Study guide: Build Fact Strategies and Solve Two-Step Problems
Use distribution, regrouping, zero/one patterns, and multiple operations.
Ideas to explain in your own words
- A factor can be split into parts that are easier to multiply.
- Multiplication of three factors can be grouped in different ways without changing the product.
- Multiplying by one gives one copy of an amount, so it preserves the amount.
- A two-step problem may first create an equal-group total and then change that total.
Useful vocabulary
- distribute
- Multiply each part of a split amount and combine the products.
- identity factor
- The factor one, which preserves a quantity in multiplication.
Watch your reasoning
- Multiply both parts before combining their products.
- Regrouping changes parentheses, not the operations or factor values.
- A zero factor gives zero, not the other factor.
- A removal in the story is subtraction, not another multiplication factor.
A worked review example
For 6×8, split eight into five and three. Then 6×5=30 and 6×3=18, so 6×8=48. The six-row array has five columns and three more columns. Multiplying only one part would leave columns uncounted. The split parts must add back to the original factor. Multiply both parts before combining their products. Split an array into two non-overlapping column sections.
Make a practice plan
- Split a Factor and Combine Partial Products: Find 9×7 as 9×5+9×2. Expected: 63.
- Regroup Three Factors to Make an Easier Product: Find 4×5×2. Expected: 40.
- Explain Zero, One, and Even-Product Patterns: Explain 2×7 without only naming fourteen. Expected: two copies of seven form seven pairs.
- Finish a Two-Step Multiplication Story: Six packs of eight gain eleven loose cards. Expected: 59 cards.