Multiply & Add Problems
Solve problems involving multiplying and adding, including using the distributive law, integer scaling problems, and harder correspondence problems
What a learner can do afterwards
- Use the distributive law to solve 14 × 6 as 10 × 6 + 4 × 6
- Solve a scaling problem (e.g. 'A tower is 3 times as tall as a 15 m building')
- Solve a correspondence problem (e.g. '3 types of bread, 4 types of filling: how many different sandwiches?')
1 · Read
You already know how to multiply and how to split numbers apart. This time, you'll use both skills together. To multiply a bigger number, split it into two smaller parts, multiply each part, then add the answers.
14 × 6 splits into 10 × 6 and 4 × 6. That gives you 60 + 24, which equals 84.
A shop sells 3 kinds of bread and 4 kinds of filling. Every bread can pair with every filling, so there are 3 × 4 = 12 different sandwiches.
When you split a number apart, every part needs to be multiplied. If you skip a part, your answer comes out too small.
Split a number into parts, multiply each part, then add the results together.
More to read
Use the break apart and distribute strategy to multiply with units of 6 and 8
Tough tables fall apart into easy ones. To multiply by 8, double three times: double the number, double again, then once more. To multiply by 6, multiply by 5 and add one more group.
Keep a list of facts you know well. Every new fact is just a small step from one you already own.
Multiply by using place value strategies and the distributive property
Big multiplications split by place value. To work out 14 x 6, do 10 x 6 and 4 x 6, then add. Both parts are easy, and the sum is exact.
Draw the split as two smaller rectangles stuck together.
Count by units of 9 to multiply
Nines have rhythms. Count 9, 18, 27, 36 and watch the tens climb while the ones fall. Your fingers can even do the 9 times table with a simple folding trick.
Patterns like these turn memory into music. Chant the multiples until they sing themselves.
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2 · Watch
به انگلیسیTake it off screen
Where it sits
Learn first
Optional connections
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17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.