Subitizing and ten frames
How can a child know there are three without counting one, two, three?
Where you are 23 in Counting and cardinality
When you reach for it
Subitizing means naming how many are in a very small group at a glance, without counting them one by one: you see three dots and simply know “three”. It only works for small groups, so a larger group is seen as small groups put together (5 and 2 make 7), which is what dice, dominoes and ten frames are built for. Reach for it once a child can count a small set; it makes counting faster, and it is the first step toward seeing numbers as parts.
Each day below takes about ten to fifteen minutes. Keep it a game: a quick look, a guess out loud, then a second look to check.
Day 1: Quick looks at one, two and three
You need: a few index cards with 1, 2 or 3 dots drawn in marker, and a sheet of paper to cover them.
Hold up a card for about two seconds, then cover it. Ask, “How many dots did you see?” Then ask the more important question: “How did you know?” A child who says “I just saw it” is subitizing. A child who tried to touch and count needs a shorter look, not a longer one; the quick flash is what nudges the eyes to take in the whole group at once.
Mix the arrangements. Three in a row and three in a triangle are both three, and saying so is the point. Flash fingers too: hold up 2 fingers, hide your hand, and ask for the number. Then let the child flash fingers at you.
Practice. Flash each card for two seconds.
- Card A. How many? Answer: 2.
- Card B. How many? Answer: 3, in a triangle.
- Card C. How many? Answer: 1.
- Card D. How many? Answer: 3, in a row. Ask whether B and D show the same number. They do: both are 3, arranged differently.
- You flash 3 fingers, then hide them. How many? Answer: 3.
Day 2: Dice and dominoes
You need: one large die and a few dominoes (or dominoes drawn on paper).
Roll the die and ask the child to say the number before touching any dots. Dice patterns are built to be seen at once: four is a square, five is the square with one dot in the middle, and six is two rows of three. Roll a few times and talk about the shapes: “Five looks like four with a dot in the middle.”
Then bring out dominoes. Each half is a dice pattern, so a domino is two small groups. Cover one half with your hand, name it, then the other half, then ask for the whole: “Two here, three here. How many dots on the whole domino?” Keep totals to 5 for now.
Practice. Look at each domino quickly, then say the total.
- Domino A. Answer: 5, because 2 and 3 make 5.
- Domino B. Answer: 4, because 1 and 3 make 4.
- Domino C. Answer: 4, because 2 and 2 make 4.
- Domino D. Answer: 2, because 1 and 1 make 2.
- Roll the die until it shows the square with a dot in the middle. What number is it? Answer: 5.
Day 3: Seeing a group as smaller groups
You need: cards with two little groups of dots and a gap between them, and both hands.
Start with fingers. Ask the child to show 5 on one hand, then 5 using both hands. There are several ways: 4 and 1, 3 and 2, 2 and 3, 1 and 4. Each one is still five.
Now flash a card with two groups. Ask, “How many? What little groups did you see?” You want to hear something like “I saw three and two, that’s five.” The child sees each small group at a glance and puts them together, which is the start of counting on and of number bonds. Any honest way of seeing the groups is right; one child may see four as two and two, another as three and one.
Practice. Flash each card, then ask for the total and the groups.
- Card A. Answer: 4, seen as 2 and 2.
- Card B. Answer: 5, seen as 3 and 2.
- Card C. Answer: 5, seen as 4 and 1.
- Card D. Answer: 3, seen as 2 and 1.
- Show 4 using both hands. Answer: any of 3 and 1, 2 and 2, or 1 and 3.
Day 4: Ten frames
You need: a ten frame (two rows of five boxes, drawn on paper) and some pennies or small stickers.
Show the empty frame and count the boxes together: 10. Point out that each row is 5, just like one hand. Fill boxes always in the same order: the top row from left to right first, then the bottom row. Because of that habit, a full top row is 5 without counting, and 7 is a full top row and 2 more.
Place some pennies, let the child look for two seconds, and cover the frame with paper. Ask, “How many pennies? How did you see it?” Then ask about the empty boxes: “How many more fill the frame?” That second question is the first taste of making ten.
Practice. Flash each frame, then ask.
- Frame A. How many? Answer: 5, a full top row.
- Frame B. How many? Answer: 7, a full row and 2 more.
- Frame C. How many? Answer: 9, a full row and 4 more.
- Frame C. How many boxes are empty? Answer: 1, since 9 and 1 make 10.
- Frame D. How many? Answer: 3.
Exercises
Flash each picture in the check figure for about two seconds, then cover it.
- Frame A. How many pennies are there, and how many boxes are empty?
- Card B. How many dots are there, and what small groups did you see?
Answers
- 8 pennies and 2 empty boxes. A child who has it says something like “a full row is 5, and 3 more is 8”, and sees the 2 empty boxes because 8 and 2 make 10.
- 6 dots, seen as 4 and 2. A child who has it names both groups without touching a dot. This card was not in the practice, so a right answer shows the skill, not a remembered card.
Where this goes next
Seeing 5 as a full row leads straight into Ten frames, where a number is read as how full the frame is and how far it is from 10. Seeing a group as two parts becomes number bonds, and seeing the first group at a glance and continuing from it becomes counting on. Later, a full ten frame becomes the “ten” in Tens and ones, so 13 is one full frame and 3 more.