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Activity
The purpose of this activity is to extend the definition of exponents to include negative exponents. The meaning of zero exponents is also revisited. When students use tables to explore expressions with negative exponents, they are noticing and making use of structure (MP7).
Launch
Arrange students in groups o... | 8 |
Triangle
$${{{CDE}}}$$
underwent a transformation that created triangle
$${{{C'D'E'}}}$$
.
###IMAGE0###
a. Describe how triangle
$${{{CDE}}}$$
was transformed to become triangle
$${{{C'D'E'}}}$$
.
b. What features stayed the same?
c. What features changed?
d. Is triangle
$${{{CDE}}}$$
congruent to triangle
$${{... | 8 |
Problem 3
Pre-unit
###IMAGE0###
Label the tick marks on the number line.
Locate and label 45 and 62 on the number line.
| 2 |
Task
Antonio and Juan are in a 4-mile bike race. The graph below shows the distance of each racer (in miles) as a function of time (in minutes).
###IMAGE0###
Who wins the race? How do you know?
Imagine you were watching the race and had to announce it over the radio, write a little story describing the race.
| 8 |
Warm-up
This number talk helps students think about what happens to a quotient when the divisor is doubled. In this lesson and in upcoming work on ratios and unit rates, students will be asked to find a fraction of a number and identify fractions on a number line.
Launch
Display one problem at a time. Tell students to ... | 5 |
Narrative
The purpose of this activity is for students to make a reasonable estimate for a given product.
In addition to estimating the product, students also decide whether the estimate is too large or too small. In the activity synthesis, students consider about how far their estimate is from the actual product.
I
n ... | 5 |
Activity
When students are finding values to aid in their method, consider allowing them to research typical values online at hardware websites or search for values that would be useful. If these tools are not available, some values are provided here.
Values that may be useful for students:
Typical (modern) shower head... | 7 |
Narrative
This activity serves two main purposes. The first is to allow students to apply their understanding that the result of
\(a \times \frac{1}{b}\)
is
\(\frac{a}{b}\)
. The second is for students to reinforce the idea that any non-unit fraction can be viewed in terms of equal groups of a unit fraction and express... | 4 |
Activity
In this activity, students continue to compute probabilities for multi-step experiments using the number of outcomes in the sample space. The first problem involves a situation for which students have already seen the sample space. Following this problem, the class will discuss the merits of the different repr... | 7 |
Narrative
The purpose of this activity is for students to begin to distinguish rectangles from other shapes. By working with variants and non-examples of rectangles, students begin to develop their understanding of what makes a shape a rectangle. When they discuss which group a shape should be placed in, students infor... | K |
Narrative
In a previous lesson, students described an angle to a peer so that they might draw the angle accurately without seeing it. Students learned what an angle is and have reasoned about how to describe the size of an angle.
In this activity, students use the features of an analog clock (minute hand, hour hand, an... | 4 |
Stage 4: Grade 3 Shapes
Required Preparation
Materials to Copy
Blackline Masters
Shape Cards Grade 3
Triangle Cards Grade 3
Quadrilateral Cards Grade 3
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. Student... | 3 |
Activity
Previously, students worked with ratios in which one quantity (distance run) had the same value and the other (time elapsed) did not. In the context of running, they concluded that the runners did not run at the same rate. Here, students work with two ratios in which neither quantity (number of tickets bought ... | 6 |
Problem 1
How much is a million?
Problem 2
Make a model to represent the size of 1,000,000.
Problem 3
a. Use a place value chart to model the size of 1,000,000, building it from bundles of 10 starting with the ones place.
b. Use your work in Part (a) to solve each of the following:
10
$$\times$$
10 = ______________... | 5 |
Warm-up
By now, students understand that lengths in a scaled copy are related to the original lengths by the scale factor. Here they see that the area of a scaled copy is related to the original area by the
square
of the scale factor.
