Lesson 5 — Taking Away: Subtracting Within 20

Summary

Learners discover that subtracting means taking some away from a group and seeing what is left. They take away real objects, count what remains, practice the “count back” strategy, and meet the written number sentence with the minus sign — always with real things first.

Objectives

• Add and subtract within 20 using objects, drawings, or counting strategies, and explain what the operation means. (D05.S1.01.02)

Connection

A child gives two of his five flatbreads to a friend and wants to know how many he has left; a market seller sells three of her ten mangoes and counts the rest; a farmer lets some water out of the irrigation channel and measures what remains. When some go away and you ask “how many are left?”, that is subtracting. It is the partner of adding — the same story told backward.

Materials

• A collection of small objects (up to 20)
• Paper or slate and a writing tool

Preparation

• Give each learner or pair up to 20 objects and a writing surface.
• Plan to model one take-away problem fully before learners try their own.
• Prepare a few take-away story-starters (“I had seven, I ate two …”).

Facilitator note

This lesson is written to the learner (“you”). Subtracting is a skill, so teach it with a worked example and guided practice first (philosophy §13). The one new idea is that taking some away leaves a smaller group whose size you can count; the written signs (−, =) come after the objects. Keep starting numbers within 20. Offer “count back” as one tool, not the only one — counting what is left is equally correct. The number sentence is a record of what the hands did. Use take-away stories of sharing and giving, which let fairness (ethics) enter gently without moralizing. For learners who are Deaf or hard of hearing, act out taking away in sign or by moving objects; for learners who are blind or low-vision, remove objects from a bowl and count what remains by touch and sound. A learner who does not speak shows what is left by pointing to a number card or holding up fingers. Never rank learners by speed; a correct “what is left” is correct however it was reached.

Procedure

1. Gather — recall adding (5 min). Yesterday you joined two groups — that was adding. Today we learn the opposite: taking some away. That is subtracting.
2. Worked example — take away (10 min). Watch and help: here are 7 pebbles. Take 2 away and put them to the side. Count what is left: 1, 2, 3, 4, 5. Five are left! Taking 2 from 7 leaves 5.
3. Meet the signs (5 min). We can write what we did: 7 − 2 = 5. The minus sign − means “take away.” Read it: “seven minus two equals five.” The number on the left is what you started with; the number on the right is what is left.
4. Count back (10 min). Try another way: start at the big number and count backward. With 9 beans, take away 3. Say “nine,” then count back — eight, seven, six. So 9 − 3 = 6. Try “counting back” with your own pile.
5. Your turn — take away and record (12 min). Start with your pile, take some away, count what is left, and write your number sentence. Check yourself: put the objects back and count the whole pile again. Does your starting number come back?
6. Close (3 min). Subtracting is taking away — and the number left is always there to count. Tomorrow we will practice both joining and taking away and say what each one means.

Differentiation

• Support: Keep starting numbers small (under 10) and take away just one or two; count what is left together before writing anything.
• Support (motor): A partner removes objects while the learner counts and directs; use large, easy-to-grip objects.
• Extension: Write three different subtraction sentences about the same pile (for example, 10 − 2, 10 − 4, 10 − 6) and act out each one.

Assessment

• Formative (observation): Can the learner take away from a group within 20, find what is left, and record it as a number sentence?
• Formative (oral): Can the learner explain in their own words that subtracting means taking some away and finding what is left?

Home connection

At home, count a small group of things, take some away (or eat a few!), and tell a grown-up how many are left — then write the number sentence together.

Resources

• Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2015). Children’s Mathematics: Cognitively Guided Instruction (2nd ed.). Heinemann. (Separate/take-away problems as the foundation of subtraction, and children’s counting strategies.)