options: Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve problems involving multiplication and division.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with addition and subtraction equations.

Rewrite rational expressions.

Gain familiarity with factors and multiples.

Use properties of operations to generate equivalent expressions.

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

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

Perform arithmetic operations on polynomials.

Use polynomial identities to solve problems.

Represent and solve problems involving addition and subtraction.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Create equations that describe numbers or relationships

Solve systems of equations.

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

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

Generate and analyze patterns.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

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

Work with radicals and integer exponents.

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

Analyze patterns and relationships.

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

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

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
problem_activity: Activity
In this activity, students continue to develop their understanding of square roots. Students first find the areas of three squares, estimate the side lengths using tracing paper, and then write the exact side lengths. Then they make a table of side-area pairs. They then graph the ordered pairs from the table and use the graph to estimate the values of squares with non-integer side lengths, such as the ones they drew in the previous activity.
Digital
Launch
Arrange students in groups of 2. Provide access to calculators. Remind students about the meaning and use of square root notation. Have students work together on the first problem and check each other’s work. Have them make their graphs independently and then check with their partners that they look the same. Follow with a whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts. Check in with students after the first 2-3 minutes of work time. Check to make sure students have attended to all parts of the original figures.
Supports accessibility for: Organization; Attention
Student Facing
Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact lengths for the sides of each square.
[IMG]
Complete the tables with the missing side lengths and areas.
|       | side length,                               \(s\) |   |   |   |   |   |   |
|-------|--------------------------------------------------|---|---|---|---|---|---|
| row 1 |    area,                               \(a\)     |   |   |   |   |   |   |
|       | side length,                               \(s\) |   |   |   |   |   |   |
|-------|--------------------------------------------------|---|---|---|---|---|---|
| row 1 |    area,                               \(a\)     |   |   |   |   |   |   |
Plot the points,
\((s, a)\)
, on the coordinate plane shown here.
Use this graph to estimate the side lengths of the squares in the first question. How do your estimates from the graph compare to the estimates you made initially using your geometry toolkit?
Use the graph to approximate
\(\sqrt{45}\)
.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Print
Launch
Arrange students in groups of 2. Provide access to calculators. Remind students about the meaning and use of square root notation. Have students work together on the first problem and check each other’s work. Have them make their graphs independently and then check with their partners that they look the same. Follow with a whole-class discussion.
Action and Expression: Internalize Executive Functions.
Chunk this task into more manageable parts. Check in with students after the first 2-3 minutes of work time. Check to make sure students have attended to all parts of the original figures.
Supports accessibility for: Organization; Attention
Student Facing
Find the area of each square and estimate the side lengths using your geometry toolkit. Then write the exact lengths for the sides of each square.
[IMG]
Complete the tables with the missing side lengths and areas.
| side length,                               \(s\) |   |   |   |   |   |   |   |
|--------------------------------------------------|---|---|---|---|---|---|---|
|    area,                               \(a\)     |   |   |   |   |   |   |   |
| side length,                               \(s\) |   |   |   |   |   |   |   |
|--------------------------------------------------|---|---|---|---|---|---|---|
|    area,                               \(a\)     |   |   |   |   |   |   |   |
Plot the points,
\((s, a)\)
, on the coordinate plane shown here.
[IMG]
Use this graph to estimate the side lengths of the squares in the first question. How do your estimates from the graph compare to the estimates you made initially using your geometry toolkit?
Use the graph to approximate
\(\sqrt{45}\)
.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Invite students to share their graphs from the second problem and display the graph for all to see. Ask: “What relationship does the graph display?” (The relationship between the side length and area of a square.) Select 2–3 students to share their answers to the last problem, including how they used the graph to estimate
\(s\)
for the tilted square they drew earlier.
Speaking: MLR8 Discussion Supports.
Use this routine to support whole-class discussion. After a student shares their response to the last problem, ask students to restate and/or revoice what they heard using mathematical language. Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the class. Ask the original speaker if their peer was accurately able to restate their thinking. Call students' attention to any words or phrases that helped to clarify the original statement.
Design Principle(s): Support sense-making


correct_option_index: 28