Unit 6, Lesson 10
Using Algorithms with Partial Products: 2 Two-Digit Numbers
Grade 4
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The purpose of this Warm-up is for students to compare ways to keep track of composing units in addition problems and in multiplication problems in which the partial products have a newly composed unit. While students may notice and wonder many things about these ways of recording, the important discussion point is to invite students to consider whatever way they currently record composing a new unit when they add, and then to use it when they multiply if there’s a need to compose a new unit when they add up the partial products.
This prompt gives students opportunities to look for and make use of structure (MP7) as they attend to ways to record newly composed units when they add partial products.
What do you notice? What do you wonder?
MLR1 Stronger and Clearer Each Time
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In this activity, students analyze multiplication involving 2 two-digit factors. Students make sense of work where the partial products are recorded, but there is no indication of where each product came from. After making sense of work, students use the same strategy of finding and keeping track of partial products to evaluate
This activity uses MLR1 Stronger and Clearer Each Time. Advances: reading, writing
“Find the value of
“Why did Tyler record a small 1 in the thousands place?” (It shows that we composed a new thousand when adding the values in the hundreds place because 15 hundreds is composed of 1 thousand and 5 hundreds.)
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When using an algorithm that uses partial products, students may be inclined to pay attention only to single digits in each number and pay little attention to the value of the digits. For example,
To help students see that the place value of the digits impacts each partial product, consider displaying a diagram that shows partial products alongside the vertical notation.
Decide with your partner who will find each product. Show your thinking. Organize it so it can be followed by others.
Here is Han’s computation of
Show the correct computation for finding the value of
Help us improve by sharing suggestions or reporting issues.
MLR1 Stronger and Clearer Each Time
Tyler uses an algorithm to find the value of
Describe each step in Tyler’s method. How do you think he arrived at the last five numbers? Record your thinking.