Teen numbers as ten and some more
How is a number from eleven to nineteen a full ten and some more?
Where you are 15 in Place value
Why this exists
Every number from 11 to 19 is ten ones and some more ones: 13 is a full ten and 3 more, so 13 = 10 + 3. The English words hide this (“thirteen” does not say “ten and three”, and “eleven” and “twelve” give no clue at all), so the child needs to see and build it with objects. This week the child makes a full ten and some extra ones, takes a teen number apart into ten and some more, and records it as 10 + 3 = 13.
The child can already say the counting words to twenty, count a set of objects and read a ten frame. Each day takes about ten to fifteen minutes. You need two ten frames drawn on paper, about 20 counters, and about 20 straws or craft sticks with a few rubber bands. Keep the talk to “ten ones and some more ones”; calling the ten a single unit and reading the digits as tens and ones comes later.
Day 1: A full frame and some more
You need: two ten frames side by side and 20 counters.
Ask the child to fill the first frame, one counter in each box, top row first. “How many? Is it full?” It holds 10, and the child knows that from the empty boxes being gone, not from counting. Now put 2 counters in the second frame. “How many in all?” Let the child count on from the full frame if needed: “ten, eleven, twelve.” Then say it the new way: “Twelve is a full ten and 2 more.”
Clear the second frame and build other numbers the same way. The left frame never changes; only the right frame does. Ask each time, “How many in the full frame? How many more?” The first answer is always 10, and that sameness is the point.
Practice.
- Picture A. How many counters? Answer: 11, a full frame and 1 more.
- Picture B. How many counters? Answer: 14, a full frame and 4 more.
- Picture C. How many counters? Answer: 17, a full frame and 7 more. The child may see the 7 as a full row of 5 and 2 more.
- Build 15 on two frames. What does it look like? Answer: a full frame, and the top row of the second frame full.
- In every picture, how many counters are in the left frame? Answer: 10, always.
Day 2: Taking a teen number apart
You need: about 20 straws or craft sticks and a few rubber bands.
Give the child a loose pile of 13 straws. First the child counts them. Then ask the child to count out ten and snap a rubber band around them. “How many in the bundle? How many are left over?” The bundle holds ten ones, and 3 straws are left: thirteen was ten and three the whole time. Now take the band off and count all the straws again. Still 13. Bundling did not change how many there are; it only made the ten easy to see.
Do it again with other piles. Each time, the child counts out exactly ten for the bundle and then says what is left: “Ten and 6 more.” If a bundle comes out with 9 or 11 straws, count it again together; the band must hold exactly ten.
Practice.
- Picture A. How many sticks in all? Answer: 13, a bundle of 10 and 3 loose sticks.
- Picture B. How many sticks in all? Answer: 18, a bundle of 10 and 8 loose sticks.
- Picture B. How many sticks are not in the bundle? Answer: 8.
- Count out 12 loose straws and bundle ten of them. How many are left over? Answer: 2, because twelve is ten and 2 more.
- You bundle ten straws and 5 are left over. Then you take the band off. How many straws are there? Answer: 15. The band changes nothing about how many.
Day 3: Writing it down
You need: the two ten frames, counters, straws, rubber bands, and paper and a pencil.
Build 14 on the frames, a full frame and 4 more. Say it, then write it with the child:
Point to each part as you read it: “Ten, the full frame. Plus four, the extra ones. Makes fourteen.” Write the other way too, with the total first: 14 = 10 + 4. Both say the same thing, and the child should meet both. Point out that the 4 at the end of 14 matches the 4 extra ones; leave it there and do not name the 1 yet.
Then turn it around: write an equation and let the child build it, or build a picture and let the child write the equation. A drawing works too: a ten frame with all ten boxes filled and some dots beside it.
Practice.
- Picture A. Write it as ten and some more. Answer: 10 + 4 = 14.
- Picture B. Write it as ten and some more. Answer: 10 + 3 = 13.
- Build 10 + 5. What number is it? Answer: 15, a full frame and 5 more.
- Fill in the blank: 12 = 10 + \underline{\quad}. Answer: 2, since twelve is a full ten and 2 more.
- Draw 11 as ten and some more. Answer: a full ten frame and 1 dot, recorded as 11 = 10 + 1.
Day 4: Fingers, names and matching
You need: both of your hands, the child’s hands, and the frames and straws from earlier days.
Hold up all ten of your fingers and keep them up. Ask the child to hold up 3. “My ten and your three. How many fingers?” Thirteen. Your hands are the full frame and the child’s fingers are the extra ones. Swap roles: the child holds up ten, you show some more.
Then talk about the names. “Fourteen” says “four” first and “teen” (ten) second, but the number is still ten and four more; write 10 + 4 = 14 beside the word to show it. “Eleven” and “twelve” do not sound like ten at all, which is why building them matters most. Finish with a quick match: you say an equation, the child builds it either way (frames or straws) and names the number.
Practice.
- You show ten fingers and the child shows 7. How many fingers? Answer: 17, because 10 + 7 = 17.
- Is eleven ten and one more? Answer: yes, 11 = 10 + 1, even though the word does not say ten.
- Build 10 + 2 with straws. What number is it? Answer: 12, a bundle and 2 loose straws.
- Which has more extra ones, 15 or 18? Answer: 18, with 8 extra ones against 5. Both have the same full ten.
- Is 3 + 10 the same number as 10 + 3? Answer: yes, both are 13: the same full ten and the same 3 extra, just said in a different order.
Exercises
Show the check figure. Let the child look as long as needed; this is not a flash.
- Picture A. How many counters are there? Write it as ten and some more.
- Picture B. How many sticks are there? How many sticks are not in the bundle?
Answers
- 16 counters, written 10 + 6 = 16 (or 16 = 10 + 6). A child who has it says “a full ten and 6 more” without counting the left frame.
- 19 sticks, with 9 loose sticks outside the bundle, so 19 = 10 + 9. A child who has it starts from ten for the bundle and counts on the loose sticks, or sees them as ten and nine. Neither number was in the practice, so a right answer shows the idea, not a remembered card.
Where this goes next
A full ten and some more grows into Tens and ones, where the ten becomes one unit and 13 is read as one ten and three ones. Seeing a teen number as 10 and a part also leads to making ten to add, where 8 + 5 becomes 10 + 3.