Number Lines, Expanded Form & Compensation

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A number line is a helpful path that shows numbers in order from left to right. Early learners can use it to count, compare, add, and subtract by making small hops. Expanded form helps children see that a number is made of tens and ones, like 47 = 40 + 7. Compensation is a friendly math trick that makes a problem easier by adjusting numbers and then balancing the change.

Key Facts

Numbers get bigger as you move right on a number line.
Numbers get smaller as you move left on a number line.
Expanded form shows place value, such as 36 = 30 + 6.
To add on a number line, start at the first number and hop right.
To subtract on a number line, start at the first number and hop left.
Compensation example: 29 + 6 = 30 + 5 = 35.

Vocabulary

Number line: A number line is a straight path with numbers placed in order.
Expanded form: Expanded form shows a number as the value of its tens and ones.
Tens: Tens are groups of 10 in a number, such as the 4 in 47 meaning 40.
Ones: Ones are single units in a number, such as the 7 in 47.
Compensation: Compensation is changing a number to make a problem easier, then adjusting the other number to keep the same answer.

Common Mistakes to Avoid

Counting the starting number as the first hop is wrong because hops count the spaces you move, not the number where you begin.
Moving left when adding is wrong because adding makes the number larger, so the hops should go to the right.
Writing 42 as 4 + 2 is wrong because the 4 is in the tens place, so 42 = 40 + 2.
Changing one number in compensation without balancing the other is wrong because it changes the total.

Practice Questions

1 Start at 24 on a number line and hop right 8 spaces. What number do you land on?
2 Write 58 in expanded form, then use it to find 58 + 10.
3 Mia solves 39 + 7 by thinking 40 + 6. Explain why this gives the same answer.

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