Math · Unit 3 · Weeks 13–18
Properties, Patterns & Two-Step Problems
The big idea
Your child learns why multiplication works: factors can switch places, be grouped differently or be broken apart into easier facts. Then the unit moves to two-step word problems written with a letter for the unknown, patterns on the multiplication chart, and products like 4 × 60. Mid-year practice and the Quarter 2 review pull all of the × and ÷ work together.
Standards in plain words
- 3.OA.B.5 Uses the properties of operations (switching the order of factors, regrouping factors, breaking a factor apart) as strategies to multiply and divide.
- 3.OA.C.7 Multiplies and divides within 100 quickly and accurately using strategies, and by the end of the year knows from memory all products of two one-digit numbers.
- 3.OA.A.3 Uses multiplication and division within 100 to solve word problems about equal groups, arrays and measurements, with drawings and equations that use a symbol for the unknown number.
- 3.OA.A.4 Finds the unknown number in a multiplication or division equation, such as 8 × ? = 48 or 5 = ? ÷ 3.
- 3.OA.D.8 Solves two-step word problems with all four operations, writes equations with a letter for the unknown, and checks that answers make sense with mental math, estimation and rounding.
- 3.OA.D.9 Finds patterns in the addition and multiplication tables and explains them with properties of operations, for example why 4 times any number is even.
- 3.OA.A.2 Understands a quotient like 56 ÷ 8 as the number in each share when 56 is split into 8 equal shares, or as the number of shares when 56 is split into groups of 8.
- 3.OA.B.6 Understands division as finding an unknown factor: 32 ÷ 8 is the number that makes 32 when multiplied by 8.
- 3.NBT.A.3 Multiplies a one-digit number by a multiple of 10 from 10 to 90, such as 9 × 80, using place value.
What mastery looks like
- Breaks a hard fact into two easier facts, such as 7 × 6 = 5 × 6 + 2 × 6, and adds the two parts.
- Says whether a strategy switches, regroups or breaks apart factors, and knows the rules for multiplying and dividing with 0 and 1.
- Finds both steps in a word problem, writes an equation with a letter for the unknown, and checks the answer with rounding.
- Multiplies or divides before adding or subtracting in an expression like 3 + 4 × 2.
- Multiplies a one-digit number by a multiple of 10, such as 6 × 50 = 300, and explains it as 30 tens.
- Finds and tests a rule in an in/out table and predicts whether a product will be even or odd.
Materials
- Counters and small cups
- Graph or grid paper and crayons in two colors
- Multiplication chart
- A property reference card made in the notebook
- Place-value chart
- Index cards and sticky notes
- Timer
Watch across the unit
Watch for: Breaking apart both factors, or forgetting to add the two partial products at the end.
Try: Split only one factor, color the two parts of the array, write each product inside its part, then add.
Watch for: Stopping after step 1 of a two-step problem and giving the 'hidden' number as the answer.
Try: Underline the final question before solving and ask at the end, 'Did I answer what it asked?'
Watch for: Writing only the basic fact for a problem like 4 × 60 (24 instead of 240).
Try: Say the unit aloud, '4 × 6 tens is 24 tens,' and show 24 tens on the place-value chart.
Pacing
Short week: Keep Monday's lesson and the Friday quiz. In Week 15, do not skip the day on finding both steps; two-step problems return on every later test. In Weeks 17 and 18, which are practice and review, choose the practice day that matches your child's weakest skill.
Flex week: Week 14 is the flex week. Catch up on division models and breaking apart hard facts, or enrich with the Party Planner Challenge, which uses arrays and two-step problems. Finish with the Weeks 10 to 13 review and a short reflection.
Week by week
| Week | Topic | Check |
|---|---|---|
| Week 13 | Properties of multiplication | Use the commutative, associative and distributive properties |
| Week 14 | Flex week: catch up, deepen or enrich | Choice practice on Weeks 10–13 |
| Week 15 | Two-step word problems with a letter for the unknown | Solve and check two-step problems |
| Week 16 | Patterns & multiplying by multiples of 10 | Find patterns and products like 4 × 60 |
| Week 17 | Mid-year practice: × and ÷ | Mixed practice |
| Week 18 | Quarter 2 review | Unit 3 test |