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3.OA.C.7
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...
5.NBT.B.5
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.NBT.B.7
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 ...
8.G.C.9
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 ...
7.RP.A.2
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...
S-ID.B.5
Activity The mathematical purpose of this activity is for students to gain an understanding of the relationship between a two-way frequency table and a two-way relative frequency table. Students have the same information in a two-way table and a segmented bar graph, then are asked to interpret the information given in ...
8.EE.C.8a
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...
K.CC.B.4
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...
5.OA.B.3
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...
G-GMD.A.1
Warm-up The purpose of this warm-up is to elicit the idea that the more sides an inscribed polygon has the closer it comes to approximating a circle, which will be useful when students calculate perimeter and eventually \(\pi\) in later activities. While students may notice and wonder many things about these images, ap...
F-BF.B.4a
Below is a set of coordinate points. Graph these points, connect the points into a linear function, and then graph the inverse of this function. $${(-2,-4)}$$ $${(1,-2.5)}$$ $${(2,-2)}$$
6.NS.A.1
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.RP.A.3c
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...
8.G.A.5
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...
G-CO.A.2
Problem 1 This slider shows a triangle dilated using different scale factors. Slide the point to the right and to the left. What do you notice as you change the scale factor of this figure? Problem 2 Below is $${{\overline{BC}}}$$ , with a length of $$5$$ units and its dilation about the point $$O$$ , $${\overline{B'C'...
2.OA.A.1
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...
6.EE.B.5
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...
8.EE.C.7a
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...
1.OA.A.1
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:...
F-IF.A.2
Task Imagine Scott stood at zero on a life-sized number line. His friend flipped a coin 50 times. When the coin came up heads, he moved one unit to the right. When the coin came up tails, he moved one unit to the left. After each flip of the coin, Scott's friend recorded his position on the number line. Let $f$ assig...
A-CED.A.4
Activity In earlier activities, students gained some insights on the structure of equations in systems that have infinitely many solutions and those that have no solutions. In this activity, they apply those insights to sort systems of equations based on the number of solutions (one solution, many solutions, or no solu...
7.G.B.4
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?”...
8.G.A
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?
A-SSE.A.1
Activity In this activity, students continue to reason about half-lives and exponential functions to solve problems. Both questions provide possible reasoning for a calculation and then prompt students to construct an argument to justify their position (MP3). The context continues to be the decay of carbon-14 and stude...
A-REI.C.6
Activity Earlier, students saw that adding or subtracting the equations in a system creates a third equation that can help us solve the system. In this activity, students reconnect the idea of the solution to a system to the intersection of the graphs of the equations. They graph each original pair of equations and the...
8.EE.B.6
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 ...
A-REI.B.4
Activity In this activity, students evaluate quadratic functions for a given value and compare the results. The given value is a zero of the function. In the associated Algebra 1 lesson, students examine the zero product property to find zeros of quadratic functions. This activity gives students the chance to notice pa...
1.OA.A.1
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...
3.OA.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 ...
3.G.A.1
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...
7.SP.B.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...
6.NS.B.4
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}}=\...
A-SSE.A.2
Activity In this activity, students consider factors of values and then examine those factors to find a particular sum. In the associated Algebra 1 lesson, students factor quadratic expressions and knowing pairs of values that have a certain product and sum is important. It is not essential that students solve the chal...
F-LE.A.2
Activity This activity is a preview of the work in the associated Algebra 1 lesson. Students have a scaffolded opportunity to determine a decay factor from a given graph, and make connections between graphs and equations. Launch The context and types of questions continue from the previous activity, so students can con...
3.NBT.A.1
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.MD.C.5
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.OA.C.7
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...
5.NF.A.1
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?
1.NBT.B
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...
K.OA.A.3
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,...
7.EE.B.3
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...
3.OA.B.5
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...
6.NS.C.5
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 $$−10...
8.EE.A.3
Nyan Cat travels at $$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...
6.NS.A.1
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...
1.OA.C.6
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...
6.RP.A
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...
7.G.A.2
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...
1.MD.A.1
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...
F-BF.B.4
Activity In this activity students use the situation of creating a square planter to find the area within the planter based on the side lengths and the side lengths based on the area. In the associated Algebra 1 lesson students begin looking at inverse functions. This activity supports students by getting them to find ...
5.G.B.3
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?
8.G.A.2
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...
5.G.A.1
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.
7.NS.A.3
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...
6.RP.A.3b
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 ...
2.MD.B.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...
6.EE.A.1
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)$$
6.NS.C
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...
K.OA.A.1
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...
1.G.A.2
Task How many rectangles are in this picture? ###IMAGE0###
G-SRT.B.5
Task Pablo is practicing bank shots on a standard 4 ft.-by-8 ft. pool table that has a wall on each side, a pocket in each corner, and a pocket at the midpoint of each eight-foot side. Pablo places the cue ball one foot away from the south wall of the table and one foot away from the west wall, as shown in the diagram ...
