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Fifth Grade CurriculumEquations and Expressions

Table of ContentsTopic Page

Balancing Equations

Balancing Expressions

Part IExample 1Example 2Example 3Example 4Example 5Balancing Expressions – Balance MeWriting Equations with a Variable

1 – 23 – 44 – 56 – 77 – 8

910 - 11

Property of Cy-Fair ISD Elem. Math Dept. (5th Grade) 2014 – 2015

Part I

TEKS: 5.4 The student applies mathematical process standards to develop concepts of expressions and equations. Materials: SmartBoard, IMN to be used as a recording sheet, dry erase markers and page protectors

Vocabulary: variable, algebraic expression, unknown, balance variable- a symbol, usually a letter, that can stand for a quantity that

changes or an unknown quantity. The meaning of variable can be interpreted in many ways.

expression-a combination of numbers, symbols, and operations that represent a value. It does not have an equal sign. Expressions may have grouping symbols.

Background: Earlier in the year students were introduced to writing algebraic equations during the first unit on Representing Rules, Patterns and Relationships. Lesson goals:

The values on both sides of an equation are the same. A letter can be used to represent a variable (unknown quantity). This

will be seen as a lower case letter and it will be italicized. Provide students with additional opportunities to simplify expressions

Use the SmartBoard to go through the lesson.Slide 2Begin the lesson by showing the students the video on this slide as a hook. Discuss what students see and notice about the video. Students will be asked to write a journal entry after slide 7, relating a teeter totter/ see saw to balancing equations.Slide 3

Example 1In this part, students will use a model of a balance to represent equations and understand what it means for an equation to be “balanced”. Begin the lesson by showing students objects on a balance on the Smartboard.

Property of Cy-Fair ISD Elem. Math Dept. (5th Grade) 2014 – 2015 1

Discuss with students that when a balance has objects with the same weight that the balance will be horizontal. If the weight is heavier on one side, the balance will tip to that side. In math, we are going to use a balance to represent equal values.

Write an equation with the students to represent the picture.

How many pentagons do we have on the left side of the balance? 3Label 3 below the left side of the balance on the SB.

How many pentagons do we have on the right side of the balance? 3Label 3 below the right side of the balance on the SB.

What do you notice about the two sides? There are the same number of pentagons on both sides. There is an equivalent amount.

How can we represent this? With an equal sign

Label the SB with an equal sign (below the fulcrum).

Read the equation with your students. Three equals three.

Slide 4


3 = 3

Example 2

This next slide introduces writing an equation with a variable.

What are we trying to find? The number of smiley faces needed to balance the scale.

What do we know? There are 6 smiley face on the left side of the scale and there is one smiley face on the right of the scale.

How could we determine the number of smiley faces we need to add to the right side? Count on to one until we get to 6; subtract 1 from 6

Let’s represent this as an equation using a box to represent the unknown.

6 = 1 + Read the equation with your students. Six is equal to 1 plus a number.

Review with students that earlier in the year they learned that an unknown quantity can be represented with a letter. The unknown is also referred to as a variable. Ask students to select a letter to represent the variable unknown quantity (maybe an s to represent smiley faces). Rewrite the equation with the variable underneath the previous equation. Then, write the equation with the value for s.


?

?

?

6 = 1 +

6 = 1 + s

6 = 1 + 5

s = 5

Slide 5

Example 3

This slide will have the following balance on it.

What are we trying to find? The weight of 1 block.

What do we know? 4 blocks on the left side of the scale and there is one on cylinder that weighs 20 grams on the right of the scale.

How could we determine the weight of 1 block? Since all of the blocks weigh the same amount, we could multiply 4 by a number to equal 20 grams.

Write the equation on the SB

4 x = 20


?

20 g

?

?

Read the equation with your students. Four times a number is equal to 20.

Select a letter to represent the unknown in the equation. Rewrite the equation replacing the box with a letter to represent the unknown.(maybe a b to represent 1 block). Rewrite the equation with the variable underneath the previous equation. Then, write the equation with the value for b.

4 x = 20

4 x b = 20

4 x 5 = 20

b = 5

Slide 6

Example 4

This slide will have the following balance on it. We will use the information we learned in the previous slide to solve this problem. Review with students that each block weighs 5 grams.


?

20 g

?

What are we trying to find? The weight of 1 brown cylinder.

What do we know? There are 3 blocks on the left side of the scale and each one weighs 5 grams (Label each block with a 5). There is a brown cylinder on the right side of the scale. The brown cylinder’s weight is equal to the weight of the 3 blocks.

How could we determine the weight of the cylinder? Since each block weighs 5 grams, we could multiply 3 and 5 to find out how much the 3 blocks weigh. This is equal to the weight of the brown cylinder. Write the equation on the SB

3 x 5 =

Read the equation with your students. Three times five is equal to a number.