Students build scaled copies of a single pattern block, using blocks of the same shap... | 7 |
Activity
The purpose of this task is to introduce students to the idea of a proportional relationship. From previous work, students should be familiar with the idea of equivalent ratios, and they may very well recognize the table as a set of equivalent ratios. Here, we are starting to expand this concept and the langua... | 7 |
Label the second quadrant on the coordinate plane, and then answer the following questions.
###IMAGE0###
a. Write the coordinates of one point that lies in the second quadrant of the coordinate plane.
b. What must be true about the coordinates of any point that lies in the second quadrant?
c. Plot and label the... | 6 |
Activity
In the previous activity, students noticed trends in the data from the scatter plot. In this activity, the association is made more precise by looking at equations and graphs of linear models for the data to determine the slope. The numerical value of the slope is then interpreted in the context of the problem... | 8 |
Activity
Students use a realistic food recipe to find equivalent ratios that represent different numbers of batches. Students use the original recipe to form ratios of ingredients that represent double, half, five times, and one-fifth of the recipe. Then they examine given ratios of ingredients and determine how many b... | 6 |
Narrative
The purpose of this activity is for students to answer questions about the data represented by their picture graphs and bar graphs. Students switch workbooks with a new partner, which is an opportunity for students to view each other’s work and see different representations of data. While students are answeri... | 2 |
Narrative
The purpose of this warm-up is to elicit the idea that number lines and tape diagrams can be used to represent the same relationships between numbers, which will be useful when students use tape diagrams and number lines in a later activity to interpret and solve story problems. While students may notice and ... | 2 |
Problem 1
A circle is divided into 16 equal wedges, as shown below. Explain or show how you can rearrange the pieces to determine the area of the circle.
###IMAGE0###
Problem 2
Find the area of a circle that has a radius of 5 inches.
| 7 |
Narrative
The purpose of this activity is for students to use their own language and the language generated by the class in the last activity to describe how objects were sorted and tell how many objects are in each category. Students walk around the room and look at how other students sorted their objects. Consider us... | 1 |
Problem 1
A dime is
$${{1\over10}}$$
of a dollar and a penny is
$${{1\over100}}$$
of a dollar.
Would you rather have 4 one-dollar bills and 1 dime, 42 dimes, or 413 pennies? Justify your answer.
Problem 2
a. Decide whether each of these has the same value as 3.57. Explain your reasoning.
357 tenths
357 hundredths
3 o... | 4 |
Stage 9: Add Fractions to 5
Required Preparation
Materials to Gather
Number cards 0–10
Materials to Copy
Blackline Masters
How Close? Stage 9 Recording Sheet
Narrative
Before playing, students remove the cards that show 10 and set them aside.
Each student picks 6 cards and chooses 4 of them to create an addition expre... | 5 |
Warm-up
By now students have written many division equations based on verbal descriptions of situations. This warm-up prompts them to go in the other direction: to interpret a division expression and write a fitting question the expression could help answer. Then, they trade descriptions with a partner and reason about... | 6 |
Problem 1
A repair technician replaces cracked screens on phones. He can replace 5 screens in 3 hours.
a. Write an equation you can use to determine how long it takes to replace any number of screens.
b. Write an equation you can use to determine how many screens can be replaced in a certain number of hours.
c. U... | 7 |
Narrative
The purpose of this activity is for students to connect story problems to the equations that represent them and to solve different types of story problems. Students identify equations with a symbol for the unknown that match a story problem and justify their decisions by describing how the equations represent... | 2 |
Problem 1
Which of the rectangles on
Template: Compare Rectangles
has the greatest area? Show or explain your thinking.
