standard_description: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)
problem_activity: Narrative
The goal of this activity is to multiply numbers with no restrictions on the number of new units composed. Students first multiply a 3-digit number by a 1-digit number and a 3-digit number by a 2-digit number with no ones. They can then put these two results together to find the product of a 3-digit and 2-digit number with many carries. They then solve one more 3-digit and 2-digit example with no scaffold. Because these calculations have new units composed in almost every place value, students will need to locate and use the composed units carefully. It gives students a reason to attend to the features of their calculation and to use language precisely (MP6).
Engagement: Develop Effort and Persistence.
Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Organization, Conceptual Processing
Launch
“You are going to find products with many new composed units. As you work, think carefully about where you place these values.”
Activity
8–10 minutes: independent work time
3–5 minutes: partner discussion
Monitor for students who use the results of the first two calculations to find the third, and for students who correctly compose all the new place values.
Student Facing
Find the value of each product using the standard algorithm.
\(647 \times 9\)
\(647 \times 50\)
\(647 \times 59\)
\(264 \times 38\)
Student Response
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Activity Synthesis
Display the expression:
\(647 \times 59\)
.
“How did you use the first two calculations to help with the third problem?” (They gave me the two partial products for the product
\(647 \times 59\)
, so I just had to add them up.)
Invite students to share their responses for the last product, focusing on the newly composed units.


aligns: no