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Getting to know the equality math lesson

This lesson engages students to:

• Understand the meaning of the equal sign and the concept of equivalence
• Explore and use relational (algebraic) thinking by noting the numeric relationships between the two sides of the equal sign rather than adding everything up to determine equivalence

Getting to know the manipulative

DreamBox Learning’s Snap Blocks provide a visual representation of numbers, which students can use to compare the relationship between quantities. They support students to develop efficient computation strategies and provide an important foundation for early algebra. There are four different levels of Snap Blocks:

• Level 1, using numbers 1-20
  One expression is always 10 + 10; the other expression is 2 pairs of addends that make 9, 10, or 11 (displayed as pairs)
• Example of a true equation: 10 + 10 = 4 + 6 + 2 + 8
• Example of a false equation: 5 + 6 + 2 + 8 = 10 + 10
• Level 2, using numbers 1-20
  One expression is always 10 + 10; the other expression is 2 pairs of addends that make 9, 10, or 11 (displayed in a random order)
• Example of a true equation: 4 + 8 + 6 + 2 = 10 + 10
• Example of a false equation: 10 + 10 = 4 + 4 + 5 + 6
• Level 3, using numbers 1-20
  Expressions have at least one common addend
• Example of a true equation: 8 + 2 + 5 = 2 + 6 + 7
• Example of a false equation: 6 + 8 + 4 = 3 + 8 + 5
• Level 4, using numbers 1-20
  Expressions have at least one common addend
• Example of a true equation: 4 + 5 + N = 8 + 1 + N
• Example of a false equation: 4 + 9 + N = 10 + 1 + N
• Level 1, using numbers 5-100
  One expression is always 50 + 50; the other expression is 2 pairs of addends that make 45, 50, or 55 (displayed as pairs)
• Example of a true equation: 50 + 50 = 20 + 30 + 10 + 40
• Example of a false equation: 25 + 30 + 10 + 40 = 50 + 50
• Level 2, using numbers 5-100
  One expression is always 10 + 10; the other expression is 2 pairs of addends that make 9, 10, or 11 (displayed in a random order)
• Example of a true equation: 20 + 40 + 30 + 10 = 50 + 50
• Example of a false equation: 50 + 50 = 20 + 20 + 25 + 30
• Level 3, using numbers 5-100
  Expressions have at least one common addend
• Example of a true equation: 40 + 10 + 25 = 10 + 30 + 35
• Example of a false equation: 30 + 40 + 20 = 15 + 40 + 25
• Level 4, using numbers 5-100
  Expressions have at least one common addend
• Example of a true equation: 20 + 25 + N = 40 + 10 + N
• Example of a false equation: 20 + N + 45 = 50 + 5 + N

Professional development ideas

• Introduce or review the terms “true” and “false” as used when evaluating mathematical statements.
• Encourage all students to participate by using hand signals or individual white boards to indicate their response of “true” or “false”.
• Identify parts of each expression that are equivalent. This can be checked or represented by placing the Snap Blocks on the holder.
• Questions to ask students/topics for discussion:
  • How did you decide this equation was true/false?
  • Some students might suggest that all of the equations are false because “there are too many numbers after the equal sign.” This is a great opportunity to discuss the meaning of equivalence.
• Have students work in teams to solve the problem. Call on teams to show unique ways they solved the problem by placing the blocks.
• Challenge students to solve the problem by placing a limited number of blocks. Which blocks are most helpful and why?