standard_description: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
problem_activity: Narrative
The purpose of this activity is for students to see how, when multiplying a number larger than ten, the distributive property can be used to decompose the factor into tens and ones, creating two smaller products. Base-ten blocks are used to help students visualize what is happening when a factor is decomposed to make two more easily known products. Factors slightly larger than ten can be naturally decomposed into a ten and some ones using place value. This will be useful in subsequent lessons as students progress towards fluent multiplication and division within 100.
When students see that you can decompose a teen number into tens and ones and use this to multiply teen numbers, they look for and make use of structure (MP7).
Required Materials
Materials to Gather
Base-ten blocks
Launch
Groups of 2
Give students base-ten blocks.
Activity
“Take a few minutes to look at Tyler’s strategy and decide if you agree or disagree with it.”
2–3 minutes: independent work time
3–4 minutes: partner discussion
Monitor for students who connect the expressions
\(7 \times 10\)
and
\(7 \times 3\)
to the tens and ones portion of the place value diagram and
\(7 \times 13\)
to the entire diagram.
Have students share why they agreed or disagreed with Tyler’s strategy with a focus on using the place value diagram as a justification.
Consider asking:
“Where do we see the
\(7 \times 13\)
in the place value diagram?”
“Where do the 10 and the 3 come from?”
“How could you use the place value diagram to figure out how to find the value of
\(7 \times 13\)
?”
“Now use Tyler’s method on your own to find the value of
\(3 \times 14\)
.”
2–3 minutes: independent work time
“Share your solution and your reasoning with your partner.”
2–3 minutes: partner discussion
Student Facing
Tyler says he can use base-ten blocks to find the value of
\(7 \times 13\)
because he knows
\(7 \times 10\)
and
\(7 \times 3\)
. He says this diagram proves his thinking.
Do you agree or disagree? Explain your reasoning.
[IMG]
Use Tyler’s method to find the value of
\(3 \times 14\)
. Explain or show your reasoning.
Student Response
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Advancing Student Thinking
If students say they don’t see
\(7\times10\)
and
\(7\times3\)
in Tyler's diagram, consider asking:
“Where do you see
\(7\times13\)
in the diagram?”
“If we separate the tens and ones, what expression could we use to describe the tens? The ones?”
Activity Synthesis
Display base-ten blocks or place value diagrams that students used to solve. As students explain their work, write multiplication expressions to represent them.
“How does this diagram (or the base-ten blocks) show how Tyler’s method could be used to multiply
\(3 \times 14\)
?” (We can see there are 3 tens which is 30. We can see that there are 3 groups of 4 ones which is 12.
\(30 + 12\)
is 42. The whole diagram represents
\(3 \times 14\)
.)
If there is time, ask students to find the value of
\(4 \times 12\)
and
\(5 \times 16\)
using the base-ten blocks and Tyler’s strategy.


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