Select a letter to represent the variable in the equation. Rewrite the equation replacing the box with a letter to represent the unknown.(maybe the letter c to represent the weight of the brown cylinder). Rewrite the expression with the variable underneath the previous equation. Then write the equation with the value for c.

3 x 5 = 3 x 5 = c


?55

5

?55 5

?

3 x 5 = 15 c = 15

Slide 7

Example 5

This slide will have the following balance on it. We will use the information we learned in the previous slide to solve this problem. Review with students what you have learned so far. Each block weighs 5 grams, each brown cylinder weighs 15 grams (it’s not on the slide) and each green cylinder weighs 20 grams.

What are we trying to find? The weight of the red cube.

What do we know? There are 6 blocks on the left side of the scale and each one weighs 5 grams (Label each block with a 5). Count and label 30 below the blocks. There is a green cylinder on the right side of the scale. We know that the green cylinder weighs 20 grams. Label the green cylinder with 20. Label 20 below the cylinder. The weight of the 6 blocks is equal to the weight of the red cube and the green cylinder. Place an equal sign between the left side and the right side (below the fulcrum). Place a box below the variable (unknown)


5

5

5

5

5 520

?

?

30 = + 20?

Read the equation with the students. Thirty equals a number plus twenty.

Select a letter to represent the variable in the equation. Rewrite the equation, replacing the box with a letter to represent the variable.(maybe an r to represent the weight of the red cube). Rewrite the equation with the variable underneath the previous equation. Then, write the equation with the value for r.

Slides 8 – 9

Balance Me

The concept of balancing is now going to be applied to simplifying expressions. One side of the balance will have an expression written on it. Simplify the expression on the balance with the students. Simplify the expressions in the shapes below the balance and drag the appropriate expression to the empty side of the balance. This will indicate that both expressions simplify to the same value. If an incorrect shape is selected, it will bounce back.


30 = + 20 30 = r + 20 30 = 10 + 20 r = 10

?

Partner/Group Work

Copy 1 set of expressions per group in your class. Place each expression in a page protector. Students will show their work as they simplify each expression on the page protectors using dry erase markers. Once simplified, students will match the expressions that have the same value.We have included 2 different sets.MATH_5_A_EXPRESSION CONNECTION SET 1 2014_RES.docxMATH_5_A_EXPRESSION CONNECTION SET 2 2014_RES.docx

Slide 10

IMN Idea: Ask students to reflect on the teeter totter/ see saw video from the beginning of the lesson. Ask students to make a journal entry on the following question.

How is balancing an equation like a teeter totter/see saw?

Slide 11

Expression Builder


Model writing an expression with a variable. Select, click and drag the numbers and mathematical symbols to build an expression to match each phrase.

Slide 12

Model writing an equation with a variable.

A medium size coffee is 12 fluid ounces. A medium coffee is 4 fluid ounces less than a large coffee. Write an equation to determine l, the number of fluid ounces in a large coffee.

Begin by recording the main idea and complete the model drawing process.


Write equation l fl oz in large cup

large

medium12

4

b - 12

l ?

How can this be written as an equation? l = 4 + 12 l – 4 = 12l = 12 + 4 12 = l – 4

The How/Justify will be determined by the equation that the students write.Slide 13

Model writing an equation with a variable.

Julissa drove 351 miles to visit her grandmother. She drove 45 miles each hour. Write an equation to determine h, the number of hours she drove. Begin by recording the main idea and complete the model drawing process.

How can this be written as an equation? h = 351 ÷ 45 351 = 45 • h45 h = 351 h (45) = 351351 = h x 45

The How/Justify will be determined by the equation that the students write.Independent PracticeStudents will complete MATH_5_A_WRITING EQUATIONS AND EXPRESSIONS IP 2014_RES.docx


Write equation h miles drove per hour

454-step process 351

h1 h2 … h?

45 45 45J miles

Part IISlides 15 – 18Use student copy from MATH_A_5_MULTI STEP EXAMPLE PROBLEMS 1-4 2014_RES.docx

Examples 1 – 4It is suggested that you model problem #4 first.ResourcesMATH_5_A_MULTI STEP CIRCUIT 2014_RES.docxMATH_5_A_MULTI STEP CIRCUIT RECORDING SHEET 2014_RES.docxMATH_5_A_MULTIPLE SOLUTIONS2014_RES.docxMATH_5_A_MULTISTEP PROCESS MATCHING CARD ACTIVITY2014_RES.docxMATH_5_A_MULTISTEP PROCESS MATCHING CARD ACTIVITY2014_RES.docx


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