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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

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

Generate and analyze patterns.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving multiplication and division.

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

Gain familiarity with factors and multiples.

Perform arithmetic operations on polynomials.

Understand the relationship between zeros and factors of polynomials.

Solve equations and inequalities in one variable.

Create equations that describe numbers or relationships

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

Solve systems of equations.

Analyze patterns and relationships.

Use polynomial identities to solve problems.

Interpret the structure of expressions.

Represent and solve equations and inequalities graphically.

Rewrite rational expressions.

Add and subtract within 20.

Multiply and divide within 100.

Work with addition and subtraction equations.

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

Write and interpret numerical expressions.

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

Represent and solve problems involving addition and subtraction.

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

Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

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


correct_option_index: 30