Multiplication strategies

Multiplication strategies

In this lesson, we will learn:

  • Understanding multiplication using arrays
  • Representing a product as either: (1) a smaller product and a sum, or (2) a bigger product and a difference
  • Tips and tricks for memorizing the 9 × multiplication table facts

Notes:

  • Multiplication is just repeated addition
Multiplication Strategies
  • Multiplication facts can be shown in an array model with circles/dots
    • Using the array model, it shows that multiplication facts can be broken into groups of smaller multiplication facts:
Subtraction Strategies
    • Using the same array model, we can find the next multiplication fact by adding another row:
Subtraction Strategies
  • Therefore, a product can be found as a smaller product and a sum
Subtraction Strategies
    • Or, it could be found as a bigger product and a difference
Subtraction Strategies
  • The 9 × multiplication tables can be memorized using your fingers!
    • Notice that the first ten multiples of 9 are mirrored after the 5-digit in 45
    • Ex. 9, 18, 27, 36, 45 \parallel 54, 63, 72, 81, 90

Lessons

  • Introduction
    Introduction to Multiplication Strategies:
    a)
    Using addition and arrays to understand multiplication

    b)
    Breaking down multiplication facts into smaller groupsr

    c)
    A product can be found using a smaller product and a sum

    d)
    A product can be found using a bigger product and a difference

    e)
    Patterns to know for memorizing multiples of 9

    f)
    Finger method of 9 times tables


  • 1.
    Understanding products using smaller products
    Turn the product into the sum of two smaller group products.
    a)
    8 × 4 = (5 × 4) + ( __ × 4)
    \qquad \qquad = _____ + _____
    \qquad \qquad = _______

    b)
    12 × 12 = (10 × 12) + ( __ × 12)
    \qquad \qquad = _______ + _______
    \qquad \qquad = _______

    c)
    20 × 35 = (10 × 35) + ( __ × 35)
    \qquad \qquad = _______ + _______
    \qquad \qquad = _______


  • 2.
    Describing multiplication array models - 1
    Fill in the blanks to describe:
    1. the product shown in the array and
    2. the sum written with the smaller product
    a)

    Multiplication Strategies

    b)

    Multiplication Strategies


  • 3.
    Describing multiplication array models - 2
    Fill in the blanks to turn the product into a smaller product and sum.
    Use an array model to help fill in the blanks.
    a)
    5 × 3 = ( __ × 3) + 3
    \qquad \qquad = _______ + 3
    \qquad \qquad = _______

    b)
    11 × 12 = ( __ × 12) + __
    \qquad \qquad = _______ + ____
    \qquad \qquad = _______


  • 4.
    Multiplication and array models with subtraction
    Fill in the blanks to turn the product into a bigger product and a difference.
    a)
    9 × 6 = ( __ × 6) - 6
    \qquad \qquad = _______ + ____
    \qquad \qquad = _______

    b)
    9 × 27 = ( __ × 27) - 27
    \qquad \qquad = _______ - ____
    \qquad \qquad = _______


  • 5.
    Relating multiplication and addition concepts
    Find the answer using the given product.
    a)
    If 6 × 86 = 516 , what is 7 × 86 = ?

    b)
    If 10 × 53 = 530 , what is 9 × 53 = ?


  • 6.
    Multiplication with 9-times tables strategy: word problems
    Use the finger method for 9-times tables to solve.
    a)
    If you put down the fourth finger, what is the 9-times tables multiplication sentence that is represented?

    b)
    If you put down the fourth finger, it represents a 9-times table fact. What finger do you need to put down for the opposite answer (when the answer's digits are flipped/mirrored)? Write the multiplication sentence for the 9-times table fact with the opposite answer