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Activity In this activity, students continue the work on finding the volume of a right rectangular prism with fractional edge lengths. This time, they do so by packing it with unit cubes of different unit fractions for their edge lengths— $\frac13$ , $\frac12$ , and $\frac14$ of an inch. They use these cubes to f...	6
Optional activity This activity gives students additional practice in using diagrams and equations to represent division situations involving whole numbers and fractions. For each problem, many kinds of visual representations are possible, but creating a meaningful representation may be challenging nonetheless. Urge st...	6
Problem 1 32 students shared 6 pizzas equally. How much pizza will each student get? a. Find the exact answer. b. Check your work. Problem 2 32 gallons of water is used to completely fill 6 fish tanks. If each tank holds the same amount of water, how many gallons will each tank hold? a. Find the exact answer. Wri...	5
Warm-up This warm-up prompts students to carefully analyze and compare features of graphs of linear equations. In making comparisons, students have a reason to use language precisely (MP6). The activity also enables the teacher to hear the terminology students know and learn how they talk about characteristics of graph...	8
Optional activity The purpose of this activity is for students to make preparations to create their scale drawings. They sketch a rough floor plan of the classroom. In groups, they plan the steps for making measurements and then carry out their plan. Some things to notice as students work: As they draw their sketch, en...	7
Optional activity In this activity, students take the triangle they selected in the previous activity and use it as the base of their triangular prism. After students have drawn their net and before they cut it out and assemble it, make sure they have correctly positioned their bases, opposite from each other on the to...	7
Task ###IMAGE0### Say what a trapezoid is in your own words. Compare your definition with a partner. Is this parallelogram a trapezoid according to your definition? Explain. ###IMAGE1###	4
Problem 3 Pre-unit Find the value of each sum or difference. $374 + 455$ $259 - 186$	3
Optional activity This info gap activity uses a quality control situation working with percent error. It is very common that products in a factory are checked to make sure that they meet certain specifications. In this case the odometer of a car is tested and the amount of liquid in a bottle that is automatically fille...	7
Narrative The purpose of this activity is for students to match situations to expressions and then find the value of the expressions (MP2). Students see expressions that show both quotients of a whole number by a fraction and quotients of a fraction by a whole number. They need to think carefully about the situations t...	5
Optional activity In this activity, students use the measurements they just gathered to create their scale floor plans. Each student selects one of the paper options, decides on a scale to use, and works individually to create their drawing. Support students as they reason about scale, scaled lengths, and how to go abo...	7
Activity The purpose of this activity is for students to draw their own axes for different sets of coordinates. They must decide which of the four quadrants they need to use and how to scale the axes. Some students may use logic such as “the largest/smallest point is this, so my axes must go at least that far.” Identif...	6
Problem 1 a. Your teacher will read you a series of situations. Explain what new information you get with each one. Version 1: Mrs. Powell buys a few boxes with some binders in each box. She plans to give out the binders to some students. Version 2: Mrs. Powell buys a few boxes with some binders in each box. She plan...	3
Task Place a decimal on the right side of the equal sign to make the equation true. Explain your reasoning for each. $3.58\times 1.25 = 044750$ $26.97 \div 6.2 = 04350$	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. Number Puzzles Check it Off Find the Pair Required Materials Materials to Gather Materials from previous centers Require...	1
Optional activity In this activity, students apply the geometric process that they saw in the last activity and are asked to make connections between the result and the greatest common factor of the side lengths of the original rectangle. They work on a sequence of similar problems, allowing them to see and begin to ar...	5
Activity The goal of this activity is for students to build fluency solving equations with variables on each side. Students describe each step in their solution process to a partner and justify how each of their changes maintains the equality of the two expressions (MP3). Look for groups solving problems in different, ...	8
