** Multiplication and Division **

Multiplication and Division is the next step up from addition and subtraction, and should be taught with a graduated spiral approach throughout the elementary school years. Both concepts can and should be introduced together, as early as second grade.

## Multiplication and Division

The topics of Multiplication and Division should be taught in stages – starting with a conceptual understanding of the operations, then learning the multiplication tables in three stages, multi-digital multiplication, division, remainder and regrouping, and finally application to word problems and higher order numbers.

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Grade 2:

- G2S1W10-MW Multiplication and Division
- G2S1W11-MW Multiplication and Division Word Problems
- G2S1W12-MW Multiplication Tables of 2
- G2S1W13-MW Multiplication Tables of 5
- G2S1W14-MW Multiplication Tables of 10
- G2S2W9-MW Multiplication Tables of 3
- G2S2W10-MW Multiplication Tables of 4
- G2S2W11-MW Multiplication Tables of 3 and 4
- G2S2W12-MW Bar Model Multiplication Division
- G2S2W13-MW Bar Model Multiplication Division

Grade 3:

- G3S1W9-MW1 Multiplication Tables of 6
- G3S1W9-MW2 Multiplication Tables of 7
- G3S1W10-MW1 Multiplication Tables of 8
- G3S1W10-MW2 Multiplication Tables of 9
- G3S1W11-MW Division
- G3S1W12-MW Multiplication No Regroup
- G3S1W13-MW Multiplication With Regroup
- G3S1W14-MW Division Quotient and Remainder without Regroup
- G3S1W15-MW Division with Regroup
- G3S1W16-MW Bar Models Multiplication and Division
- G3S1W17-MW Bar Models Division

Grade 4:

- G4S1W5-MW Multiples
- G4S1W6-MW Multiply by a 1-digit Number
- G4S1W7-MW Multiply by a 2-digit Number
- G4S1W8-MW Modeling Division with regroup
- G4S1W9-MW Dividing by a 1-digit Number
- G4S1W10-MW Multiplication Division word problem

Grade 5:

- G5S1W3-MW Whole Number Multiplication
- G5S1W4-MW Whole Number Division
- G5S1W5-MW Whole Number Order of Operations
- G5S1W6-MW Whole Number Word Problems Bar Modeling
- G5S1W13-MW Multiplying Dividing Fraction word problem
- G5S2W3-MW Multiplying Decimals
- G5S2W4-MW Dividing Decimals

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## Teaching Multiplication and Division

Students start to learn about multiplication and division in second grade. Before building up fluency in multiplication tables, students should first understand the concepts of multiplication and division. To this end, we use pictorial representation to help with understanding, e.g.

- Finding the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns, using sequential addition.
- Learn about the complementary task of division where we have a total and we want to break it up into groups. For the same division equation, there can be two different interpretation.
- Understand the difference between odd and even numbers, and that groups with even number of items can be divided into two equal groups.

Once these basic concepts are understood, multiplication tables are introduced in three stages:

- 2, 5 and 10
- 3 and 4
- 6, 7, 8 and 9

Next, we would extend these concepts to multiplying multi-digit numbers and introduce basic division – first without remainder, then with remainder. Also division with regrouping is introduced.

Finally, when students are fluent in the two operations, we would apply them to word problems with the help of bar models. In addition, we would also expand our skills to higher order numbers with more digits and thus more practice with regrouping.

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