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.


Standard options: 
A. Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
B. For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.
C. Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
D. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
E. Fluently add and subtract within 5.


Thought: This task involves representing addition with objects such as number cards and dice.
Answer: A

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} $

Standard options: 
A. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
B. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
C. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Thought: By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.
Answer: B

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?


Standard options: 
A. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
B. Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
C. Fluently multiply multi-digit whole numbers using the standard algorithm.


Thought: This set of problems involves multi-digit whole numbers because the numbers in each problem are four and two digit integers, and the mathematical calculations involved in both problems focus on multiplication. The first problem explicitly asks the student to solve its subproblems using the standard algorithm.
Answer: C

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_001477

K

im_task_000157

3

fl_problem_000674

5
options: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = �� ÷ 3, 6 × 6 = ?.

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
problem_activity: Narrative
The purpose of this activity is for students to write equations for multiplication situations and diagrams using a symbol for the unknown number. When students write an equation to represent a situation, including a symbol for the unknown number, they model a situation with mathematics (MP4).
Students find an unknown factor or unknown product in multiplication problems. In this task, the unknown factor diagrams and situations only include the “how many groups” problem type and the factors 2, 5, and 10. This sets students up to skip-count to find the unknown number.
This problem type will be revisited extensively in future lessons and will be related to division. It is not necessary to make the connection to division now. In the synthesis students explain how the equations they wrote represent the diagram or situation.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “The next time I write an equation with an unknown number, I will . . . .“
Supports accessibility for: Visual-Spatial Processing
Launch
Groups of 2
Activity
“Now you will practice writing your own equations with a symbol for the unknown.”
2–3 minutes: independent work time
“Share your equations with your partner. Discuss how you know each equation matches the diagram or situation.”
2–3 minutes: partner discussion
Have a whole-class discussion focused on how the equations match the different representations.
Consider asking:
“How did you use the representations to write an equation with a symbol for the unknown?” (I looked for what was missing in the diagram. I thought about the situation to figure out if it was the number in each group, the number of groups, or the total that was missing.)
“Now find the missing number in each equation and write a new equation that includes the solution.”
3–5 minutes: partner work time
Student Facing
Write an equation to represent each diagram or situation. Use a symbol for the unknown. Be prepared to share your reasoning.
Find the number that makes each equation true. Rewrite the equation with the solution.
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 diagram or situation                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 | equation with symbol | equation with solution |
|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|----------------------|------------------------|
| |https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275|  |https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275| image:: https://cms-im.s3.amazonaws.com/gf3w2hjep7il38vg6usxrnj0zj9v?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-152934.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-152934.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e5ec58d09b006a5b2fe4be0a8c6e1be79921b2ef4899756a6a2fb56b666e8275 |                      |                        |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Jada has some packs of sports cards. Each pack has 5 cards. If Jada has 45 cards, how many packs of cards does she have?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |                      |                        |
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| |https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408|  |https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408| image:: https://cms-im.s3.amazonaws.com/jg4dxs24ozz1huvon7s4enxj1zdl?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148282.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148282.svg&response-content-type=image%2Fsvg%2Bxml&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240208%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240208T163829Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8cf7dafc0a1b5a31eead8875981bb2db673480a12c4a842012b6e72effafc408 |                      |                        |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         The school has 6 bags. Each bag has 10 basketballs in it. How many basketballs does the school have?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         |                      |                        |
Student Response
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Advancing Student Thinking
If students write an equation without a symbol for the unknown number, consider asking:
“How does your equation represent the diagram (or situation)?”
“How could you show the number that was unknown with a symbol?”
Activity Synthesis
“What strategies did you use to find the unknown numbers?” (I counted by 2 to get the total. I counted by different numbers until I found a number that gave me the product.)
“How did each equation change as you found the unknown number?” (The symbol was replaced with the number.)


correct_option_index: 0

3