Problem 2
Area is measured in
square units
. We can cover a shape with unit squares, then count the number of squares that make up a shape to find its area. For example, if a shape is covered by 12 un... | 3 |
Activity
In this activity, students use the area measures from the previous task to solve problems about the amount of painting time, using their understanding of ratio, rate, and percentage along the way. The problems can be approached in a number of ways, giving students additional opportunities to model with mathema... | 6 |
Narrative
In this activity, students are given expressions that represent strategies for finding the area of rectangles. The strategies are based on the distributive property and the associative property of multiplication. Students interpret the expressions by marking or shading area diagrams and connect each expressio... | 3 |
Narrative
The purpose of this True or False is to elicit insights students have about numbers being represented in different ways. The reasoning students do here deepens their understanding of how numbers can be composed and decomposed in different ways using tens and ones.
Launch
Display one statement.
“Give me a sign... | 1 |
Activity
The purpose of this activity is for students to find the areas of regions involving different-sized circles and compare the strategies used. The first question introduces subtraction as a strategy to find the area around the outside of a circle. The second question introduces division to find the area of fract... | 7 |
In a bag of 80 Skittles, 35% of the candies are orange. How many orange Skittles are in the bag?
Show your answer using two different strategies.
| 6 |
Coordinates for points are shown in the table.
###TABLE0###
Graph all the points from the table in the coordinate grid. Label them with their corresponding letters.
###IMAGE0###
| 5 |
Problem 1
Ms. Macklin puts thirty-two pencils into 4 pencil jars. She puts an equal number into each jar.
a. How many pencils are in each pencil jar?
b. How many pencils are in 3 pencil jars?
Problem 2
Mr. Bader has 5 pans of brownies, each of which he cuts into 6 pieces. He then puts an equal number of brownie sli... | 3 |
Narrative
This warm-up prompts students to compare four area diagrams that have been decomposed into two areas, each representing a product. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in... | 3 |
Narrative
The purpose of this activity is for students to use their understanding of place value to find the number that makes each equation true. Students must consider how units may be composed or decomposed to find the unknown number (MP7). The number choices intentionally emphasize the types of compositions and dec... | 2 |
Activity
Students reason abstractly and quantitatively about temperatures over time graphed on coordinate axes (MP2). The goal of this activity is for students to use inequalities to describe the location of points on a coordinate grid in one direction. This activity also introduces the idea of vertical difference on t... | 6 |
Narrative
The purpose of this activity is for students to count a collection of objects and show on paper how many there are so that others can understand how they counted. This collection of objects is a teen number of connecting cubes to encourage students to unitize a ten (MP7). In the synthesis, students consider r... | K |
Problem 1
In a 30-minute television show, 12 minutes of the airtime are spent on commercials.
a. Draw a visual representation of the problem.
b. Determine what percent of the television show’s airtime is spent on commercials. Choose any strategy.
c. Find a peer who used a different strategy to solve than you did.... | 7 |
Activity
This activity gives students first-hand experience in relating ratios of time and distance to speed. Students time one another as they move 10 meters at a constant speed—first slowly and then quickly—and then reason about the distance traveled in 1 second.
Double number lines play a key role in helping student... | 6 |
Activity
In this activity, students get a chance to practice solving equations with a single variable. The equations resemble the types of equations students see in the associated Algebra 1 lesson after they substitute for a variable. Students will work in pairs and each partner is responsible for answering the questio... | 8 |
Task
Lin wants to put some red and blue tiles on a wall for decoration. She is thinking about several different patterns of tiles she could create. She wants to choose a pattern that would let her use exactly as many red tiles as blue tiles.
Is it possible to create the pattern below using the same number of red tiles ... | 2 |
Problem 1
For parts (a) and (b) below,
Solve. Show or explain your work.
Assess the reasonableness of your answer.
a. 910 × 233
b. 852 × 488
Problem 2
Damian’s work on a multiplication problem is shown below.
###IMAGE0###
a. Why is Damian’s answer not reasonable? Use estimation in your explanation.
b. What mist... | 5 |
Optional activity
In this optional activity, students use expressions and number line diagrams to represent situations involving the changing height and depth of sea animals. They discuss how there is more than one correct way to write an equation that represents each situation. As students work, identify students who ... | 7 |
Narrative
The purpose of this optional activity is for students to practice the verbal count sequence to 10. This activity is optional because it is an opportunity for extra practice that not all students may need. Based on formative assessment data and observation from previous sections and during the first activity, ... | K |
A florist shop is preparing bundles of flowers to sell over the weekend. In a bundle of flowers, the shop uses 3 roses for every 4 carnations. Create a table of equivalent ratios to represent the relationship between roses and carnations in the bundles of flowers.
