Making Sums to 20

Overview

Today students will learn to add and subtract numbers within 20 using strategies such as part-part-whole knowledge to 10, and will show thinking using an abacus model and a number line/mental strategy.

Learning intentions

WALT add and subtract within 20 using part-part-whole (to 10) strategies.

• Students will represent number stories using physical materials and drawings.
• Students will choose a strategy (abacus or number line/mental) and explain how it works.
• Students will check if answers make sense (for both addition and subtraction).

Success criteria

• I can solve addition and subtraction within 20.
• I can show my thinking using the abacus or a number line.
• I can say how I know my answer is correct.
• I can use part-part-whole to 10 (for example, “make 10”) to help me.

Curriculum links

• Number — add and subtract numbers within 20, using physical and virtual materials, part-part-whole knowledge to 10 and a variety of calculation strategies.
• Number — represent and explain additive story problems using “plus”, “minus”, and the equal sign, connecting materials to the numbers.
• Number — use mathematical modelling to solve practical problems involving addition and subtraction (simple story contexts).

Lesson structure (45 minutes)

1. 0–3 min · Warm-up (counting back-and-forth). Teacher writes “Start: 8” and asks the student to count up from 8 by 1 to 12, then count back from 12 by 1 to 8; student answers out loud and points to a number strip.

2. 3–8 min · Quick part-part-whole to 10. Teacher prompts: “Let’s make 10.” Students show on fingers or with dots: for 7+? to make 10, then for 13−? using the same pair idea (e.g., 13 is 10 and 3).

3. 8–20 min · Main teaching (abacus then number line/mental).

• 8–13 min · Abacus model worked example (addition). Teacher sets 13 + 5 using an abacus: “13 is 10 and 3.” Move 5 across as 3 to reach 16 then 2 more to reach 18, saying: “3 parts first, then finish the rest.” Student mirrors the moves and writes the equation: 13 + 5 = 18.
• 13–16 min · Abacus model worked example (subtraction). Teacher models 18 − 7: “Start at 18, take away 7 as 3 to reach 15, then 4 more to reach 11.” Student tracks the abacus removal and records 18 − 7 = 11.
• 16–20 min · Mental/number line strategy (no abacus). Teacher asks for a faster method: “Use a number line jump strategy.” Example 9 + 6: student says “Jump to 10 (need 1), then 5 more to 15.” Teacher records: 9 + 6 = 15.

4. 20–29 min · Student guided practice (label abacus vs no-abacus). Teacher points to two sections on the page:

• Abacus only (use the abacus, show part-part-whole to 10): A1) 12 + 6 = ____ A2) 17 − 5 = ____
• No abacus (use number line or mental make 10/counting on/back): N1) 8 + 7 = ____ N2) 14 − 6 = ____

Student solves each, writes the equation, and adds a one-sentence explanation: “I used make 10” or “I counted on/back.”

5. 29–34 min · Critical-thinking prompt. Teacher asks: “A1 is 12 + 6. If we swap the numbers, what would happen to the answer and how do you know?” (Student responds: same sum, because combining doesn’t change the total; gives an explanation using parts to 10.)

6. 34–43 min · Game (one student at home, abacus on specific rounds). Game: Plus/Minus Track (15 cards).

• Materials:
• 1 small board/grid made from paper (e.g., 20 spaces in a row)
• Counters for start/position (1 colour)
• 15 number cards (handwritten) with symbols: + and − paired with answers in range 0–20 (example prompts: “10 + 7”, “16 − 9”, “9 + 8”, “15 − 6”)
• Abacus available
• Score sheet with 3 columns: Round, Correct?, Points
• Rules:

1. Start at 0.
2. Flip one card. If it is “Abacus Round” (marked by a star on the score sheet: rounds 2, 5, 11), the student must solve using the abacus. Otherwise, they must solve using number line/mental strategy.
3. Student solves and reads the answer aloud.
4. Move the counter forward by the answer for “+” cards; move it backward by the answer for “−” cards (if the move would go below 0, the student must correct using the subtraction meaning: “take away” from the current starting number).
5. Scoring: +1 point for a correct answer AND correct movement; 0 points if incorrect.
6. Play 10 rounds (or until 43 minutes). Record points each round.

• Tracking: After each round, student ticks Correct? and writes points (1 or 0), then totals at the end.

7. 43–45 min · Quick check exit. Teacher asks two questions (fast, no abacus):

• Q1) 11 + 8 =?
• Q2) 16 − 9 =? Student writes answers and says one phrase for each: “I made 10” or “I counted back.”

Resources

• Abacus (real or physical/virtual)
• Number line (0–20) or number strip
• Printed worksheet or notebook page with “Abacus only” and “No abacus” sections
• Small counters and paper game board (0–20)
• Handwritten cards with +/− within 20 contexts
• Score sheet for game rounds

Assessment

• During practice: listen for correct strategy choice and part-part-whole language (“make 10”, “take away”, “3 to reach 10”).
• During quick check: record answers to Q1 and Q2 and note whether student used correct reasoning (one sentence explanation).
• Record a simple score on the worksheet: correct/needs support for each of A1, A2, N1, N2.

Differentiation

• Support step (confidence): Provide a “make 10” helper line on the page (e.g., 8→10 needs 2) and allow the student to whisper-count on the number line before writing the answer.
• Challenge step (advanced): After the guided practice, give one extra equation to solve mentally: “7 + 9 = ____. Then use the same parts to write a subtraction fact: ____ − ____ = ____.” Student must explain how it connects (part-part-whole).

Extension (for an advanced learner)

• Advanced pattern task: Student creates two related equations using the same 10-part idea. Example structure: 13 + 7 = 20, so 20 − 13 = 7. Student chooses their own numbers within 20, writes both equations, and explains “How do you know they match?” using part-part-whole to 10.