1 · Groups that are the same
3 baskets with 3 pencils in each. The groups are equal: every basket has the same number.
To count them all, add the same number again and again: 3 + 3 + 3 = 9.
2 · "Groups of"
4 boxes with 4 flowers in each is "4 groups of 4." That is 4 + 4 + 4 + 4 = 16.
Later you will write this as 4 × 4. For now, "groups of" and adding again and again is all you need.
3 · Arrays: neat rows
Line the dots up in rows. 3 rows with 5 in each row is an array. Count a row (5), then add: 5 + 5 + 5 = 15.
Turn it: 5 rows of 3 is 3 + 3 + 3 + 3 + 3 = 15. Same dots, same answer.
4 · Doubles
Double means two groups of the same. Double 7 is 7 + 7 = 14. Double 14 is 14 + 14 = 28.
To double a bigger number, double the tens and double the ones: double 14 = 20 + 8 = 28.
5 · Skip count to count groups
Groups of 2: count by 2s. Groups of 5: count by 5s. Groups of 10: count by 10s.
4 hands have 5 fingers each: 5, 10, 15, 20 fingers. 4 jumps of 5 on the number line.
6 · Sharing fairly
12 cookies shared by 3 kids. Deal them out one at a time, like cards, until they are gone. Each kid gets 4.
A fair share means everyone gets the same. 12 shared by 3 is 4 each.
7 · How many groups?
12 cookies, 4 in each bag. How many bags? Make groups of 4 until the cookies run out: 3 bags.
Same drawing, different question. "How many each?" and "how many groups?" are the two ways to share.
8 · Half of a shape
Half means 2 equal parts. Shade 1 of the 2 parts and you have one half, written 1/2.
The two parts must be the same size, or they are not halves.
9 · Half of a number
Half of 8 sweets: split 8 into 2 equal groups. Each group has 4. Half of 8 is 4.
Half of 20 apples is 10. Half of 14 is 7. Half is the opposite of double: double 4 is 8, half of 8 is 4.
10 · Quarters
A quarter is 1 of 4 equal parts, written 1/4. Cut a circle into 4 and shade 1.
A quarter of 12: split 12 into 4 equal groups, 3 in each. A quarter of 8 is 2.
11 · Thirds
A third is 1 of 3 equal parts, written 1/3. Shade 2 of the 3 parts and you have 2/3.
The bottom number says how many equal parts. The top number says how many you shaded.
12 · When it does not share evenly
7 cookies shared by 2 kids: 3 each, and 1 left over. Odd numbers do not split in half evenly.
Even numbers (2, 4, 6, 8...) always split into 2 equal groups. You are ready for the test! 🎉
Ready to check what stuck?
Take the free 24-question test. It starts easy and builds to harder, ISEE-style reasoning. It's auto-scored, and you can review every answer afterward.