###TABLE0###
| 6 |
Activity
The purpose of the task is for students to compare signed numbers in a real-world context and then use inequality signs accurately with negative numbers (MP2). The context should help students understand “less than” or “greater than” language. Students evaluate and critique another's reasoning (MP3).
Launch
Al... | 6 |
Warm-up
This warm-up prompts students to estimate the volume of different glasses by reasoning about characteristics of their shape. As students discuss their reasoning with a partner, monitor the discussions and identify students who identified important characteristics of each of the glasses in their response.
Launch... | 5 |
Problem 1
The same image of a cat is shown at three different zoom levels on a computer.
###IMAGE0###
What do you notice about what happens to the scale as you zoom in and out on the image?
Problem 2
Your computer shows you a map of Washington Park in Eugene, Oregon. The scale in the bottom right corner of the map tell... | 7 |
Activity
In this activity, students explore two unit rates associated with the ratio, think about their meanings, and use both to solve problems. The goals are to:
Help students see that for every context that can be represented with a ratio
\(a:b\)
and an associated unit rate
\(\frac{b}{a}\)
, there is another unit ra... | 6 |
Narrative
Previously, students classified fractions based on their relationship to
\(\frac{1}{2}\)
and 1 (whether they are less than or more than these benchmarks). They used these classifications to compare fractions. In this activity, students are presented with fractions that are in the same group (for example, both... | 4 |
Warm-up
In this warm-up, students are presented with tape diagrams with a shaded portion, and they identify the percentage that is shaded.
Launch
Display the image in the task statement for all to see, and ask students to think of at least one thing they notice. Ask a few students to share something they notice. It is ... | 4 |
Warm-up
The purpose of this Math Talk is to elicit strategies and understandings students have for dividing fractions. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to divide one probability (often in the form of a fraction) by another pro... | 7 |
Narrative
The purpose of this activity is for students to ask and answer questions using their bar graphs from a previous activity. Students work with the group they collected survey data with to create questions that can be answered with their bar graphs. Then students are paired up with a new partner to use these que... | 3 |
Warm-up
The purpose of this warm-up is to help students recall information about scatter plots, which will be useful when students expand their understanding in a later activity.
While students may notice and wonder many things about these images, the relationship between the number of people and the maximum noise leve... | 8 |
Activity
The purpose of this activity is for students to begin to observe and describe translations and rotations. In groups of 2, they describe one of 3 possible dances, presented in cartoon form, and the partner identifies which dance is being described. Identify students who use specific and detailed language to des... | 8 |
Task
In triangle $\Delta ABC$, point $M$ is the point of intersection of the bisectors of angles $\angle BAC$, $\angle ABC$, and $\angle ACB$. The measure of $\angle ABC$ is $42^\circ$, and the measure of $\angle BAC$ is $64^\circ$. What is the measure of $\angle BMC$?
###IMAGE0###
This task adapted from a problem pu... | 8 |
Narrative
The purpose of this Choral Count is for students to practice counting back by 10 and notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to decompose hundreds.
Launch
“Count back by 10, starting at 590.”
R... | 2 |
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 |
Warm-up
This prompt gives students opportunities to see and make use of structure (MP7). The specific structures they might notice is the table and how it relates to a linear relationship between
\(x\)
and
\(y\)
(specifically, that
\(y = 3x + 6\)
).
Monitor for students who:
describe patterns only vertically or only in... | 8 |
Narrative
The purpose of this activity is for students to identify shapes as flat and solid as they sort shapes into groups. A sorting task gives students opportunities to analyze the structure of the shapes and identify common properties and characteristics (MP7).
