few_shots: Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Thought: This task teaches students to understand addition as putting together counters, or adding to already placed counters.
Answer: AB

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Understand ratio concepts and use ratio reasoning to solve problems.
problem_activity: Activity
In groups, students rotate through five different stations, where they measure one or more quantities using different units, and answer a series of summary questions afterward. Here are the quantities being measured and the units used at each station:
Station 1:
Volume of a box, in cubic inches and cubic centimeters.
Station 2:
Length, in meters and feet.
Station 3:
Volume of water, in gallons, quarts, and liters.
(If desired, you can have students measure water with actual containers instead of watching the video
https://vimeo.com/illustrativemathematics/water
.)
Station 4:
Weights and masses of 2–3 objects, in ounces, pounds, grams, and kilograms.
(You can have students weigh actual objects, use the digital simulation
http://ggbm.at/eQQVYB7D
, or use the paper simulations from the blackline master. If using one of the simulations instead of a real scale, prepare some real objects labeled with their weight or mass for students to hold and feel the weight of.)
Station 5:
Volume of salt, in milliliters and teaspoons.
You will need the blackline master for this activity. Page 1 is a net for the box needed for station 1. If you are using the paper scale simulation instead of a real scale or the applet, pages 2–13 are the parts needed to assemble Station 4.
Digital
Launch
Tell students they will further investigate the idea of using different units to measure the same set of items. Introduce the five stations, what students are expected to do at each, the protocol for rotating through them, and the questions to answer at the end. Then, demonstrate how to use the straightedge to measure a level teaspoon of salt. If students do not use a level teaspoons of salt, they will not be able to answer the last set of questions about volume.
Arrange students into 5 groups and assign a starting station for each group.
If students have devices, Stations 3 and 4 can be digital.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy. For example, “I noticed _____ so I think…”
Supports accessibility for: Language; Social-emotional skills
Speaking, Representing: MLR8 Discussion Supports.
Use this routine to support small-group discussion. As students rotate through stations, encourage students to solidify their own understanding by pressing for details and questioning their peers' explanations. Provide sentence frames for students to use, such as "I agree/disagree because . . .”, "How do you know . . .”, and “Can you give an example?” This will help students clarify their reasoning about comparing different measurements for the same quantity using different units.
Design Principle(s): Support sense-making; Cultivate conversation
Student Facing
Station 1
Each large cube is 1 cubic inch. Count how many cubic inches completely pack the box without gaps.
Each small cube is 1 cubic centimeter. Each rod is composed of 10 cubic centimeters. Count how many cubic centimeters completely fill the box.
|                   | cubic inches | cubic centimeters |
|-------------------|--------------|-------------------|
| volume of the box |              |                   |
Station 2
Your teacher showed you a length.
Use the meter stick to measure the length to the nearest meter.
Use a ruler to measure the length to the nearest foot.
|                            | meters | feet |
|----------------------------|--------|------|
| length of ________________ |        |      |
Station 3
Watch the video.
Count how many times you can fill the quart bottle from the gallon jug.
Count how many times you can fill the liter bottle from the gallon jug.
Video
Quarts and Liters
available at
https://player.vimeo.com/video/304136597
.
|                   | quarts | liters |
|-------------------|--------|--------|
| 1 gallon of water |        |        |
Station 4
Use the applet to record the weights of different objects in different units.
Record their weights in ounces, pounds, grams, and kilograms.
| object | ounces | pounds | grams | kilograms |
|--------|--------|--------|-------|-----------|
|        |        |        |       |           |
|        |        |        |       |           |
|        |        |        |       |           |
Station 5
Count how many level teaspoons of salt it takes to fill the graduated cylinder to 20 milliliters, 40 milliliters, and 50 milliliters.
Pour the salt back into the original container.
|                                                 | milliliters | teaspoons |
|-------------------------------------------------|-------------|-----------|
| small amount                           of salt  |             |           |
| medium amount                           of salt |             |           |
| large amount                           of salt  |             |           |
After you finish all five stations, answer the following questions with your group.
Which is larger, a cubic inch or a cubic centimeter? Did more cubic inches or cubic centimeters fit in the cardboard box? Why?
Did it take more feet or meters to measure the indicated length? Why?
Which is bigger, a quart or a liter? Explain your reasoning.
Use the data from Station 4 to put the units of weight and mass in order from smallest to largest. Explain your reasoning.
About how many teaspoons of salt would it take to fill the graduated cylinder to 100 milliliters?
If you poured 15 teaspoons of salt into an empty graduated cylinder, about how many milliliters would it fill?
How many milliliters per teaspoon are there?
How many teaspoons per milliliter are there?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Tell students they will further investigate the idea of using different units to measure the same set of items. Introduce the five stations, what students are expected to do at each, the protocol for rotating through them, and the questions to answer at the end. Then, demonstrate how to use the straightedge to measure a level teaspoon of salt. If students do not use a level teaspoons of salt, they will not be able to answer the last set of questions about volume.
