Topic: Early multiplication and fact automaticity
In this unit, the context of preparing a turkey dinner highlights students' multiplication strategies, and supports automatizing the facts, using the ratio table, and developing the distributive property with large numbers. Strings of related problems guide learners toward computational fluency with whole-number multiplication and build automaticity with multiplication facts by focusing on relationships. The big ideas in this unit include utilizing the distributive property of multiplication over addition and over subtraction, utilizing the commutative property of multiplication, recognizing the place value patterns that occur when multiplying by the base, and proportional reasoning. Strategies that are used include using partial products, using ten-times, using a t-chart or ratio table build understanding around doubling and halving.
Partial Products Use a fact you know to make another. For example, 5 packages of paper towels (4 rolls in each package) contains 20 rolls, and 3 packages contain 12, then 8 packages contain 32.
Five-times and Ten-times Once students begin to make use of partial products, this strategy becomes helpful. Knowing the ten times can be helpful for nine times (just subtract one group from the ten-times). 6 ten-times is 60, take away one group of 6 is 54 ( 6 nine-times). The same goes for five-times to help with four-times and six-times.
Doubling and halving As student’s multiplicative reasoning becomes stronger, the develop the ability to group more efficiently. They begin to realize that if they double the number of groups and want the total to be the same, they need to have halve the amount in each group.
4 x 6 = 8 x 3
Ratio Table
Number of Pounds Cost
1 - $ 1.25
2 - $ 2.50
4 - $ 5.00