Sydney Laughlin
Part A:
Standard: 4.OA.A.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement
that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of
multiplicative comparisons as multiplication equations.
Concepts in standard:
1.
2.
3.
4.
5.
6.
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Multiplication facts to 12.
Missing Factors . EX: _ *3=12
Read and write multi-digit whole numbers using base ten numerals.
Use representations to display multiplication:
Array, lattice, grid, groups, repeated addition, number line, and equations.
Multiplication Properties:
Commutative property: When two numbers are multiplied together, the product is the
same regardless of the order of the numbers. EX: 4*2=4*2
Associative: when three or more numbers are multiplies the product is the same
regardless of the grouping of the factors. EX: (2*3)*4=2*(3*4)
Identity: The product of any number and one is that number. EX: 1*2=2
Distributive: The sum of two numbers times a third number is equal to the sum of each
addend times the third number. EX: 4*(6+3) = 4*6+4*3
Materials needed: Plastic math tiles, vocabulary index cards, pencil, paper, interview question
sheet.
Misconceptions of multiplication:
 The student may know the commutative property of multiplication but fails to apply it
to simplify the “work” of multiplication.
 The student knows how to multiply but does not know when to multiply (other than
because he was told to do so, or because the computation was written as a
multiplication problem).
 The student under generalizes the results of multiplication by powers of 10. To find
products like 3 × 50 = 150 or 30 × 50 = 1,500, she must “work the product out” using a
long method of computation.
 The student can state and give examples of properties of multiplication but does not
apply them to simplify computations.
 The student misapplies the procedure for multiplying multidigit numbers by ignoring
place value.
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The student generalizes what she learned about single-digit multiplication and applies it
to multidigit multiplication by multiplying each column as a separate single-digit
multiplication.
Thinking that the operation that needs to be performed (+, –, ×, ÷) is defined by the
numbers in the problem.
Part B: Interview of USIMS Student
Vocabulary: Each one of these key terms will be displayed on an index card. One by one I will ask the
student to explain what each term means in their own words. Each vocabulary word will be introduces
with “In mathematics what does _________ mean?”
Representation-
Multiples-
Comparison-
Equation-
Factors-
Multiplication-
Having introduced the vocabulary to the student I will move onto the computation.
How many ways can you represent a multiplication equation?
Using the tiles provided solve the equation 5x3.
Using the representation given create a word problem for 5X3.
What types of problems can be used by this representation?
What does the 5 represent in the word problem?
What does the 3 represent in the word problem?
How would it affect the story if the numbers 5 and 3 switched places?
How would it affect the answer if the numbers 5 and 3 switched places?
Create a multiplication equation using the numbers 30 and 50.
What do these numbers have in common with the equation 3x5?
Without solving the equation can you tell me the answer?
If a piece of rope is 3 times as thick as a piece of twine, which is thicker the rope or the twine?
How do you know?
What is the statement demonstrating?
Solve the following equation: A 10 foot alligator is how many times larger than a 2 foot alligator.
What type of math problem is this?
What is the problem asking you to find?
How did you complete this problem? Why?