Narrative The purpose of this Number Talk is to elicit strategies and understandings students have for the structure of adding within 20. These understandings help students develop fluency and will be helpful later in this lesson when students use relationships between addends to make equivalent expressions to find sum...	1
Problem 1 Look at your yardstick and 12-inch ruler again. Ms. Cole says that 1 foot is equivalent to $$\frac{1}{3}$$ yard. Do you agree or disagree? Explain. Using similar reasoning, determine what fraction of a foot an inch is. Use your reasoning from Part (a) to solve the following conversions. $$\frac{2}{3}$$ yard =...	4
Activity The purpose of this activity is for students to use rational approximations of irrational numbers to place both rational and irrational numbers on a number line, and to reinforce the definition of a cube root as a solution to the equation of the form $x^3=a$ . This is also the first time that students have t...	8
Narrative In this activity, students analyze addition and subtraction calculations, identify errors, and explain what makes certain ways of calculating problematic. The work here gives students opportunities to construct logical arguments and critique the reasoning of others (MP3). MLR8 Discussion Supports. During grou...	4
Activity Students design districts in three towns to “gerrymander” the results of elections. In two of the towns, the election results can be skewed to either color. In the third, it isn’t possible to skew the results. Launch Arrange students in groups of 2–4. Explain the history of gerrymandering: Sometimes people in ...	6
Warm-up This activity prompts students to reason about equivalent ratios on a double number line and think of reasonable scenarios for these ratios as a review of their work in grade 6. As students discuss their answers with their partner, select students to share their answers during the whole-class discussion. Launch...	6
Narrative This warm-up prompts students to carefully analyze and compare representations of patterns. Listen for the language students use to describe and compare the elements of each pattern and give them opportunities to clarify what they mean when they use numbers to describe the patterns (MP6). Launch Groups of 2 D...	4
Activity Following the concept developed in the warm-up, students will continue to use the idea that outcomes from previous experiments can help inform the likelihood of an outcome when the experiment is repeated. In this activity, students play a game while collecting data. Bags of colored blocks are set up with diffe...	7
Optional activity Earlier in this lesson, students found the area of regions around circles and the area of fractions of circles in separate problems. In this activity, students combine these two strategies to find the area of a complex real-world object. Students engage in MP2 as they decide how to decompose the runni...	7
Narrative The purpose of this How Many Do You See is for students to subitize or use grouping strategies to describe the images they see. Students may see equal groups in the rows or the columns of the array. Recording the equations for each way of seeing the groups is an opportunity to reinforce the commutative proper...	3
Narrative The purpose of this warm-up is to elicit the idea that quantities can be compared, which will be useful when students compare connecting cube towers in order to make them have the same number of cubes, in a later activity. While students may notice and wonder many things about this image, comparing the quanti...	1
Activity In the previous activity, students interpreted given tape diagrams and explained how they represented a story. Here, they have a chance to draw tape diagrams to represent a story. The first story is a bit more scaffolded because it specifies what $x$ represents. In the other two stories, students need to dec...	7
Narrative The purpose of this activity is for students to practice using the subtraction algorithm introduced in a previous lesson. Provide base-ten blocks for students who choose to use them to support their reasoning about the algorithm. MLR8 Discussion Supports: Synthesis: Before students share their reasoning, remi...	3
Narrative The purpose of this activity is for students to count their collection in a way that makes sense to them. Students are invited to represent how many objects are in their collection. Some students may choose to create a drawing, make a group with the same number of objects, or just demonstrate how they counte...	0
Narrative The purpose of this How Many Do You See is for students to recognize and name small groups of dots and describe how they see them. This is the first time the images are quickly flashed instead of being displayed for students to look at for as long as necessary. This encourages students to determine the number...	0
Task Decide if the equations are true or false. Explain your answer. 4 x 5 = 20 34 = 7 x 5 3 x 6 = 9 x 2 5 x 8 = 10 x 4 6 x 9 = 5 x 10 2 x (3 x 4) = 8 x 3 8 x 6 = 7 x 6 + 6 4 x (10 + 2) = 40 + 2	3
