standard_description: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
problem_activity: Narrative
The purpose of this activity is for students to find quotients of a whole number by tenths or hundredths. This activity focuses on divisors of 0.2 and 0.02 to build on students' previous work dividing by 0.1 and 0.01. The strategies, diagrams and place value reasoning used in the previous lessons still apply. Students may also think about the problems using multiplication. For example
\(1 \div 0.2 = 5\)
because
\(5 \times 0.2 = 1\)
.
Required Materials
Materials to Copy
Small Grids
Launch
Groups of 2
Give students access to blackline masters with grids.
Activity
1–2 minutes: quiet think time
8–10 minutes: partner work time
Monitor for students who represent their reasoning with:
diagrams
expressions or words using multiplication
Student Facing
Find the value of each expression. Explain or show your reasoning.
\(1 \div 0.2\)
\(2 \div 0.2\)
\(3 \div 0.2\)
\(4 \div 0.2\)
Find the value of each expression. Explain or show your reasoning.
\(1 \div 0.02\)
\(2 \div 0.02\)
\(3 \div 0.02\)
\(4 \div 0.02\)
What patterns do you notice?
Student Response
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Advancing Student Thinking
If a student is not able to use the value of the first expression in each set to find the value of the later expressions, ask them to describe what they notice and wonder about each set of expressions. Use numbers and symbols when possible to record the relationships they describe.
Activity Synthesis
Ask selected students to share the representations listed above.
“How are the representations the same? How are they different?” (They both figured out how many tenths or hundredths are in one whole. Then they multiplied that by the number of wholes. One of them used a picture and one of them reasoned about the size of tenths and hundredths to find how many 0.2's and 0.02's are in one whole.)
Display a student's completed work showing the values of the quotients.
“What patterns do you see across the sets of equations?” (The quotients with a divisor of 0.01 are 10 times larger than those with a divisor of 0.1. The quotients with a divisor of 0.1 are a tenth of the value of those with a divisor of 0.01.)
Record the patterns as students describe them.


aligns: no