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Unit 6

Tess Baze

Created on February 10, 2026

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Expressions and Equations

Unit 6 | 6th Grade Math

index

Lesson 5
Lesson 4
Lesson 3
Lesson 8
Lesson 7
Lesson 6 & Quiz
Lesson 12

12

Lesson 13

13

Lessons 9 & 10
Lesson 15 & Quiz

15

Lesson 14

14

Lesson 16

16

Lesson 19

19

Lesson 17

17

Vocab

Vocab

Dependent Variable

Equivalent Expressions

Independent Variable

Solution

Term

Coefficient

Variable

Back to Index

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

Variable

A variable is a letter that represents a number. Different numbers can be chosen for the value of the variable. In the expression 10-X, the variable is X.

Solution to an Equation

A solution to an equation is a number that can be used in place of the variable to make the equation true.

Coefficient

A coefficient is a number that is multiplied by a variable. In the expression 3X x 5, the coefficient of X is 3.

Lesson 3

For each diagram, make:

1. One statement that must be true
2. One statement that cannot possibly be true

Lesson 3

Match each expression with a diagram by replacing "?" with w, x, or y.

6 = ? + 1

3 x ? = 6

? + 3 = 6

Lesson 3

For each diagram:

1. Write an equation to represent the relationship between the weights.
2. Explain how to reason with the diagram or the equation to find the value of the variable

Cool-Down

Make sure your name is on your paper before you turn it in.

Staying in Balance

Learning Targets: I will be able to solve addition and multiplication equations with one variable. Success Criteria: I can solve equations by doing the same to each side.

Lesson 4

Cool-Down

Make sure your name is on your paper before you turn it in.

Represent Situations with Equations

Learning Targets: I will be able to use equations to represent and solve real-world problems. Success Criteria: I can explain how an equation with a variable represents a real-world problem. I can use equations with variables to solve real-world problems.

Lesson 5

Jada reads 25 pages of a book every day. After several days, she has read the entire book.

What information do we need to be able to better understand the problem?

Lesson 5

Jada reads 25 pages of a book every day. After several days, she has read the entire book. 25n = 200

If this equation represents the situation, what might the variable represent?

Lesson 5

For each situation, find one equation that represents it. Some of the equations will go unused.

x = 20 + 5
5x = 20
x + 5 = 20
5 ⋅ 20 = x
20x = 5
x + 20 = 5

1. After Elena rode her bike for 5 miles on Friday, she had biked a total of 20 miles forthe week. She biked x miles before Friday.

2. Andre’s school has 20 clubs, which is five times as many clubs as his cousin’s school has. His cousin’s school has x clubs.

3. Jada volunteers at the animal shelter. She divides 5 cups of cat food equally to feed 20 cats. Each cat receives x cups of food.

Lesson 5

Select all of the equations that describe each situation. Then find the solution for those equations and tell what it means in the situation.

3. Han is charging a school tablet with a new charging cable, which is 2 5/6 feet longer than the old cable. The new cable is 6 feet long. How long is the old cable? x = ?

2. Clare learned that on a sunny day, one solar panel produces 1.5 kilowatt hours (kWh) of electricity. That’s enough electricity to charge a smartphone 100 times! How many kWh of electricity is used to charge a smartphone one time? p = ?

1. Kiran scores 223 fewer points in a computer game than Mai. Mai scores 409 points. How many points does Kiran score? z = ?

x + 2 5/6 = 6
x = 6 + 2 5/6
x - 6 = 2 5/6
6 - 2 5/6 = x
223 = 409 - z
409 - 223 = z
409 + 223 = z
409 = 223 + z
1.5p = 100
1.5 = 100p
p = 1.5 ⋅ 100
1.5 ÷ 100 = p

Cool-Down

Make sure your name is on your paper before you turn it in.

Percentages and Equations

Learning Target: I can use equations to find percentages. Success Criteria: I can solve percent problems by writing and solving equations.

Lesson 6

Percentages as Decimals

All percentages can be converted into decimals easily by thinking of them as a fraction. Every percentage can be written over 100 (30% = 30/100, 4% = 4/100), and once we know that, we can quickly convert them into decimals. 30% = 30/100 = 0.3 4% = 4/100 = 0.04 79% = 79/100 = 0.79

Lesson 6

6% of x is 120.

For these kinds of problems, we first have to write the equation.

6% • x = 120

Once we have the equation, we can then move into solving for the variable.

9 & 10

The Distributive Property

Learning Targets: I will be able to use the distributive property to describe expressions. Success Criteria: I can use a diagram of a rectangle split into two smaller rectangles to write different expressions representing its area. I can use the distributive property to explain how two expressions with numbers are equivalent.