1.OA.D.8
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...
K.CC.B
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 ...
3.NF.A.3d
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...
A-APR.B.3
Warm-up In this activity, students have an opportunity to notice and make use of structure (MP7) in order to identify a point where the graphs of two given functions intersect. The work here leads directly into the next activity in which students use algebraic methods to identify all points of intersection between two ...
6.EE.A.1
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...
4.NF.B.3d
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...
N-CN.A.1
Problem 1 Write the following as an imaginary number. $${\sqrt{-72}}$$ Why is this not a complex number? Problem 2 What kind of roots will the following quadratic function have? $${4x-3x^2=10}$$
4.NBT.A.3
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...
F-BF.A.2
Problem 1 Four sequences are shown below. Which one does not belong and why? ###TABLE0### Problem 2 Complete each sequence by filling in the missing terms. Then identify each sequence as arithmetic or geometric and name the common difference or common ratio. a. $${-2}$$ , $$4$$ , ___, ___, ___, $${28}$$ , ... b. $${{1\...
6.G.A.1
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...
8.G.A
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...
2.MD.D.10
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...
3.NF.A.3
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.MD.C.5
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...
K.CC.B.5
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.
F-LE.A.2
Task Algal blooms routinely threaten the health of the Chesapeake Bay. Phosphate compounds supply a rich source of nutrients for the algae, Prorocentrum minimum, responsible for particularly harmful spring blooms known as mahogany tides. These compounds are found in fertilizers used by farmers and find their way into t...
3.G.A.1
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...
S-ID.A.1
Warm-up The mathematical purpose of this activity is for students to compare different distributions using shape, measures of center, and measures of variability. This warm-up prompts students to compare four distributions representing recent bowling scores for potential teammates. It gives students a reason to use lan...
4.NBT.A.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...
F-BF.A.1b
Task Using the graphs below, sketch a graph of the function $s(x) = f(x) + g(x)$. ###IMAGE0###
K.OA.A.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 ...
F-IF.C.7a
Activity In this activity, students create a table consisting of the coordinates of the points around a graph’s vertex. This prepares them to reason using the structure of expressions in the associated Algebra 1 lesson, where they perform a similar analysis without being prompted to create a table first. Launch Display...
3.NF.A.3d
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$$ . Use <, >, or = to record your comparison. b. Explain how you know your answer in Part A is correct. Draw a picture or a number line to support your reasoning.
4.OA.A.3
Narrative The purpose of this warm-up is to elicit students’ knowledge about 1 year as a measure of time and the ways it can be represented. The reasoning and conversations here will be helpful as students solve problems that involve time in years later in the lesson. Launch Display: “1 year” “What do you know about 1 ...
8.EE.B.6
Problem 1 Tickets to a concert are available for early access on a special website. The website charges a fixed fee for early access to the tickets, and the tickets to the concert all cost the same amount with no additional tax. A friend of yours purchases 4 tickets on the website for a total of $162. Another friend pu...
3.G.A.1
Stage 3: Grade 3 Shapes Required Preparation Materials to Copy Blackline Masters Centimeter Grid Paper - Standard Shape Cards Grade 3 Quadrilateral Cards Grade 3 Can You Draw It Stage 3 Directions Narrative Partner A chooses a shape card and describes it to their partner. If Partner B draws the shape correctly, they k...
5.NF.B.4b
Activity One purpose of this activity is to practice seeing the total length of a segment as the sum of its pieces, and using the whole side length of a rectangle to express its area. Another is to generate examples of equivalent expressions, and understand why they are equivalent based on an understanding of area and ...
K.MD.A.2
Task Materials: Sheets of paper for each student that are folded in half with the words "Heavier" and "Lighter" written at the top of each side. ###IMAGE0### A box of large blocks. A box of different objects with different weights to compare with a block from the first box. Some should be lighter than a single block an...
F-TF.B.6
Find two values where $${\mathrm{cos}x=-1}$$ . What is $${\mathrm{arccos}(-1)}$$ ?
6.NS.C.6c
Problem 1 Consider the set of numbers $$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...
K.G.B.4
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...
K.OA.A.1
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...
K.G.B.4
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 ...
8.G.A.2
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,...
5.NF.B.4b
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...
6.SP.B
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.RP.A.3
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...
7.EE.B.4b
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...
S-CP.A.3
Task Cecil has two six-sided dice, a red one and a white one. If Cecil throws the two dice, what is the probability that the red die is a 1? What is the probability that the sum of the dice is 7? Are the two events described part (a) independent? Explain. What is the probability that the red die is a 2? What is the p...