standard_description: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
problem_activity: Narrative
The purpose of this activity is for students to analyze a common error when using the standard algorithm to subtract decimals. This activity is recommended if students need additional practice with the standard algorithm when the two numbers do not have the same number of decimal places. The standard addition algorithm requires students to subtract digits with the same place value. In the given example the two numbers are “right aligned” as when subtracting whole numbers and this leads to the error of subtracting hundredths from tenths, tenths from ones, and so on as if these digits had the same place value.
When students identify and correct Elena's error they construct viable arguments and critique the reasoning of others (MP3).
This activity uses
MLR3 Clarify, Critique, and Correct
. Advances: Reading, Writing, Representing.
Launch
Groups of 2
Activity
1–2 minutes: quiet think time
6–8 minutes: partner work time
MLR3 Clarify, Critique, Correct
Display Elena’s solution and explanation.
Read the explanation aloud.
“What do you think Elena means? Is anything unclear?” (She says the answer will be less than 622.3, but she doesn’t say how much less. The answer will be a lot less than 615.21.)
“With your partner, work together to write a revised solution and explanation.”
(Optional) Display and review the following criteria:
Explanation of mistakes
Specific words and phrases
Decimal point
Place value
Labeled diagram
Correct solution
3–5 minutes: partner work time
Select 1–2 groups to share their revised explanation with the class.
“What is the same and different about the revised solutions and explanations?”
Student Facing
Find the value of
\(622.35 - 71.4\)
. Explain or show your reasoning.
Elena and Andre found the value of
\(622.35 - 71.4\)
. Who do you agree with? Explain or show your reasoning.
[IMG]
Student Response
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Advancing Student Thinking
If a student does not have a strategy to solve problem 1, ask them to explain how they would find the value of
\(622 - 51\)
.
Activity Synthesis
Display Andre’s solution and explanation.
“Why do you think Andre wrote 71.40 instead of 72.4?” (It helps him keep the place values and decimals in line so he doesn’t mix up the places when he is subtracting. 71.40 is equivalent to 71.4.)
Display Elena’s solution.
“How can you see without finding the difference that Elena’s answer is not correct?” (Taking 71 away from 622 is a lot less than 615.
\(620-70=550\)
so the answer should be around 550.)


aligns: no