Activity This activity continues the work begun in the previous activity for this lesson. Students compute the means for sample ages to determine what shows might be associated with each sample (MP2). They also consider the variability to assess the accuracy of population estimates. A sample from a population with less...	7
Warm-up The purpose of this warm-up is to familiarize students with an isometric grid. While students may notice and wonder many things, characteristics such as the measures of the angles in the grid and the diagonal parallel lines will be important properties for students to notice in their future work performing tran...	7
Stage 3: Grade 2 Shapes Required Preparation Materials to Copy Blackline Masters Shape Cards Grade 2 Narrative Students lay out the shape cards face up in rows. One partner chooses a shape. The other partner asks questions to figure out what shape they chose. Students work with triangles, quadrilaterals, and hexagons....	2
Problem 1 Julia, Keller, and Isreal are volunteer firefighters. On Saturday, the volunteer fire department held its annual coin drop fundraiser at a streetlight. After one hour, Keller had collected $42.50 more than Julia, and Isreal had collected $15 less than Keller. The three firefighters collected $125.95 in total....	7
Activity The purpose of this activity is to give students practice finding missing side lengths in a right triangle using the Pythagorean Theorem. Teacher Notes for IM 6–8 Math Accelerated Adjust time to 15 minutes. After 2–3 minutes of work time, select 1–2 groups to share their work for the first question before cont...	8
Narrative This optional activity gives students an additional opportunity to practice using “jumps” on number lines to subtract fractions, decomposing any whole numbers as needed along the way. (It is similar in structure to an optional activity in an earlier lesson on addition.) Students are given four number lines wi...	4
Activity This activity introduces students to graphic scales. Students interpret them, use them to find actual measurements (heights of tall buildings), and express them non-graphically. In earlier lessons, students used markings on an index card or sheet of paper to measure a drawing and create scaled copies. Here, th...	7
Task Use <, =, or > to compare the following sums: $\frac12 + \frac14$ ________ $\frac13 + \frac15$ $\frac13 + \frac12$ ________ $\frac13 + \frac14$	4
Narrative The purpose of this Estimation Exploration is to recall the concept of area. Students need to think strategically because the one point of reference for the size of the grassy area in the image is the car and the road. In order to facilitate mental calculation, expect students to choose multiples of ten for t...	5
Narrative The purpose of this activity is for students to have an opportunity to apply their place value understanding to estimate quantities of objects and accurately count familiar objects. Required Materials Materials to Gather Bags Collections of objects Required Preparation Each group of 2 needs a bag of a collect...	1
Task The high and low temperatures, in degrees Fahrenheit, are plotted in the coordinate plane for 8 days in Nome, Alaska. ###IMAGE0### What was the warmest high temperature? What was the coldest low temperature? What was the biggest same-day difference between the high and low temperature? On what day did it occur?	6
Narrative The purpose of this warm-up is for students to experience a new part of the Questions About Us routine. Students consider concepts of number in a familiar context. This warm-up focuses on cardinality, or knowing that the last number tells us how many, and keeping track of which images have been counted. In th...	0
Stage 5: Subtract Two-digit Numbers Required Preparation Materials to Gather Base-ten blocks Number cubes Materials to Copy Blackline Masters Target Numbers Stage 5 Recording Sheet Narrative Students subtract two-digit numbers to get as close to 0 as possible. Students start their first equation with 100. Then, they t...	2
Warm-up The purpose of this warm-up is to help students recall that in an expression involving multiplication, the product is not affected by the order of the factors. Launch Set a timer for 15 seconds. Ask students to write as many expressions as they can think of that are equal to 0.6 without using addition or subtra...	5
Problem 3 Pre-unit How many dots are in each array? Explain or show your reasoning. ###IMAGE0### ###IMAGE1### ###IMAGE2###	2
Narrative The purpose of this activity is for students to generate two patterns from rules and then graph them on the coordinate grid. Students first identify a point on the coordinate grid with one of the pairs of numbers from the patterns and then plot the rest of the points. Students may notice that the points on th...	5
Problem 1 a. Solve. $$0.03 \times 10$$ = ___________ $$0.106 \times 10$$ = ___________ $$54.8 \times 10$$ = ___________ b. What do you notice about Part (a)? What do you wonder? Problem 2 a. Solve. $$0.09 \times 10 =$$ ___________ $$0.09 \times 100=$$ ___________ $$0.09 \times 1,000= $$ ___________ b. What do y...	5
