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.


Concept/skill: 
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.

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

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} $

Concept/skill: 
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.

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

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?


Concept/skill: 
Fluently multiply multi-digit whole numbers using the standard algorithm.

Answer: 
Yes. 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.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_pos_0

5
standard_description: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
The purpose of this activity is for students to observe and use the structure of diagrams to find areas of shaded regions with non-unit fraction side lengths. Students build on what they learned in the previous activity, solidifying their understanding of why the numerator of a product of two fractions is the product of the numerators and the denominator of a product of fractions is the product of the denominators.
Action and Expression: Internalize Executive Functions.
Invite students to verbalize their strategy for writing multiplication expressions to represent the area of the shaded rectangle in each figure before they begin. Students can speak quietly to themselves, or share with a partner.
Supports accessibility for: Organization, Conceptual Processing, Language
Launch
Groups of 2
Activity
“Start working on completing the table independently. After a couple minutes, you'll work with your partner to complete the table and answer the rest of the questions.”
1–2 minutes: independent work time
5-8 minutes: partner work time
Monitor for students who:
notice the area of the shaded regions is always twentieths
write the expression
\(\frac{6}{5}\times\frac{4}{5}\)
to represent the shaded region of the last diagram in the table
explain that the expression
\(\frac{6\times4}{5\times4}\)
represents the shaded part of the last diagram in the table because
\(6\times4\)
represents the number of pieces that are shaded and
\(4 \times 5\)
represents the number of those pieces in the unit square
Student Facing
Complete the table.
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                diagram                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | multiplication                       expression | shaded area                       (square units) |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------|--------------------------------------------------|
| A                |https://cms-im.s3.amazonaws.com/ui5g959sm5gv0dm8y5muaeuevuxb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-147492.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-147492.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=da65b42438b700b09e62286557fa329bb057a4e3c43b71d5a338b3b21f3a4bad|  |https://cms-im.s3.amazonaws.com/ui5g959sm5gv0dm8y5muaeuevuxb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-147492.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-147492.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=da65b42438b700b09e62286557fa329bb057a4e3c43b71d5a338b3b21f3a4bad| image:: https://cms-im.s3.amazonaws.com/ui5g959sm5gv0dm8y5muaeuevuxb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-147492.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-147492.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=da65b42438b700b09e62286557fa329bb057a4e3c43b71d5a338b3b21f3a4bad |                                                 |                                                  |
| B                |https://cms-im.s3.amazonaws.com/dx240g4b4kkym1gkgs7khx0yw7ri?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149071.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149071.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=216cb8ca62660faf0bab04b1fb04fd987604857004a334e4036d514267493e92|  |https://cms-im.s3.amazonaws.com/dx240g4b4kkym1gkgs7khx0yw7ri?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149071.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149071.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=216cb8ca62660faf0bab04b1fb04fd987604857004a334e4036d514267493e92| image:: https://cms-im.s3.amazonaws.com/dx240g4b4kkym1gkgs7khx0yw7ri?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149071.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149071.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=216cb8ca62660faf0bab04b1fb04fd987604857004a334e4036d514267493e92 |                                                 |                                                  |
|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                diagram                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                | multiplication                       expression | shaded area                       (square units) |
|-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------------------------------|--------------------------------------------------|
| C                |https://cms-im.s3.amazonaws.com/9mw9803l8i0vjwwj588r8xkqowrt?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149072.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149072.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=80f7eec3ac67d9991858cc362c8526df4c2ac740536b8a7383a5ba2034426a7e|  |https://cms-im.s3.amazonaws.com/9mw9803l8i0vjwwj588r8xkqowrt?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149072.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149072.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=80f7eec3ac67d9991858cc362c8526df4c2ac740536b8a7383a5ba2034426a7e| image:: https://cms-im.s3.amazonaws.com/9mw9803l8i0vjwwj588r8xkqowrt?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149072.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149072.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=80f7eec3ac67d9991858cc362c8526df4c2ac740536b8a7383a5ba2034426a7e |                                                 |                                                  |
| D                |https://cms-im.s3.amazonaws.com/wy0o9qune26s9u7htzi5ilsfmts4?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149073.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149073.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=57e693708d062f1a9de3113218a2c369f9dbe92ca8b9a751cd2729b2d6cbb65d|  |https://cms-im.s3.amazonaws.com/wy0o9qune26s9u7htzi5ilsfmts4?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149073.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149073.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=57e693708d062f1a9de3113218a2c369f9dbe92ca8b9a751cd2729b2d6cbb65d| image:: https://cms-im.s3.amazonaws.com/wy0o9qune26s9u7htzi5ilsfmts4?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149073.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149073.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=20240208T165553Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=57e693708d062f1a9de3113218a2c369f9dbe92ca8b9a751cd2729b2d6cbb65d |                                                 |                                                  |
What patterns do you notice in the table?
Explain or show how the expression
\(\frac{6\times4}{5\times4}\)
represents the last diagram in the table.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not explain that the product of the numerators represents the number of pieces in the shaded region and the product of the denominators represents the number of pieces in the whole, consider asking: “What is the same and what is different about diagrams A and B?”
Activity Synthesis
Ask previously selected students to share their reasoning.
“How do the expressions in the table represent the number of pieces shaded in and the size of the pieces shaded in?” (If we multiply the numerators, we get the number of pieces that are shaded in. If we multiply the denominators, we get the size of the pieces.)
Refer to diagrams and draw on each diagram to show how the multiplication of the numerators and denominators represents the number of shaded pieces and the size of the shaded pieces (that is, the number of those pieces in the whole).


aligns: no