MISSION · Operations
Making Sense of Multiplication
See multiplication as groups, not a list to memorise
LEVEL 1 · EXPLORE
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LEVEL 2 · LEARN
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Open the chapters in any order. Try the examples as you go.
The idea in one sentence
Multiplication is a fast way to count equal groups.
Picture an array
For \(4 \times 3\), draw 4 rows with 3 dots in each row:
\[3 + 3 + 3 + 3 = 12\]The array shows why \(4 \times 3 = 12\). It also shows why \(3 \times 4\) has the same total: turn the array sideways.
Break a hard fact into easy facts
Suppose \(7 \times 8\) is hard to remember. Split 7 into 5 and 2:
\[7 \times 8 = (5 \times 8) + (2 \times 8) = 40 + 16 = 56\]This is the distributive property, but the name is less important than the move: break one group into friendlier chunks.
Useful patterns
- Multiplying by 2 means doubling.
- Multiplying by 5 gives an answer ending in 0 or 5.
- Multiplying by 10 shifts every digit one place left and adds a zero for whole numbers.
- Multiplying by 9 is the same as multiplying by 10 and subtracting one group.
Common mix-ups
- Counting uneven groups as multiplication. The groups must be equal.
- Forgetting what each number represents. In 4 rows of 3, 4 counts the rows and 3 counts each row.
- Believing order changes the answer. It changes the picture, but not the total.
Check yourself
Use a friendly split to solve \(6 \times 7\).
One way: \((5 \times 7) + (1 \times 7) = 35 + 7 = 42\).
LEVEL 3 · REFLECT
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