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In 2nd grade, the focus was to develop foundational understandings of multiplication as equal groups by building and drawing.
In 2nd grade, the focus was to develop foundational understandings of multiplication as equal groups by building and drawing.
In 3rd grade students extend these understandings:
In 3rd grade students extend these understandings:
~ use pictures, arrays, and area models to illustrate multiplication and division
~ use pictures, arrays, and area models to illustrate multiplication and division
~ explore the relationship between multiplication & division
~ explore the relationship between multiplication & division
~ commutative property: 8 x 5 has the same product as 5 x 8
~ commutative property: 8 x 5 has the same product as 5 x 8
~ distributive property: 8 x 5 has the same product as (3 x 5) + (5 x 5)
~ distributive property: 8 x 5 has the same product as (3 x 5) + (5 x 5)
~ facts up to 10 x 10
~ facts up to 10 x 10
Equal Groups
Equal Groups
Array
Array
Area Model
Area Model
As students explore multiplication and division concepts, it is important for them to have a variety of opportunities to build, draw, and make connections. To develop automaticity with facts, students also need to engage in meaningful repeated practice.
Check out this video from Graham Fletcher who outlines the progression of multiplication and division in elementary school.
Try this puzzle...
Try this puzzle...
Consider a collection of pennies with the following constraints:
When the pennies are put in groups of 2 there is one penny left over. When they are put in groups of three, five, and six there is also one penny left over. But when they are put in groups of seven there are no pennies left over. How many pennies could there be?
Watch this short video and consider:
Watch this short video and consider:
What do you notice? What do you wonder?
What is the same? What is different?
Does this work with other numbers?
How could this make solving other problems easier?
Games to Play
Games to Play
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