few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Your response:
{
  "explanation": "This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6
options: Fluently add and subtract within 5.

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

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.

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.

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).
problem_activity: Narrative
The purpose of this activity is for students to learn stage 1 of the What’s Behind My Back center. Students find multiple decompositions of a number. Students snap a tower of connecting cubes into 2 parts and record each decomposition with a drawing and an expression. It may be helpful to give each group of students a single color of connecting cubes so the color of the cubes doesn’t distract students from identifying the two parts. In future stages of this center students hide cubes behind their back after snapping a tower. If needed, you can choose not to use the name What’s Behind My Back when playing this stage or let students know they will do that in future stages of this center.
The recording sheet is printed in the student book for this activity. There is a blackline master available for students to use during centers in future activities and lessons.
When students write an expression to match the connecting cubes, they reason abstractly and quantitatively (MP2).
MLR8 Discussion Supports.
Display and read aloud the following sentence frame to support small-group discussion: “You broke your tower into a group of ____ and a group of ____.” invite students to chorally repeat this sentence in unison 1–2 times.
Advances: Speaking, Conversing, Representing
Required Materials
Materials to Gather
Connecting cubes
Crayons
Materials to Copy
What's Behind My Back Stage 1 Recording Sheet
Required Preparation
Each group of 2 needs 8 connecting cubes of the same color.
Launch
Groups of 2
Give each group of students at least 8 connecting cubes and access to 2 different color crayons.
“We are going to learn a center called What’s Behind My Back?”
Display a cube tower with 8 cubes.
“Start with a tower of 8 cubes. One partner breaks the tower into 2 parts.”
Demonstrate breaking the tower into 2 parts.
“The other partner describes what happened to the tower. Tell your partner what happened to my tower.” (You broke your tower into a group of 5 and a group of 3.)
30 seconds: partner discussion
Share responses.
“Both partners record the two parts with a drawing and an expression.”
Demonstrate completing the recording sheet with a drawing and an expression.
“Then put your tower back together, and play again. Take turns snapping the tower of 8 cubes into 2 parts.”
Activity
5 minutes: partner work time
Student Facing
8 cubes
{"table": [{"_attributes": {"align": "center", "border": "1"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}]}]}]}
8 cubes
{"table": [{"_attributes": {"align": "center", "border": "1"}, "tbody": [{"tr": [{"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}, {"td": [{"_attributes": {"style": "text-align:center"}, "figure": [{"_attributes": {"class": ["embedded-content", "embedded-content-tikz-file", "embedded-content-image"], "data-embedder-target": "web", "data-record-id": "149768", "data-record-model": "TikzFile"}, "span": [{"_attributes": {"class": ["c-figure__label"]}}], "img": [{"_attributes": {"alt": "8 blank cubes.", "role": "image", "src": "https://cms-im.s3.amazonaws.com/df6rew3ew18xkglzjtjc1ovvv7tb?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-149768.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-149768.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=20240208T165232Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9f474d428c909466a00a81ca41a2962ba593a89bd8f1c6d903531db14b6c15ce"}}], "figcaption": [{"_attributes": {"class": ["c-figcaption"]}}]}], "br": [{}], "_value": "expression: _________________________"}]}]}]}]}
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 snap the cubes the same way each time, consider asking:
“Are there any other ways that you can snap the tower into 2 parts?”
“What if you snapped only 1 cube off of the tower?”
Activity Synthesis
“What did you notice each time you snapped the tower?” (There were always 8 cubes. The 2 parts that we broke the tower into were different each time.)
“What are the different ways that you and your partner found to break the tower of 8 cubes into 2 parts?”
Display a tower of 2 and a tower of 6.
“What expression can we write to represent the 2 parts of this tower?” (
\(2 + 6\)
)


correct_option_index: 4