Problem 1 a. Create as many rectangles as you can with a perimeter of 16 units. Find the area of each rectangle that you found. Then record the length, width, perimeter, and area of each rectangle in the table below: ###TABLE0### b. What do you notice about the rectangles you created? What do you wonder? Problem 2 ...	3
Narrative The purpose of this activity is for students to practice adding within 1,000 with an emphasis on adding by place. Throughout the activity, students have opportunities to explain their methods and representations to peers. In the synthesis, students have opportunities to question and critique the work of their...	2
Optional activity In this activity, students use what they know about corresponding lengths and angles to show that one picture of a bird is not a scaled copy of the other. Unlike in previous tasks, minimal scaffolding is given here, so students need to decide what evidence is necessary to explain or show an absence of...	7
Narrative The purpose of this Number Talk is to elicit strategies and understandings students have for dividing within 100. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to divide fluently within 100. Launch Display one expression. “Give m...	3
Task Find a number greater than 0 and less than 1,000 that: Is closer to 500 than 0, and Is closer to 200 than 500. ###IMAGE0### There are many correct answers to this problem. Describe all of the numbers that are correct.	4
Task Jamie is planning to cover a wall with red wallpaper. The dimensions of the wall are shown below: ###IMAGE0### How many square feet of wallpaper are required to cover the wall? Wallpaper comes in long rectangular strips which are 24 inches wide. If Jamie lays the strips of wallpaper vertically, can she cover the w...	6
Task What fraction of the rectangle below is shaded? ###IMAGE0### Laura says that $\frac14$ of the rectangle is shaded. Do you think she is correct? Explain why or why not by using the picture.	4
Activity The purpose of this activity is to begin to think of a dilation with a scale factor as a rule or operation on points in the plane. Students work on a circular grid with center of dilation at the center of the grid. They examine what happens to different points on a given circle when the dilation is applied and...	8
Stage 4: Within 100 with Composing Required Preparation Materials to Copy Blackline Masters Number Puzzles Digit Cards Number Puzzles Addition Stage 4 Gameboard Narrative Students use digit cards to make addition and subtraction equations true. They work with sums and differences within 100 with composing and decompos...	2
Stage 2: Centimeters and Inches Required Preparation Materials to Gather Rulers (centimeters) Rulers (inches) Materials to Copy Blackline Masters Estimate and Measure Stage 2 Recording Sheet Narrative Students choose an object and a unit (inches, feet, centimeters) to measure it with. They estimate the length of the o...	2
Narrative The purpose of this activity is for students to see how other students solved one of the problems that involves a factor of a teen number. While students look at each other’s work, they will leave sticky notes describing why they think the answer does or does not make sense (MP3). The synthesis will look spec...	3
Narrative In this activity, students continue to use the relationship between multiplication and division to reason about situations that involve division. Students divide three-digit numbers by single-digit divisors and find results with and without a remainder. Launch Groups of 2 Activity 5 minutes: independent work ...	4
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
Stage 2: Factors and Multiples Required Preparation Materials to Gather Centimeter cubes Materials to Copy Blackline Masters Find the Number Stage 2 Directions and Gameboard Narrative Students find factors and multiples for a given number. To start, one player chooses an even number less than 50. The other player cove...	4
Activity In this activity, students mix different numbers of batches of a color recipe to obtain a certain shade of green. They observe how multiple batches of the same recipe produce the same shade of green as a single batch, which suggests that the ratios of blue to yellow for the two situations are equivalent. They ...	6
Activity Note: if it is possible in your local environment, we recommend using the digital version of this activity. This activity is intended to help students identify correspondences between parts of a table, graph, and an equation of a line through the origin in the first quadrant. Students are guided to notice: Any...	7
Narrative The purpose of this activity is for students to subtract one-digit and two-digit numbers from a three-digit number using the methods that make sense to them. Each difference would require students to decompose a ten to subtract by place. They may count back or count on by place to find the difference. They ma...	2