Arrange students into 5 groups and assign a starting station for each group.
If students have devices, Stations 3 and 4 can be digital.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their strategy. For example, “I noticed _____ so I think…”
Supports accessibility for: Language; Social-emotional skills
Speaking, Representing: MLR8 Discussion Supports.
Use this routine to support small-group discussion. As students rotate through stations, encourage students to solidify their own understanding by pressing for details and questioning their peers' explanations. Provide sentence frames for students to use, such as "I agree/disagree because . . .”, "How do you know . . .”, and “Can you give an example?” This will help students clarify their reasoning about comparing different measurements for the same quantity using different units.
Design Principle(s): Support sense-making; Cultivate conversation
Student Facing
Station 1
Each large cube is 1 cubic inch. Count how many cubic inches completely pack the box without gaps.
Each small cube is 1 cubic centimeter. Each rod is composed of 10 cubic centimeters. Count how many cubic centimeters completely fill the box.
|                                                   | cubic                                 inches | cubic                                 centimeters |
|---------------------------------------------------|----------------------------------------------|---------------------------------------------------|
| volume of                                 the box |                                              |                                                   |
Station 2
Your teacher showed you a length.
Use the meter stick to measure the length to the nearest meter.
Use a ruler to measure the length to the nearest foot.
|                                                              | meters | feet |
|--------------------------------------------------------------|--------|------|
| length of                                 __________________ |        |      |
Station 3
If not using real water, open
https://vimeo.com/illustrativemathematics/water
.
Count how many times you can fill the quart bottle from the gallon jug.
Count how many times you can fill the liter bottle from the gallon jug.
|                                                   | quarts | liters |
|---------------------------------------------------|--------|--------|
| 1 gallon                                 of water |        |        |
Station 4
If not using a real scale, open
http://ggbm.at/eQQVYB7D
.
Select 2–3 different objects to measure on the scale.
Record the weights in ounces, pounds, grams, and kilograms.
| object | ounces | pounds | grams | kilograms |
|--------|--------|--------|-------|-----------|
|        |        |        |       |           |
|        |        |        |       |           |
|        |        |        |       |           |
Station 5
Count how many level teaspoons of salt fill the graduated cylinder to 20 milliliters, 40 milliliters, and 50 milliliters.
Pour the salt back into the original container.
|                                                       | milliliters | teaspoons |
|-------------------------------------------------------|-------------|-----------|
| small amount                                 of salt  |             |           |
| medium amount                                 of salt |             |           |
| large amount                                 of salt  |             |           |
After you finish all five stations, answer these questions with your group.
Which is larger, a cubic inch or a cubic centimeter?
Did more cubic inches or cubic centimeters fit in the cardboard box? Why?
Did it take more feet or meters to measure the indicated length? Why?
Which is larger, a quart or a liter? Explain your reasoning.
Use the data from Station 4 to put the units of weight and mass in order from smallest to largest. Explain your reasoning.
About how many teaspoons of salt would it take to fill the graduated cylinder to 100 milliliters?
If you poured 15 teaspoons of salt into an empty graduated cylinder, about how many milliliters would it fill?
How many milliliters per teaspoon are there?
How many teaspoons per milliliter are there?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
People in the medical field use metric measurements when working with medicine. For example, a doctor might prescribe medication in 10 mg tablets.
Brainstorm a list of reasons why healthcare workers would do this. Organize your thinking so it can be followed by others.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
At Station 1, students may count the number of base-10 centimeter rods rather than the number of centimeter cubes. Remind them that the question prompts for the number of cubes.
At Station 2, students may need reminders about measuring objects at the zero marking on the ruler and about keeping the ruler going straight, both of which will affect the answer. Show them they can measure along the edge of the object to make sure the ruler is not veering off in one direction or another.
At Station 4, students may be unclear about how to change the output unit on the scale for each object. Consider showing the class ahead of time. Students who are able to distinguish between weight and mass might say they cannot accurately compare their measurements. Clarify that we are talking only about the weight of the objects on Earth’s surface.
At Station 5, some students may consistently use under-filled or rounded teaspoons of salt, so their data will not reveal the
\(5 : 1\)
ratio of milliliters to teaspoons. Repeat the demonstration of how to measure a level teaspoon for them.
Students may answer 3 milliliters for the question about 15 teaspoons because they divided by 5 instead of multiplying by 5. Encourage them to pay attention to which unit is bigger and ask what that tells them about which numerical value should be larger.
Activity Synthesis
Though much of the discussion will take place within groups, spend a few minutes ensuring that everyone understands the answers to the five questions. To conclude the activity, invite students to share anything that surprised them from the measuring work.


correct_option_index: 1