options: Understand solving equations as a process of reasoning and explain the reasoning.

Solve systems of equations.

Multiply and divide within 100.

Work with equal groups of objects to gain foundations for multiplication.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving addition and subtraction.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Gain familiarity with factors and multiples.

Understand the relationship between zeros and factors of polynomials.

Interpret the structure of expressions.

Analyze patterns and relationships.

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Understand properties of multiplication and the relationship between multiplication and division.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand and apply properties of operations and the relationship between addition and subtraction.

Write expressions in equivalent forms to solve problems.

Use polynomial identities to solve problems.

Use properties of operations to generate equivalent expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.

Generate and analyze patterns.

Rewrite rational expressions.

Work with radicals and integer exponents.

Understand the connections between proportional relationships, lines, and linear equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Represent and solve problems involving multiplication and division.
problem_activity: Narrative
The purpose of this activity is for students to find the value of quotients where the divisor is less than 1 and where the dividend is large enough that drawing a complete diagram is cumbersome. Instead, students are encouraged to use a diagram to find
how many divisor sized groups are in 1 whole and then multiply the dividend by that number to find the value of the quotient. When students use the value of
\(1 \div 0.2\)
and multiplication to find the value of
\(12 \div 0.2\)
they are using regularity in reasoning (MP8).
This activity uses
MLR1 Stronger and Clearer Each Time.
Advances: Conversing.
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, for finding the value of the expression. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Copy
Small Grids
Launch
Groups of 2
Give students access to blackline masters with hundredths grids.
Activity
3–5 minutes: independent work time
Monitor for students who use the following strategies for problem 1:
reason about how many divisor-sized groups are in 1 whole, possibly with a diagram, and then multiply by the dividend
use multiplication equations to find the value of the division expressions
Student Facing
Find the value of the expression. Use a diagram if it is helpful.
\(12 \div 0.2\)
[IMG]
This is the diagram and explanation Tyler used to justify why
\(12 \div 0.2 = 60\)
.
[IMG]
[IMG]
Explain how the expression
\(12 \times (1 \div 0.2)\)
relates to Tyler's reasoning.
Find the value of each expression.
\(14 \div 0.5\)
\(5 \div 0.25\)
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
If a student is not sure how to explain Tyler’s reasoning in problem 2, ask them to read the expression to you and record the words they use. Then ask them how those words relate to the words Tyler used.
Activity Synthesis
Ask previously identified students to share their solutions and strategies for evaluating the expression in the first problem.
“How was multiplication useful to find the value of the expression in the first problem?” (I didn't have to draw 12 wholes because I knew there were five 0.2s in each one so that would be
\(12 \times 5\)
total.)
MLR1 Stronger and Clearer Each Time
“Share your response to problem 2 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 different partners.
“Revise your initial draft based on the feedback you got from your partners.”
2-3 minutes: independent work time


correct_option_index: 30