Task A theme park has a log ride that can hold 12 people. They also have a weight limit of 1500 lbs per log for safety reasons. If the average adult weighs 150 lbs, the average child weighs 100 lbs and the log itself weighs 200, the ride can operate safely if the inequality $$ 150A + 100C + 200 \leq 1500 $$ is satisfie...	6
Task Complete the table. ###TABLE0###	4
Activity The goal of this activity, and the two that follow, is for students to solve an equation in a real-world context while previewing some future work solving systems of equations. Here, students first make sense of the situation using a table of values describing the water heights of two tanks and then use the ta...	8
Narrative The purpose of this What Do You Know About _____? is to invite students to share what they know and how they can represent the number 20. Launch Display the number 20. “What do you know about 20?” 1 minute: quiet think time Activity Record responses. Student Facing What do you know about 20? Student Response ...	1
Problem 1 Veronica is making a poster for science class. ###IMAGE0### What is the total area, in square feet, of the poster? Problem 2 Setsuko is redoing a room and wants to put wallpaper on a wall that has a window. The wall with the window, shaded, are shown in the diagram below. ###IMAGE1### How many square feet of ...	3
Activity This activity is the second of three activities in which students investigate the value of $\sqrt2$ . As a result of the previous activity, students should believe that $\sqrt2$ is about 1.5, maybe a little bit less. Students should also understand that $\sqrt2$ is a number that we can multiply by itself...	8
Narrative The purpose of this activity is for students to make sense of the structure of a Take From, Result Unknown story problem. Students have access to connecting cubes or two-color counters and 10-frames, which they may choose to use strategically to represent and solve the problem (MP5). Some students may apply t...	2
Stage 1: Add Required Preparation Materials to Gather Connecting cubes Counters Materials to Copy Blackline Masters 5-Frame Number Mat 1–5 5-frames Stages 1 and 2 Recording Sheet Narrative Students begin with a full 5-frame and roll to see how many counters to add.	0
Narrative The purpose of this activity is for students to practice identifying fractional intervals along a number line. This is Stage 2 of the center activity, Number Line Scoot. This activity encourages students to count by the number of intervals (the numerator). Students have to land exactly on the last tick mark, ...	3
Narrative The purpose of this activity is for students to find the missing value in addition and subtraction equations. This activity is optional because determining the missing value of an equation is not required by the standards. Students may “just know” some of the answers or they may use counting forward or backwa...	0
Narrative The purpose of this activity is for students to apply what they have learned in this section to compare a number to the product of that number with a fraction. There are two cases where the fraction has a value of 1. Students may identify that the value of the fraction is 1 and use what they know about multip...	5
Task Materials ruler, meter sticks, yard sticks, measuring tape paper crayons Actions Part 1 Explain that students will be working in pairs to determine the length of each partner’s foot. Ask what tools would be appropriate for determining length. Chart student thinking about appropriate tools, and today’s goal of us...	2
Task A spider walks on the outside of a box from point A to B to C to D and finally to point E as shown in the picture below. ###IMAGE0### Draw a net of the box and map out the path of the spider on the net. Compare your net with those of some other people. Cut out the net and put the box together to see if you are rig...	8
Activity After organizing the data set into a frequency table in the warm-up, students now represent the information graphically. The drawing of the plot should be fairly straightforward. The emphasis here is on using a graphical representation to study and comment on the data distribution, and to reinforce how it allo...	6
Activity In this activity, students apply the expression they previously generated to find the areas of various triangles. Each diagram is labeled with two or three measurements. Before calculating, students think about which lengths can be used to find the area of each triangle. As students work, notice students who c...	6
Problem 1 Blake wants to cover a page of his scrapbook with colored paper. The page measures 6 inches by 8 inches. How much colored paper does Blake need to cover the entire scrapbook page? Problem 2 A room is 63 square feet. Its length is 9 feet. What is its width?	3
