Balance Beam Algebra

1
Balance Beam Algebra

• Warm-Up
• Informally, share lessons

2
Warm-Up

• Describe the Balance Beam

3
Lesson 3 Objectives

• To investigate the use of manipulatives to teach
  algebra
• Balance Beams
• Pattern Blocks
• (Hands On Equations)
• (Algebra Tiles)

4
Lesson 3 Objectives

• To apply the components of Best Practices to your
  lesson
• Align
• Diagnose
• Differentiate
• Assess
• Summarize

5
ADD

• If 8x 3y 5x 4y, then
• ___ x y?
• Please complete the ADD form.
• Individually, then group discussion.

6
Objectives Balance Beams

• To understand equality as level pans or as a
  balanced beam
• To identify blocks of equivalent weight
• To replace variables with values

7
Objectives

• To understand that adding or subtracting the same
  weights on both sides of a balance will not
  change the heavier/equal/lighter relationship
• To model problem solving situations with objects

8
Warm-Up
9
Which Sentences are True?

• One blue is twice the weight of one red?
• One red is twice the weight of one blue?
• One blue is half the weight of one red?
• One red is half the weight of one blue?

10
Which Equations are True?

• B 2 R
• R 2 B
• ½ B R
• ½ R B

11

• The weights are the same as before.
• Describe the relationship
• What might make the beam balance?

12

• The weights are new.
• What will happen if we put the 3 circles on the
  left and the square on the right?
• What is the relationship between objects?
• Write the relationship algebraically.

13

• This is a new situation.
• What is the relationship between the square
  and the triangle?

14
Summary

• It is very important for children to develop the
  concept of equality.
• They need to see the as an indicator of a
  relationship between two sides

15
Summary

• They need to realize that is NOT an operator
  like the signs
• , -, x, ?
• They need to realize that it does not matter
  which side is on the left and which side is on
  the right

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Manipulatives

• Balance Beams
• Pattern Blocks
• Demonstration
• Hands On Equations
• Algebra Tiles

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Hands on Equations

• Materials
• Blue pawn x
• White pawn x
• Green cubes negative numbers
• Red cubes positive numbers

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Legal Moves

• Zero pair white and blue
• Zero pair red and green of same value
• Add the same to both sides
• Subtract the same from both sides
• Make doubles

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Model each example

• 3x 7 4x
• X 2 2x x 10
• 3x 1 x 13

20
Model each example

• 4x 2x 4 x 10
• 2x 8
• 2(x 3) 10

21
Model each example

• Three times a number plus one is twenty five.
• If 3 is added to twice a number, the result is 17

22
Algebra Tiles

• Demonstration

23
Extension Activity

• Use pattern blocks to solve the algebra problem
  represented by the balance beams pictured on the
  handout.

24
Whats next tonight?

• Exchange lessons in preparation for next session
• Assignment for session 4
• Post Assessment on Lesson 2

25
Exchange Lessons

• Please give a copy of your algebra lesson to 2
  others, who will critique it.
• Please give one copy of your algebra lesson to
  me.

26
Assignment for Session 4

• Bring written critiques of the 2 lessons you just
  received
• Use the best Practices Measure
• Be as specific and helpful as possible
• Study for the Post Assessment for the algebra
  module

27
Post Assessment for Lesson 2

• Please complete the Post Assessment for Lesson 2,
  
• Patterns to Algebra
• Work individually
• Hand in work and receive the answer key
• Leave (quietly) when finished