Multiplication and Division Fluency Continuum: Grades 3 and 4
Grade 3Trimester 1 / Grade 3
Trimester 2 / Grade 3
Trimester 2, continued / Grade 3
Trimester 2, continued / Grade 3
Trimester 3 / Grade 4
Trimester 1, 2, & 3
CCSSM
Expectations / Demonstrate fluency with single-digit addition and subtraction problems. / 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. Developing strategies for products with factors of 2 and 4. / 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. Developing strategies for products with factors of 5 and 10, 1 and 0. / 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. Developing strategies for selected products with factors of 3 and 6. / 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. Practicing strategies for remaining combinations and learned combinations. / Monitoring retention of multiplication combinations and fluency with division facts.
Visual Models:
These visual models highlight a progression of models used for multiplication.
Note:
The multiplication combinations (2s, 3s, 4s, etc.) can be used with any visual model / *See Computational Fluency Continuum: Grades K, 1, & 2 / Equal Group Model
3 x 4, draw three equal groups of 4 objects each
3 x 4 = __
4 x 3, draw four equal groups of 3 objects each
4 x 3 = __
/ See previous model
Two Interpretations of Division
How many in each group?
If 12 apples are shared equally between three friends, how many apples will each friend get?
12 3 = __
4 apples for each friend
How many groups?
Apples are packed in bags of 3. How many bags can Jen make with 12 apples?
12 3 = __
4 bags / See previous models
Array Model
Three rows with four squares in each row.
3 x 4 = __
Number Line
Three jumps of four.
3 x 4 = __
/ See previous models
Tape Diagram
Three parts of size four.
3 x 4 = __
Area Model
Say, “Three by four.” Visualize, three rows with four squares in each row.
3 x 4 = __ / See previous models
Tape Diagrams for Multiplicative Compare
A squirrel can jump 4 feet. A deer jumps three times as far as a squirrel can jump. How far can the deer jump?
3 x 4 = __
Fluency Development
Fluency means being accurate, fast, and flexible in using strategies, patterns, or knowing the combinations (within 3-5 seconds). / It is expected that students learned these combinations in Grade 2; however some third-grade students may need some additional work on some combinations, and all students will benefit from review and practice of these combinations. / Strategies:
Doubles: 2 x 3, think
2 groups of 3 makes 6
or two rows of three make 6.
Double the 2 combination:
4 x 3, reason, “If 2 groups of 3 make 6 then 4 groups of 3 would double this and make 12.”
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Fluency with related missing factor problems, for example, for 6 ÷ 2 think 2 x = 6. / Strategies:
Skip Count 5’s or 10’s: 6x5 count 6 (5’s) to get 30.
Mental Images: 1 x 4 think 1 row of 4 or 1 group of four makes 4
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Fluency with related missing factor problems, for example, for 30 ÷ 5 think
5 x = 30. / Strategies:
Use the 2 Combination and Add One More Group:
3 x 6, think 2 x 6 makes 12, so add one more group of six to make 18.
Use the Five Combination and Add One or Two More Groups: 7 x 8, break apart the 7 into 5 and 2, reason, “5 x 8 makes 40, so 2 more groups of 8 is 16. Answer is 40 + 16 = 56.
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Fluency with related missing factor problems (e.g., 56÷8 think 8x☐=56) / Strategy:
Think of Ten:
9x3 think 10 x3, think 10 rows of 3 is 30 remove one row of 3, (30 – 3) makes 27
Another example:
9x8 think 10 x 8, think 10 rows of 8 is 80, remove one row of 8, (80 – 8) makes 72.
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Fluency with related missing factor problems (e.g., 9x8 think 72÷8=9) / See previous strategies
Division Fluency:
Division is taught as an inverse relationship of multiplication in grade 3; fluency of division facts is monitored in grades 3 and 4.
20 ÷ 5 = think
5 x = 20, and reason, “I know
5 x 2 = 10 so double the factor of 2 to double the product, 5 x 4 = 20 so
20 ÷ 5 = 4.”
End of Trimester or
End of Year Combinations / *See 3rd grade, Unit 1 pp. 161-163 for intervention ideas and Computational Fluency Continuum: Grades K, 1, & 2 / 17 combinations, their turn around combinations, and their related division facts (e.g., 4x3, 3x4, 12
2x2 2x7 4x3 4x8
2x3 2x8 4x4 4x9
2x4 2x9 4x5 4x10
2x5 2x10 4x6
2x6 4x7
/ 33 combinations, their turn around combinations, and their related division facts (e.g., 4x3, 3x4, 12
5x3 1x1 1x7 0x3 0x10 3x10
5x5 1x2 1x8 0x4 6x10
5x6 1x3 1x9 0x5 7x10
5x7 1x4 1x10 0x6 8x10
5x8 1x5 0x1 0x7 9x10
5x9 1x6 0x2 0x8 10x10
5x10 0x9 / 11 combinations, their turn around combinations, and their related division facts (e.g., 4x3, 3x4, 12
3x3
3x6 6x6
3x7 6x7
3x8 6x8
3x9 6x9
/ 6 combinations, their turn around combinations, and their related division facts (e.g., 4x3, 3x4, 12
7x7
7x8
7x9
8x8
8x9
9x9 / Mixed combination practice.
Mixed multiplication and division practice and assessment.
Investigations
Games / *See Computational Fluency Continuum: Grades K, 1, & 2 / Things that Come in Groups 3rd U5
Skip Counting 3rd U5
Counting Around the Class 3rd U5 / Arranging Chairs 3rd U5
Array Cards 3rd U5
Practicing with Multiplication Cards 3rd U5 / Factor Pairs 3rd U5
Multiplication Cards 3rd U5
Count and Compare 3rd U5
Missing Factors 3rd U5 / See previous games
(more division games in Grade 4) / Making Arrays 4th U1 Multiplication Cluster
Array Cards 4th U1 Problems 4th U8
Factor Pairs 4th U1 Factor Bingo 4th U8
Quick Images 4th U1
Multiplication Cards 4th U1
Multiple Turn Over 4th U1
Small Array/Big Array 4th U3
Missing Factors 4th U3
Building Multiple Towers 4th U3
Report to Parents / Combination assessments sent home with each unit. / Combination assessments sent home with each unit. / Combination assessments sent home with each unit. / Combination assessments sent home with each unit. / Combination assessments sent home with each unit.
Developed by P. Richards, School District of South Milwaukee (May 2013) *adapted from the work of Dr. DeAnn Huinker and Janis Freckmann