Activity The purpose of this activity is for students to approximate different parts of a graph with an appropriate line segment. This graph is from a previous activity, but students interact with it differently by sketching a linear function that models a certain part of the data. They take this model and consider its...	8
Activity This activity introduces students to the term median . They learn that the median describes the middle value in an ordered list of data, and that it can capture what we consider typical for the data in some cases. Students learn about the median through a kinesthetic activity. They line up in order of the numb...	6
Narrative The purpose of this activity is for students to subtract in a way that makes sense to them. Students use a method of their choice and share their methods with one another. This can serve as a formative assessment of how students approach finding the value of a difference when a ten must be decomposed when sub...	2
Narrative The purpose of this activity is for students to solve a story problem and write an equation to match it. Students are divided into nine groups and each group gets one of the story problem cards from the blackline master. Students individually solve the story problem and write an equation to match it before cr...	1
Problem 1 Two similar situations are shown below. How are they similar and how are they different? A pair of sneakers regularly cost $40. They are on sale for 25% off. How much money will you save? A pair of boots are on sale for $40 off. This is a savings of 25%. What is the regular price of the boots? Problem 2 The A...	6
Task A mixture of concrete is made up of sand and cement in a ratio of 5 : 3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix?	6
Activity The purpose of this activity is to reinforce that some conditions define a unique polygon while others do not. Students build polygons given only a description of their side lengths. They articulate that this is not enough information to guarantee that a pair of quadrilaterals are identical copies. On the othe...	7
Warm-up In this activity, students practice determining the measurement of unknown angles using their relationship to angles with known angle measure and what students already know about the measurement of right angles and straight angles. After they have worked on the activity and shared their solutions, they are intr...	7
Stage 2: Grade 1 Shapes Required Preparation Materials to Gather Counters Materials to Copy Blackline Masters Which One Stage 2 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 ...	1
Draw a tape diagram or balance for each equation or situation below. a. You purchase 4 gift cards, each in the same amount. You spend a total of $60. b. $${x+6=18}$$ c. $${6x=18}$$	6
Problem 1 A balance is shown below. ###IMAGE0### a. Describe how you can use the balance to find the value of $$x$$ . b. Write an equation to represent the situation shown in the balance. c. Use the equation to model the actions you did in part A with the balance. d. Repeat parts A–C using the balance shown bel...	7
Problem 1 The shape below has a perimeter of 30 feet. ###IMAGE0### What is the length of the side that is missing a number? Problem 2 Tessa ropes off a rectangular part of her lawn to create a play area for her dog. She uses 32 yards of rope. What is the missing side length of the play area? ###IMAGE1###	3
Narrative The purpose of this activity is for students to interpret and compare representations that show decomposing a ten to subtract by place. One student shows decomposing a ten by crossing off a ten and drawing 10 ones. The other representation shows a student who begins their drawing with a ten decomposed into 10...	2
Narrative The purpose of this activity is for students to determine how a number line is partitioned and what fraction is marked on it with only 0, 1, and 2 labeled. Students partition and locate and mark, but don’t label, a fraction on a number line and then trade with a partner to determine the fraction their partner...	3
Activity This task is analogous to a previous activity with positive exponents. The number line strongly encourages students to think about how to change expressions so they all take the form $b \boldcdot 10^k$ , where $b$ is between 1 and 10, as in the case of scientific notation. The number line also is a useful ...	8
Problem 1 Act 1: Watch the video The Orange (Act-1) . a. What do you notice? What do you wonder? b. How many linking cubes will it take to even out the balance scale? Make an estimate. Problem 2 Act 2: Use the following information to determine how many cubes it will take until the balance is level with the orange ...	3
Activity In the previous lesson, students analyzed the graph of a linear, non-proportional relationship (number of cups in a stack versus the height of the stack). This task focuses on interpreting the slope of a graph and where it crosses the $y$ -axis in context. Students are given cards describing situations with ...	7

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