If the sorting mat provided in the student workbook is... | K |
Stage 5: Fractions of Angles
Required Preparation
Materials to Gather
Protractors
Materials to Copy
Blackline Masters
Target Measurement Stage 5 Recording Sheet
Target Measurement Stage 5 Spinner
Narrative
Students spin a spinner to get a denominator for their target fraction. They choose a fraction less than one with... | 5 |
Stage 5: Add within 100 without Composing
Required Preparation
Materials to Gather
Paper clips
Two-color counters
Materials to Copy
Blackline Masters
Five in a Row Addition and Subtraction Stage 5 Gameboard
Narrative
Partner A chooses two numbers and places a paper clip on each number. They add the numbers and place a... | 1 |
Task
Find two different ways to add these two numbers:
$$1\frac{1}{3} + 2\frac{3}{5}$$
| 5 |
Problem 1
Point
$$Q$$
is located at
$$(-3,2)$$
. It is reflected over at least one axis and is now located at
$$(-3,-2)$$
. Describe the reflection that took place.
Problem 2
Riley reflects point
$$L$$
, located at
$$(5,4)$$
, over the
$$y$$
-axis. They determine its new location is at
$$(4,-5)$$
. Did Riley correctly ... | 6 |
Activity
In this activity, students think a little more deeply about the data we would like to know and how that compares to the data we can collect easily and quickly (MP1). They are presented with a statistical question that does not have an obvious answer. Students are then asked to consider ways they might begin ga... | 7 |
Narrative
The purpose of this card sort is for students to connect words and phrases to visual representations of partitioned shapes. Students begin by sorting the cards in a way that makes sense to them, and then are invited to sort the shapes based on the language that can be used to describe them. In the activity sy... | 1 |
Task
Jonathan wants to save up enough money so that he can buy a new sports equipment set that includes a football, baseball, soccer ball, and basketball. This complete boxed set costs \$50. Jonathan has \$15 he saved from his birthday. In order to make more money, he plans to wash neighbors’ windows. He plans to charg... | 7 |
Warm-up
In middle school, students explored scale drawings including how measurements in a scaled copy of a figure relate to measurements in the original figure. In this activity students remind themselves of these relationships by studying an example and a non-example.
Student Facing
###IMAGE0###
Diego took a picture ... | 7 |
Activity
In this task, students explore division situations (in the context of baking cookies) where the number of groups and a total amount are given, but the size of 1 group is unknown. They write multiplication equations in which the missing factor answers the question “how much in each group?” instead of “how many ... | 6 |
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 |
Activity
Students recall that subtracting a number (or expression) is the same as adding its additive inverse. This concept is applied to get students used to the idea that the subtraction sign has to stay with the term it is in front of. Making this concept explicit through a numeric example will help students see its... | 7 |
Narrative
The purpose of this warm-up is for students to notice that they can use the structure of the analog clock to count by 5. They compare what they know about number lines that label intervals of 5 to the labeled numbers on a clock. This will be useful when students tell time in a later activity. While students m... | 2 |
Activity
Students practice using precise wording (MP6) to describe the positive or negative association between two variables given scatter plots of data.
Launch
Display the scatterplot for all to see. Remind students that we investigated the relationship between car weight and fuel efficiency earlier.
###IMAGE0###
Ask... | 8 |
Task
The figure below gives the depth of the water at Montauk
Point, New York, for a day in November.
###IMAGE0###
How many high tides took place on this day?
How many low tides took place on this day?
How much time elapsed in between high tides?
| 8 |
Activity
The purpose of this activity is for students to extend what they learned about square roots and
\(\frac12\)
exponents to cube roots and
\(\frac13\)
exponents.
Launch
Tell students that they will use the same reasoning as in the previous activity to make sense of numbers to the
\(\frac12\)
power or
\(\frac13\)
... | 8 |
Find the prime factorization of the numbers below. Show your work.
200 56 91
| 6 |
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