Lesson Guide
Explanation
Taking away is easier if you count up instead of down. For forty-three take twenty-seven, start at twenty-seven and hop to the next ten, which is thirty — that is three. Then hop in tens to forty, which is ten more. Then three more to forty-three. Add up all the hops: three and ten and three makes sixteen. So forty-three take twenty-seven is sixteen. Hop to the next ten first, then in tens, then the last bit.
Your Turn
Try 52 − 38 by hopping: 38 to 40 is 2, 40 to 50 is 10, 50 to 52 is 2. Check: 14.
Watch Out
Add up the HOPS, not the numbers on the line. The hops are the answer.
Explanation
To add a number that is near a hundred, split it into easy pieces. A hundred and nine is a hundred and nine ones. Sixty-eight plus a hundred is a hundred and sixty-eight, and nine more is a hundred and seventy-seven. Splitting the harder number works for any addition. And check the size of your answer at the end: sixty-eight and a hundred and nine are both small numbers, so something near a hundred and seventy-seven looks right.
Your Turn
Try 45 + 102 by splitting 102 into 100 and 2. Check: 147.
Watch Out
Split only ONE of the numbers. Splitting both makes more work, not less.
Explanation
Adding and taking away undo each other. Two parts sit inside one whole, and that one picture gives you three number sentences: twenty-seven and sixteen make forty-three, forty-three take twenty-seven is sixteen, and forty-three take sixteen is twenty-seven. They all say the same thing. So to check a take-away, add your answer back on — sixteen plus twenty-seven should give you forty-three. And to find a missing part, take the part you know away from the whole.
Your Turn
A number plus 38 makes 92. Take 38 from 92. Check: 54, and 54 + 38 = 92.
Watch Out
Checking means adding your ANSWER to the number you took away — not adding the two big numbers.
Explanation
Change questions are two steps. First add up what was spent: two dollars eighty plus two dollars five is four dollars eighty-five. Then take that from the note: ten dollars take four eighty-five. Hop up — four eighty-five to five dollars is fifteen cents, and five dollars to ten dollars is five dollars, so the change is five dollars fifteen. Check by adding back: four eighty-five and five fifteen make ten dollars. And watch out, because four dollars eighty-five is the total spent, not the change, and the test always offers it as an answer.
Your Turn
Spend $3.60 and $2.90 from a $10 note. Check: spent $6.50, change $3.50.
Watch Out
The total spent is NOT the change. Read which one the question wants.
Explanation
Four moves cover this strand. To take away, count up to the next ten and then in tens. To add a big number, split it. To find a missing part, take the part you know from the whole. And for change, add up the spending and then take it from the note. Every one of them can be checked by adding back, and if you have a spare moment in the test, that is the check to do. Quiz and exercises now.
Your Turn
Check 43 − 27 = 16 by adding back. Check: 16 + 27 = 43. ✓
Watch Out
Two-step questions are where the marks go. Work out what the first step even is before you start.
📌 Key Points — this lesson in a nutshell
- To take away, count up from the smaller number to the bigger one.
- To add a number near a hundred, split it: 109 is 100 and 9.
- Adding and taking away undo each other. Use that to check, and to find a missing part.
- Change from a note: add up what you spent first, then take that from the note.
Step 1: Introduction
Step 1 of 5
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