Equivalent Expressions

Equivalent expressions are always equal to each other. If the expressions have variables, they are equal whenever the same value is used for the variable in each expression.

Term

A term is a part of an expression. It can be a single number, a variable, or a number and a variable that are multiplied together. 7, y, and 9a are examples of terms. The expression 5x+3 has 2 terms: 5x and 3.

Lessons 9 & 10

Writing Equations

1. A plant measured x inches tall last week and 8 inches tall this week. 2. Each tree needs 1.2 liters of water. Write an expression that represents the amount of water needed for n trees.

Lessons 9 & 10

Select all the expressions that represent the area of the large, outer rectangle in Figure A.

Lessons 9 & 10

Select all the expressions that represent the area of the large, outer rectangle in Figure B.

Lessons 9 & 10

Select all the expressions that represent the area of the large, outer rectangle.

Lessons 9 & 10

Select all the expressions that represent the area of the large, outer rectangle.

Lessons 9 & 10

The Distributive Property

1) 2 ( 7 + 4 ) 2) 6 ( 9 + 2 ) 3) 9 ( 9 + 5 ) 4) 4 ( 6 + 3 ) 5) 2 ( 6 + 2 ) 6) 6 ( 2 + 7 ) 7) 4 ( 5 + 5 ) 8) 5 ( 4 + 7 )

Lessons 9 & 10

The Distributive Property

1) 2 ( 4 + 9w ) 2) 2 ( 3v + 4 ) 3) 4 ( 6z + 4 ) 4) 9 ( 9k + 9 ) 5) 2 ( 5d + 1 ) 6) 8 ( 2 + 9v ) 7) 4 ( 5f + 8 ) 8) 9 ( 8 + 5t )

9 & 10

Cool-Down

Make sure your name is on your paper before you turn it in.

12

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

13

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

14

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

15

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

16

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

17

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

19

Staying in Balance

Learning Targets: I can compare the process of removing or grouping weights to keep a hanger diagram balanced and the process of subtracting or dividing numbers to solve an equation. I can explain what a balanced hanger diagram and a true equation have in common. Success Criteria: I can write equations that could represent the weights on a balanced hanger diagram.

summary

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relevant data

90%

of the information we assimilate is received through sight. Tell stories with graphs!
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Timeline

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1990

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90%

To highlight super relevant info. 90% of the information we assimilate is received through sight.

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TablE + text

Visual content is a transversal, universal language, like music. We can understand images from millions of years ago, even from other cultures.

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List / Process

We are visual beings.

Social beings.

Narrative beings

We teach through stories. They entertain us and help hold our attention.
We need to interact with one another. We learn in a collaborative way
We can understand images from millions of years ago, even from other cultures.

List / Process

Interactive visual communication, step by step:

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Insert an awesome video for your presentation.

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Calmly and concisely. Summarize the content.

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Tip: Interactivity is the key to capturing the interest and attention of your class. A genially is interactive because your students explore and engage with it.

In Genially you’ll find more than 1,000 templates that are all ready for you to enter your content and customize, and that are super handy for your classes?

¿Sabías que...Retenemos un 42% más de información cuando el contenido se mueve? Es quizá el recurso más efectivo para captar la atención de tu alumnado.

Did you know? 90% of the information we assimilate is received through sight? Visual resources are a huge help for reinforcing your materials: images, illustrations, gifs, videos ... Not only because they stay in our memories, but because they’re more attractive and easier to understand.

Truquito: La interactividad es la pieza clave para captar el interés y la atención de tus estudiantes. Un genially es interactivo porque tu alumnado explora yse relaciona con él.

¡Ojo! En Genially utilizamos AI (Awesome Interactivity) en todos nuestros diseños, para que subas de nivel con interactividad y conviertas tus clases en algo que aporta valor y engancha.

In Genially you’ll find more than 1,000 templates that are all ready for you to enter your content and customize, and that are super handy for your classes?

The important thing is that everything fits the theme.

Did you know?...In Genially you’ll find more than 1,000 templates that are all ready for you to enter your content and customize, and that are super handy for your classes?

Tip: Interactivity is the key to capturing the interest and attention of your class. A genially is interactive because your students explore and engage with it.

Emotional connection or engagement with your class increases when they identify with the message you want to communicate.

Emotional connection or engagement with your class increases when they identify with the message you want to communicate.

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Plantea una pregunta o problema que haga pensar a la clase; Es el ingrediente esencial para mantener su atención. Se suele plantear al inicio del tema para fomentar su pensamiento crítico y participación.

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