Unit 1 exam information

I haven't written the exam yet, so I don't know how long it is, or if it will be in one part or two, but the content you need to study and know is:

Relational thinking:

How to solve an unknown number equation by reasoning about relationships between the numbers on the two sides of the equals sign. Examples:**

• 25 + 18 = ___ + 17
• 25 - 18 = ___ - 17
• 20 × 7 = 10 × ___

Correct use of the equals sign.

• Explain how children often misunderstand the meaning of the equals sign
• Fix this equation to show the same thinking, but using equals signs correctly**
  • 7+7=14+14=28 (solving 7×4)
  • 20+30=50+4=54+3=57 (solving 24+33)

Know how children learn to count.

• How is understanding cardinality different from knowing the counting sequence?
• What are some problem spots when children are learning to count?

Know the CGI problem type organization for problems for addition, subtraction, multiplication and division

• Be able to write a problem of a given problem type
• Be able to identify the problem type of a given problem.
• Note: somewhere on the test, you will be given these grids so you can check your memory of what the vocabulary names are:

Know which addition and subtraction types are more difficult than the others (from a direct modeling standpoint). I will ask you to put in order of difficulty some word problems that have different problem types. The problem types will be ones where the difference in difficulty of the problem type is clear. You may find this summary helpful if you don't have good notes on this.

Direct modeling

Given a word problem that has an associated direct modeling strategy (multiplication, partitive division, measurement division, JRU, SRU, JCU, SCU, CDU)

• Identify the problem type
• Identify the direct modeling strategy that is most closely associated with the problem type
• Describe how a child would use that direct modeling strategy to solve the word problem.

Vocabulary: From a number problem or word problem be able to identify and name the parts of the problem sum, difference, minuend, etc.)

Arrays for multiplication:

• Draw array diagrams
• Explain the commutative law
• Explain the distributive law

Counting and derived fact strategies for basic facts.

• Given an addition, subtraction or multiplication problem be able to identify one or more efficient strategies for computing it, and describe how to use those strategies.
• Given a counting or derived fact strategy, be able to identify basic facts for which that strategy would be efficient or not efficient. Describe how to use the strategy for a math fact that it is an efficient strategy for.
• Strategies you should be prepared to explain are:
  • Addition
    • count on
    • use doubles
    • use 10/make 10
  • Subtraction:
    • count back
    • count up to
    • back down through 10
    • build up through 10
    • use addition
  • Multiplication
    • skip count
    • double (for 2), double twice (for 4)
    • count up from a known fact
    • break down into known facts (distributive law)
  • Division
    • skip count up to
    • use multiplication

Fact families: Write the fact family for an addition, subtraction, multiplication or division problem.

**Answers to example problems

• 25 + 18 = ___ + 17. The unknown number is 26: because 17 is one less than 18, to keep the sum the same, the unknown number must be one more than 25.
• 25 - 18 = ___ - 17. The unknown number is 24: because 17 is one less than 18, to keep the difference the same, the subtrahend must be one less than 25.
• 20 × 7 = 10 × ___. The unknown number is 14: because 10 is half of 20, the other factor must be double 7.

• 7+7=14+14=28 (solving 7×4)
  • 7+7=14
  • 7+7=14--Note: this step could be omitted, but clarifies the process of getting 7×4 using this strategy.
  • 14+14=28
• 20+30=50+4=54+3=57 (solving 24+33)
  • 20+30=50
  • 50+4=54
  • 54+3=57