options: Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

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

Understand the relationship between zeros and factors of polynomials.

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

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

Work with addition and subtraction equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

Multiply and divide within 100.

Generate and analyze patterns.

Write and interpret numerical expressions.

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

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Analyze patterns and relationships.

Write expressions in equivalent forms to solve problems.

Solve systems of equations.

Represent and solve equations and inequalities graphically.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

Gain familiarity with factors and multiples.

Represent and solve problems involving multiplication and division.

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

Add and subtract within 20.

Reason about and solve one-variable equations and inequalities.

Solve equations and inequalities in one variable.

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

Use polynomial identities to solve problems.

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

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

Use properties of operations to generate equivalent expressions.
problem_activity: Activity
In the previous activity, students interpreted given tape diagrams and explained how they represented a story. Here, they have a chance to draw tape diagrams to represent a story. The first story is a bit more scaffolded because it specifies what
\(x\)
represents. In the other two stories, students need to decide which quantity to represent with a variable and choose a letter to use. As with all activities in this lesson, students are
not
expected to write and solve an equation. This preliminary work supports the understanding needed to be able to represent such situations with equations.
Digital
Launch
Keep students in the same groups. You might have
each
student draw
all three
diagrams and compare them with their groups, working together to resolve any discrepancies. Or if time is short, you might assign
each
student in the group
a different story—
ask each student to explain their diagram to their group to see if their group members agree with their interpretation.
For classrooms using the digital version of the materials, take a minute to demonstrate how the controls work in the applet. Some students may prefer to draw the diagrams in their notebooks or on scratch paper.
Action and Expression: Internalize Executive Functions.
Provide students with a blank template of a tape diagram to represent each story.
Supports accessibility for: Language; Organization
Student Facing
Here are three more stories. Draw a tape diagram to represent each story. Then describe how you would find any unknown amounts in the stories.
Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts
\(x\)
stickers in each bag. After filling 4 bags, they have used a total of 44 items.
Noah’s family also wants to blow up a total of 60 balloons for the party. Yesterday they blew up 24 balloons. Today they want to split the remaining balloons equally between four family members.
Noah’s family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags.
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
Keep students in the same groups. You might have
each
student draw
all three
diagrams and compare them with their groups, working together to resolve any discrepancies. Or if time is short, you might assign
each
student in the group
a different story—
ask each student to explain their diagram to their group to see if their group members agree with their interpretation.
For classrooms using the digital version of the materials, take a minute to demonstrate how the controls work in the applet. Some students may prefer to draw the diagrams in their notebooks or on scratch paper.
Action and Expression: Internalize Executive Functions.
Provide students with a blank template of a tape diagram to represent each story.
Supports accessibility for: Language; Organization
Student Facing
Here are three more stories. Draw a tape diagram to represent each story. Then describe how you would find any unknown amounts in the stories.
Noah and his sister are making gift bags for a birthday party. Noah puts 3 pencil erasers in each bag. His sister puts
\(x\)
stickers in each bag. After filling 4 bags, they have used a total of 44 items.
Noah’s family also wants to blow up a total of 60 balloons for the party. Yesterday they blew up 24 balloons. Today they want to split the remaining balloons equally between four family members.
Noah’s family bought some fruit bars to put in the gift bags. They bought one box each of four flavors: apple, strawberry, blueberry, and peach. The boxes all had the same number of bars. Noah wanted to taste the flavors and ate one bar from each box. There were 28 bars left for the gift bags.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Design a tiling that uses a repeating pattern consisting of 2 kinds of shapes (e.g., 1 hexagon with 3 triangles forming a triangle). How many times did you repeat the pattern in your picture? How many individual shapes did you use?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
Much of the discussion will take place in groups. Here are some ideas for synthesizing students’ learning about creating tape diagrams:
Ask students if they had any disagreements in their groups and how they resolved them.
Ask students how they decided which unknown quantity to find in the story. The first story specifies
\(x\)
stickers, but the other stories do not define a variable.
Display one diagram for each story and ask students to explain how they are alike and how they are different.


correct_option_index: 29