MAFS.3.OA.3.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 • 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
MAFS.3.OA.2.5: Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
It is not expected students will attain fluency with facts from the Standard within the timeframe of a single Unit. Fluency should be focused on and assessed throughout the year using interactive activities such as games to promote automaticity of facts. It is the goal of the standard that students attain fluency with multiplication facts and related division facts within totals of 10 x 10 by the end of the year.
The concepts about basic facts and fluency with basic facts are too important to rush through because these facts become the foundation for multi-digit multiplication and division in subsequent grade levels. In this unit we will focus solely on developing fluency with multiplication facts of ×2, ×10, ×5, ×1, and ×0. Students will use their understanding and fluency of multiplication facts as they explore division facts in a later unit.
The sequence of the global concept guides within this unit for exploring multiplication facts is recommended as each fact set builds on and connects to previous understandings about numbers, patterns, and properties. Each of the following 6 subsequent Units will also contain one fluency lessons focused around facts of ×3, ×4, ×6, ×9, ×8, and ×9.
GCG 1 – Learning Goal: As a mathematician,I will be able to use strategies to fluently multiply by 2
- Step 1: Connect doubles facts in addition to fluently multiply by 2
- Step 2: Apply the commutative property to solve related ×2 facts (i.e. the product of 2×6 is the same as 6×2)
GCG 2 – Learning Goal: As a mathematician,I will be able to use strategies to fluently multiply by 10
- Step 1: Relate skip counting by 10s to build fluency of ×10 facts
- Step 2: Explain the place value pattern in products of ×10 facts (i.e. 4×10=40 means 4 tens)
GCG 3 – Learning Goal: As a mathematician,I will be able to use strategies to fluently multiply by 5
- Step 1: Relate skip counting by 5s (and explore patterns) to build fluency of ×5 facts
- Step 2: Connect products of ×5 facts to ×10 facts (i.e. 5 is half of 10, so if 4×10=40, then 4×5=20)
GCG 4 – Learning Goal: As a mathematician,I will be able to use strategies to fluently multiply by 1 & 0
- Step 1: Explore patterns and understand why multiplying a number by one always results in a product of that number (i.e. identity property)
- Step 2: Explore patterns and understand why multiplying by zero always results in a product of zero (i.e. zero property)
GCG 5 – Learning Goal: As a mathematician,I will be able to increase fluency by playing games and centers
- Step 1: Apply patterns and relationships between math facts to build fluency
- Step 2: Students track their own progress towards demonstrating fluency of their multiplication facts