Ten frames

Why this exists

A ten frame is a card with two rows of five boxes, 10 boxes in all, filled one counter per box, top row first. Because every row is 5 and the whole frame is 10, a filled frame tells two things at once: how many counters there are, and how many empty boxes are left before ten. The child met the frame while naming small groups at a glance; this week the child builds numbers on it, reads 6 to 9 as “five and some more”, finds how far a number is from ten, and compares two frames.

Each day takes about ten to fifteen minutes. Use a ten frame drawn on paper (two rows of five boxes, each box big enough for a counter) and about 20 counters, pennies or beans. Stay with numbers from 0 to 10; numbers past ten come later.

Day 1: Building a number on the frame

You need: one ten frame and 10 counters.

Say a number and let the child build it: one counter in each box, top row from left to right first, then the bottom row the same way. Watch the order more than the total. A child who drops counters anywhere has a pile in a box, not a ten frame, so gently move them into the top row and say, “We always start here.” Then switch jobs: you build a number, and the child reads it.

Ask after each build, “How many counters? How did you know without counting them all?” and “Is the top row full yet?” Show the empty frame and ask how many counters it holds. The answer is 0, and an empty frame is a fine way to show zero.

Practice.

1. Frame A. How many counters? Answer: 4, all in the top row with one box still open there.
2. Frame B. How many counters? Answer: 10, every box is full.
3. Frame C. How many counters? Answer: 0, the frame is empty.
4. Build 1. Where does it go? Answer: in the top left box, the box every build starts in.
5. Build 4, then add one more counter. How many now? Answer: 5, and the top row is full.

Day 2: Five and some more

You need: one ten frame, 10 counters, and both hands.

Start with hands. Ask the child to hold up one whole hand: 5. Then 6: a whole hand and one more finger. The two hands are the two rows of the frame, five and five. Now build 6 on the frame and put the hands beside it: “A full row, like a full hand, and one more.”

Build 7, 8 and 9 the same way. Each time, ask, “How many in the full row? How many more in the bottom row?” The goal is for the child to see 8 as “five and three” without counting the first five, because a full row is always five.

Practice.

1. Frame A. How many counters? Answer: 6, a full row of 5 and 1 more.
2. Build 7. What does the frame look like? Answer: a full top row and 2 counters in the bottom row.
3. Build 9. What does the frame look like? Answer: a full top row and 4 in the bottom row, with 1 box still empty.
4. Show 8 on your fingers. Answer: one whole hand and 3 fingers on the other hand.
5. “I am thinking of a full row and 2 more.” What number is it? Answer: 7.

Day 3: How far from ten?

You need: one ten frame and 10 counters.

When the child first met the frame, the empty boxes were something to name in a quick look. Now the child does something with them. Build a number, ask, “How many more fill the frame?”, and let the child fill it, counting only the new counters: “one, two, three.” The number of new counters is how far the number was from ten.

Then turn the question around. With the child’s eyes closed, fill the frame partway and cover the counters with your hand, leaving only the empty boxes in view: “Three boxes are empty. How many counters are under my hand?” The empty boxes and the counters together are always the whole frame, so either one tells the other. Hands work the same way: the fingers still down are how many more make ten. You are only asking how far a number is from ten; pairs that make ten get their own lesson later.

Practice.

1. Frame A. How many more fill the frame? Answer: 9, a whole empty bottom row and 4 empty boxes in the top row.
2. Frame B. Fill it, counting only the new counters. How many did you add? Answer: 6, the last box of the top row and the whole bottom row.
3. “My frame has 3 empty boxes.” How many counters are in it? Answer: 7, a full row and 2 more.
4. Hold up 6 fingers. How many fingers are still down? Answer: 4, since the two hands together make 10.
5. Which is closer to ten, 4 or 8? Answer: 8, because its frame has only 2 empty boxes and the frame of 4 has 6.

Day 4: Comparing two frames

You need: two ten frames and 20 counters.

Build a number on each frame and lay one frame right above the other so the boxes line up. Ask, “Which frame has more? How do you know?” Every counter in the top frame has a partner box right below it. Where one frame has a counter and the other has an empty box, that counter has no partner, and those counters are how many more. A child who says “this one has a full row and that one does not” is already comparing.

Build the same number on both frames once, and ask again. The frames look exactly alike, so neither has more: they show the same number.

Practice.

1. Frames A and B. Which has more, and how many more? Answer: Frame A has more, 5 more, because 5 of its counters sit over empty boxes in B.
2. Frames C and D. Which has more, and how many more? Answer: Frame D has more, 6 more, the 6 counters over the empty boxes of C.
3. Build 4 on both frames. Which has more? Answer: neither; both show 4 and every counter has a partner.
4. Build 9 on one frame and 10 on the other. Which has more? Answer: the full frame, by 1.

Exercises

1. Frame A. How many counters are there, and how many more would fill the frame?
2. Frames A and B. Which frame has more counters, and how many more?

Where this goes next

A full frame and some more is how the child will meet the numbers eleven to nineteen, and later the full frame becomes the “ten” in Tens and ones. Seeing how many more fill the frame grows into the pairs that make ten and into making ten to add. Lining up two frames is matching, the same idea as telling which group has more.