options: Analyze and solve linear equations and pairs of simultaneous linear equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Solve systems of equations.

Generate and analyze patterns.

Write expressions in equivalent forms to solve problems.

Understand the relationship between zeros and factors of polynomials.

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

Work with equal groups of objects to gain foundations for multiplication.

Understand and apply properties of operations and the relationship between addition and subtraction.

Analyze patterns and relationships.

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

Understand solving equations as a process of reasoning and explain the reasoning.

Work with addition and subtraction equations.

Represent and solve equations and inequalities graphically.

Use properties of operations to generate equivalent expressions.

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

Understand properties of multiplication and the relationship between multiplication and division.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

Reason about and solve one-variable equations and inequalities.

Solve equations and inequalities in one variable.

Rewrite rational expressions.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Write and interpret numerical expressions.

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Understand the connections between proportional relationships, lines, and linear equations.

Use polynomial identities to solve problems.
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?                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               |                      |                        |
| |https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.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=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19|  |https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.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=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19| image:: https://cms-im.s3.amazonaws.com/clhjdxlivcrwuhnz8p74h3wdr0sr?response-content-disposition=attachment%3B%20filename%3D%22tikz-file-148281.svg%22%3B%20filename%2A%3DUTF-8%27%27tikz-file-148281.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=d838c3f51f69439465afa72015e1148ef93bd40389ba4d8f653044f160e7cc19 |                      |                        |
| |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: 14