standard_description: Interpret multiplication as scaling (resizing), by:
- Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
- Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
problem_activity: Narrative
The purpose of this activity is for students to understand that the standard algorithm for addition can be used with decimals. Students first find the value of a sum of decimals using a strategy that makes sense to them and then see calculations organized using the standard algorithm. They recognize the importance of organizing the calculations and carefully recording any newly composed units.
When students share their explanation of Han's calculations with a partner and revise their work after receiving feedback they critique the reasoning of others and improve their arguments (MP3).
This activity uses
MLR1 Stronger and Clearer Each Time.
Advances: Conversing
Launch
Groups of 2
“Work on the first two problems on your own.”
Activity
5–6 minutes: independent work time
MLR1 Stronger and Clearer Each Time
“Share your description of Han’s work with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.”
3–5 minutes: structured partner discussion.
Repeat with 2–3 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2–3 minutes: independent work time
Student Facing
Find the value of
\(5.61 + 2.53\)
. Explain or show your reasoning.
Han used the standard algorithm to add decimals. This is Han’s work. Describe what Han did in each step.
[IMG]
Use the standard algorithm to find the value of
\(6.62+3.74\)
.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students do not get the correct solution, ask, “What 2 whole numbers will the answer be between?”
Activity Synthesis
“Solve the last problem on your own.”
2–3 minutes: independent work time
“What was helpful about using the standard algorithm?” (It was helpful to line up the numbers and keep track of everything. It was also helpful to add everything in order, step by step.)
“How was the standard algorithm with decimals the same as for whole numbers?” (I add numbers with the same place value and then when I get a new unit, like the 1 here, I write it over the correct place value.)


aligns: no