Adding puts parts together; subtracting starts with the whole and finds the part that is missing. Counting on and counting back, doubles and doubles plus one, the pairs that make ten, and making a ten to add 8 + 5. Fact families with their four facts, a missing number in any place, and the equals sign as ‘the same as’. Story problems that put together, take from and compare. Study cards, hints, a practice quiz at three levels, and four workshop activities that check themselves.
Parts make the whole. The whole minus one part is the other part. Adding and subtracting are the same picture, read two directions.
Two things people get wrong
⚠️People often think…
7 + 2 is 8, because you count “7, 8.”
The 7 is where you start, not a step you take. Say 7, and THEN count two more: 8, 9. Counting the start number is the most common wrong answer at this level, and it is always off by exactly one.
Say the start number, then start counting.
⚠️People often think…
The word “more” always means add.
“How many MORE does Sam have than Ana?” is a comparison, and you subtract to answer it. Read the whole question, not one word in it.
Key words lie. Picture the parts and the whole.
Find the parts, find the whole
1Watch one
7 + 2.
Start at 7. Do not count it.
Count one more: 8.
Count one more: 9.
9. Two steps, not two numbers said.
2Do one with me
8 + 5. Make a ten first.
8 needs how many to reach 10?
That leaves how much of the 5?
10 + 3 =
💬One sentence, then you move on
Why don't you count the first number when you add?
3Try one
Something minus 5 leaves 9. What was the starting number?
I want a hint first
The 5 and the 9 are both parts. The missing piece is the whole, so put the parts together.
Where this goes
Where this lives
Knowing how much more you need, splitting a snack, figuring out how many are missing.
What this feeds
Next unit is tens and ones — what happens once the numbers get past twenty.
One card at a time — tap “Show me” to check yourself, then Next. Start at Foundation; when those feel easy, climb.
Helpful Hints
🔟 Make a ten — the four steps
8 + 5: ask how many the big number needs to reach ten (8 needs 2) → break the small number into that and the rest (5 = 2 + 3) → add up to ten (8 + 2 = 10) → add what is left (10 + 3 = 13).
Need, break, ten, rest.
💡 The whole topic in one idea
Every problem has a WHOLE and two PARTS. Adding puts the parts together to find the whole. Subtracting starts with the whole and finds the part that is missing. Once you know which number is the whole, you know what to do.
Parts make the whole. Whole minus a part is the other part.
⚠️ Traps the test loves
Counting the start number as a step: 7 + 2 as “7, 8” = 8. Say 7, THEN count 8, 9.
Seeing the word MORE and adding. “How many more does Sam have?” is a compare: subtract.
Reading = as “the answer comes next.” 7 + 3 = 4 + 6 is true because BOTH sides are 10.
Pushing digits together: 4 + 4 = 44. Count or use the double: 8.
Forgetting the leftover in make-a-ten: 8 + 5 → 8 + 2 = 10 and stopping. Add the 3 that is left.
Subtracting to find a missing whole: ? − 5 = 9 is NOT 4. The blank is the whole, so add: 14.
🧰 Which strategy when — the chart
You see
Try
Example
+ a small number (1, 2, 3)
count on from the big one
9 + 2: 9, 10, 11
− a small number
count back
11 − 3: 11, 10, 9, 8
the same number twice
doubles
7 + 7 = 14
two neighbors
doubles plus one
7 + 8 = 14 + 1 = 15
8 or 9 plus something
make a ten
9 + 4 = 10 + 3 = 13
− a big number
think addition, count up
13 − 9: 9 + ? = 13 → 4
🎯 How the test will ask
A bare fact — “8 + 6 = ?” Pick a strategy: make a ten or doubles plus two.
A story — “How many in all? How many are left? How many more?” Find the whole and the parts before you pick + or −.
A blank in the middle — “5 + __ = 12.” Count on from the part to the whole.
A blank at the start — “__ − 4 = 7.” That blank is the whole: add.
True or false — “6 + 4 = 3 + 7?” Work out each side; same number means true.
Three numbers to add — “4 + 6 + 3.” Find the ten first.
A fact family — “Write the four facts for 3, 9 and 12.” Two adds, two subtracts; the whole leads every subtract.
✅ Before the test, can you…
Add and subtract within 10 quickly, from memory?
Count on and count back without counting the start number?
Say all the pairs that make ten, and all the doubles to 10 + 10?
Make a ten to add 9 + 7 or 8 + 6?
Write the four facts of a fact family?
Tell a put-together story from a take-from story from a compare story?
Find a missing number anywhere in a number sentence, and say if an equation is true?
Pick your level
Look back at anything you missed — the hint that appeared is exactly what to reread tonight.
How sure did you feel?
Workshop
Work like a problem solver: sort story problems by what they ask, put a make-a-ten solution in order, fill in a fact-family triangle, then decide which number sentences are true. Every activity checks itself, and hints are free.
Your practice never leaves this device. There is no account and no sign-in. Your work is saved in this browser only, and you can erase it whenever you want.
Your practice record — saved on this device
This is your record of the module on screen — it stays here and goes nowhere. Independent means you got it right on the first tap; supported means you got it after the explain-and-retry, or marked ‘I had it’ on a revealed answer. Both count, and neither is a grade. If your teacher asks, copy the row or show them this screen.
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Supported
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Hints used
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Cards studied
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Lab
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Traps met
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Explained in own words
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The answer key is for a teacher: it prints only from here, for the unit on screen. Print the study packet prints the study pages and a blank quiz — never the answers.