangle can...
3
Stage 3: Add 2 Hands Required Preparation Materials to Copy Blackline Masters Math Fingers Stage 3 Recording Sheet Narrative Each partner holds up some fingers on one hand. Partners work together to figure out how many fingers are up altogether.
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Narrative The purpose of this warm-up is to elicit the idea that there are many shapes that are visible in wax prints, which will be useful when students design a wax print in a later activity. Launch Groups of 2 Display the image. “What do you notice? What do you wonder?” 1 minute: quiet think time Activity “Discuss y...
3
Problem 1 Round to the place mentioned below. Show or explain your thinking. a. Round 4,862 to the nearest thousand. 4,862 ≈ ___________ b. Round 308,724 to the nearest hundred thousand. 308,724 ≈ __________ Problem 2 There are 97,385 people who live in Boulder, Colorado. Cathy thinks that rounds to about 100,000 p...
4
Stage 2: Make 10 Required Preparation Materials to Gather 10-frames Connecting cubes or counters Number cards 0–10 Materials to Copy Blackline Masters Find the Pair Stage 2 Recording Sheet Narrative Partner A asks their partner for a number that would make 10 when added to the number on one of their cards. If Partner ...
0
Problem 1 Fill in the blank to make the statement true. $$\frac{3}{4}>\frac{3}{\square}$$ Problem 2 a. Compare $$5\over 6$$ and $$5\over 8$$ . Use <, >, or = to record your comparison. b. Explain how you know your answer in Part A is correct. Draw a picture or a number line to support your reasoning.
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Narrative The purpose of this warm-up is to elicit students’ knowledge about 1 year as a measure of time and the ways it can be represented. The reasoning and conversations here will be helpful as students solve problems that involve time in years later in the lesson. Launch Display: “1 year” “What do you know about 1 ...
4
Problem 1 Tickets to a concert are available for early access on a special website. The website charges a fixed fee for early access to the tickets, and the tickets to the concert all cost the same amount with no additional tax. A friend of yours purchases 4 tickets on the website for a total of $162. Another friend pu...
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Stage 3: Grade 3 Shapes Required Preparation Materials to Copy Blackline Masters Centimeter Grid Paper - Standard Shape Cards Grade 3 Quadrilateral Cards Grade 3 Can You Draw It Stage 3 Directions Narrative Partner A chooses a shape card and describes it to their partner. If Partner B draws the shape correctly, they k...
3
Activity One purpose of this activity is to practice seeing the total length of a segment as the sum of its pieces, and using the whole side length of a rectangle to express its area. Another is to generate examples of equivalent expressions, and understand why they are equivalent based on an understanding of area and ...
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Task Materials: Sheets of paper for each student that are folded in half with the words "Heavier" and "Lighter" written at the top of each side. ###IMAGE0### A box of large blocks. A box of different objects with different weights to compare with a block from the first box. Some should be lighter than a single block an...
0
Problem 1 Consider the set of numbers $$6$$ , $${4 \frac{1}{2}}$$ , $$2$$ , and $$5$$ , and answer the questions that follow. a. Graph the numbers on the number line and list the numbers in order from least to greatest. ###IMAGE0### b. Write the opposites of each number and graph them on the number line. c. Order...
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Narrative The purpose of this activity is for students to identify examples of circles and triangles. The geometric terms circle and triangle are formally introduced, though some students may already be familiar with the terms and may have heard or used them in previous lessons. This activity exposes students to a wide...
0
Narrative The purpose of this activity is for students to make sense of a questionless Put Together/Take Apart, Both Addends Unknown story problem. In this activity, students are asked to show what Lin’s apples could have looked like. The focus of this activity is for students to show the two groups of apples, rather t...
0
Stage 1: Grade K Shapes Required Preparation Materials to Gather Counters Materials to Copy Blackline Masters Which One Stage 1 Gameboard Narrative One partner chooses a shape on the gameboard. The other partner asks questions to figure out what shape they chose. Students may use counters to cover up shapes that have ...
0
Activity This activity begins a sequence which looks at figures that are not polygons. From the point of view of congruence, polygons are special shapes because they are completely determined by the set of vertices. For curved shapes, we usually cannot check that they are congruent by examining a few privileged points,...
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Narrative The purpose of this activity is for students to find areas of rectangles where one side is a whole number and the other side is a fraction that is greater than 1. Students should solve the problems in a way that makes sense to them. Ask students to explain how the diagrams show the multiplication expressions...
5
Warm-up The purpose of this warm-up is to encourage students to connect the ideas they learned earlier about statistical questions and types of data (categorical and numerical) to the work on describing distributions (center and spread). There are many ways to interpret the questions and identify how each one is unique...
6
Warm-up This activity encourages students to apply ratio reasoning to solve a problem they might encounter naturally outside a mathematics classroom. The warm up invites open-ended thinking that is validated by mathematical reasoning, which is the type of complex thinking needed to solve Fermi problems in the following...
