standard_description: Use the structure of an expression to identify ways to rewrite it. For example, see x^(4) – y^(4 )as (x^(2))^(2 )– (y^(2))^(2), thus recognizing it as a difference of squares that can be factored as (x^(2 )– y^(2))(x^(2 )+ y^(2)).
problem_activity: Narrative
The purpose of this warm-up is to elicit the idea that expressions and equations can be used to represent different compositions and decompositions of 10, which will be useful when students match compositions and decompositions of 10 to equations in a later activity. While students may notice and wonder many things about these images and expressions, the fact that each image and expression represents a total of 10 is the important discussion point. Students have seen equations in previous lessons, but the synthesis is the first time that students are introduced to the term
equation
.
Launch
Groups of 2
Display the image.
“What do you notice? What do you wonder?”
1 minute: quiet think time
Activity
“Discuss your thinking with your partner.”
1 minute: partner discussion
Share and record responses.
Student Facing
What do you notice?
What do you wonder?
[IMG]
\(7 + 3\)
[IMG]
\(5 + 5\)
[IMG]
\(8 + 2\)
Student Response
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Activity Synthesis
“What is the same about each expression?” (They are all 10.)
Write
\(10 = 7 + 3\)
.
“There are 10 counters, 7 red counters and 3 yellow counters. We can write that as 10 is 7 plus 3. When we write
\(10 = 7 + 3\)
, it is called an
equation
.”
Repeat the steps with the next 2 images.


aligns: no