6
Activity The purpose of this activity is to remind students that the symbol < is read “is less than” and the symbol > is read “is greater than.” Also, remind students of the use of an open circle or closed circle to indicate that the boundary point is included. Then, the symbols \(\leq\) and \(\geq\) are introduced. Mo...
7
Narrative The purpose of this warm-up is to elicit student ideas about examples and non-examples of triangles and how to describe the attributes of a category of shapes. This will be useful when students determine the defining attributes of quadrilaterals, pentagons, and hexagons in a later activity. While students may...
1
Activity The goal of this task is to experiment with rigid motions to help visualize why alternate interior angles (made by a transversal connecting two parallel lines) are congruent. This result will be used in a future lesson to establish that the sum of the angles in a triangle is 180 degrees. The second question is...
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Stage 6: Multiply with 1–5 Required Preparation Materials to Gather Colored pencils or crayons Number cubes Paper clips Materials to Copy Blackline Masters Capture Squares Stage 6 Gameboard Capture Squares Stage 6 Spinner Narrative Students roll a number cube and spin a spinner and find the product of the two numbers ...
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Stage 6: Add and Subtract Fractions Required Preparation Materials to Copy Blackline Masters Compare Stage 6 Cards Compare Stage 3-8 Directions Narrative Students use cards with expressions with addition and subtraction of fractions with the same denominator.
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Problem 1 Figure 1 (F1) and Figure 2 (F2) are shown below. For each statement below, determine if it is true or false. Explain your reasoning. ###IMAGE0### a. A reflection over the $$x$$ -axis and a translation to the left will transform F1 to F2, making the two figures congruent. b. A rotation of $${180^{\circ}}$$...
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Task At Sea World San Diego, kids are only allowed into the Air Bounce if they are between 37 and 61 inches tall. They are only allowed on the Tide Pool Climb if they are 39 inches tall or under: ###IMAGE0### Represent the height requirements of each ride with inequalities. Show the allowable heights for the rides on s...
6
Warm-up The purpose of this warm-up is to familiarize students with one of the central graphical representations they will be working with in the lesson. As students notice and wonder, they have the opportunity to reason abstractly and quantitatively if they consider the situation the graph represents (MP2). Launch Tel...
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Warm-up This number talk encourages students to think about the numbers in a computation problem and rely on what they know about structure, patterns, and division to mentally solve a problem. Four expressions are given. The first three expressions are partial quotients that could help students evaluate the last expres...
4
Activity This activity requires students to make sense of negative powers of 10 as repeated multiplication by \(\frac{1}{10}\) in order to distinguish between equivalent exponential expressions. If students have time, instruct them to write the other expressions in each table as a power of 10 with a single exponent as ...
8
Problem 1 a. Solve. 10 $$\times$$ 23 = ___________ 10 $$\times$$ 450 = ___________ 10 $$\times$$ 10,870 = ___________ b. What do you notice about Part (a)? What do you wonder? c. Use your conclusions from Part (b) to find the solutions below. ___________ $$\times$$ 10 = 5,090 60,200 $$\div$$ 10 = ___________ ___...
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Narrative The purpose of this activity is for students to draw arrays from a given arrangements of dots. Students draw an array from dots in equal groups to reinforce the definition of an array and then draw as many arrays as they can from 16 randomly placed dots. Having cubes or counters for students to physically rea...
3
Activity The purpose of this task is for students to use the Pythagorean Theorem to calculate which rectangular prism has the longer diagonal length. To complete the activity, students will need to picture or sketch the right triangles necessary to calculate the diagonal length. Identify groups using well-organized str...
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Narrative The purpose of this True or False is to elicit strategies and understandings students have for multiplying one-digit whole numbers by multiples of 10. The reasoning students do here helps to deepen their understanding of the associative property as they decompose multiples of ten to make multiplying easier. L...
3
Narrative The purpose of this Number Talk is to elicit strategies and understandings students have for making 10 when adding. These understandings help students develop fluency with operations within 20. When students look for ways to rearrange and decompose numbers to make 10, they notice and make use of structure of ...
2
Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy? a. Write and solve an inequality to answer the question. b. Each pizza serves...
7
Activity Students have seen that the lengths of corresponding segments in a figure and its scaled copy vary by the same scale factor. Here, they learn that in such a pair of figures, any corresponding distances—not limited to lengths of sides or segments—are related by the same scale factor. The side lengths of the pol...
7
Narrative The purpose of this warm-up is to elicit different strategies for counting objects arranged in groups of 2, which will be useful when students multiply by 2 in a later activity. While students may notice and wonder many things about these images, flexible ways of seeing the groups and strategies for finding t...
3
Warm-up The purpose of this warm-up is to show what happens when shadows are cast from a lamp versus the Sun. Later in this lesson, it is important that students understand that rays of sunlight that hit Earth are essentially parallel. While students may notice and wonder many things about these images, the length of t...
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Warm-up This warm-up refreshes students’ memory about rational and irrational numbers. Students think about the characteristics of each type of number and ways to tell that a number is rational. This review prepares students for the work in this lesson: identifying solutions to quadratic equations as rational or irrati...
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