Jump Strategy Subtraction

Overview

Students develop an efficient mental strategy for subtracting two- and three-digit numbers by making jumps on an open number line. They connect subtraction to place value, partitioning and addition as the inverse operation, building on known subtraction facts and counting-on strategies.

Learning intentions

Students will:

• use an open number line to subtract by making efficient jumps;
• partition a number into hundreds, tens and ones;
• choose jumps that make a calculation easier;
• use addition to check a subtraction answer;
• explain their strategy using mathematical language.

Success criteria

• I can start at the larger number and jump backwards.
• I can partition the number I am subtracting into useful parts.
• I can record my jumps and calculate accurately.
• I can check my answer using addition.

Curriculum links

• Number — add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers.
• Algebra — extend addition and subtraction facts to develop efficient mental strategies for larger numbers.
• Algebra — recognise addition and subtraction as inverse operations and find unknown values.
• Mathematical problem-solving and reasoning — explain and justify a chosen calculation strategy.

Lesson structure (60 minutes)

1. 0–5 min · Hook and warm-up. Teacher displays the opening comparison and warm-up slides and asks, “Which is easier: 73 − 20 or 73 − 19? How could we make a helpful jump?” Students solve quick facts such as 15 − 7, 20 − 8 and 36 − 10 using mental strategies, then share how they know.

2. 5–15 min · Explicit modelling. Teacher introduces an open number line and models 84 − 23. Begin at 84, jump back 20 to 64, then jump back 3 to 61. The teacher records: 84 − 20 = 64; 64 − 3 = 61. Students copy the number line in the air, identify the starting number and explain why the jumps total 23.

Teacher then models a more efficient partition for 152 − 38: jump back 40 to 112, then jump forward 2 to 114. Explain that subtracting 38 can be changed to subtract 40 and add 2. Link this to place value and mental calculation. Students compare this with jumping back 30 and 8 and discuss which method is easier.

3. 15–25 min · Guided practice: build the jumps. Teacher opens the worked-example and guided-practice slides and works through 246 − 32, 175 − 49 and 320 − 86, pausing after each jump. Students use mini-whiteboards to draw an open number line, write the jumps and show their answer. Invite students to explain choices such as subtracting 50 then adding 1 for 49. Check answers together using addition, for example, 126 + 49 = 175.

4. 25–35 min · Partner strategy challenge. Teacher gives each pair a hundreds-chart support mat, the hundreds chart and 100-square pack, and displays the partner task on the partner activity slides. Call out problems such as 93 − 27, 214 − 36, 405 − 198 and 367 − 125. Partners take turns as “solver” and “coach”: the solver draws and explains the jumps; the coach checks that the jumps match the number being subtracted and verifies the result with addition. Students should attempt the open number line before using the chart for support.

5. 35–48 min · Guided problem solving. Teacher presents the word problem: “A school collected 352 cans. It sent 178 cans for recycling. How many cans remained?” Model identifying the whole and the amount removed, then ask students to suggest efficient jumps. Students solve in pairs using a bar model or open number line, record a number sentence and check with addition. Repeat with: “The library had 425 books and donated 197. How many books were left?” Discuss why subtracting 200 and adding 3 is efficient.

6. 48–57 min · Independent worksheet practice. Teacher distributes the jump strategy subtraction worksheet and reminds students to show their jumps, not only the answer. Students independently complete problems progressing from two-digit subtraction to three-digit subtraction, including one compensation problem and two short word problems. Teacher conferences with students who need support, asking, “Where will you start? What parts could you jump? How will you check?”

7. 57–60 min · Plenary and exit check. Teacher displays the reflection and exit-question slide and asks students to solve 263 − 98 in their books using jumps. Students write the answer, one helpful jump and an addition check, then share which strategy made the calculation easier.

Resources

• the subtraction strategy slide deck
• the jump strategy subtraction worksheet
• the hundreds chart and 100-square pack
• Mini-whiteboards and markers
• A3 paper or maths books
• Pencils and erasers
• Projector or interactive whiteboard
• Counters or place-value materials for students requiring concrete support

Assessment

• Observe warm-up responses and questioning to identify whether students understand that subtraction begins with the larger number.
• During guided and partner work, check that students partition the subtracted number accurately, make jumps in the correct direction and can explain their choices.
• Use the worksheet and exit question to assess independent accuracy, efficient strategy use and the ability to verify subtraction with addition.

Differentiation

• Support students with a pre-drawn open number line, place-value materials, smaller numbers and sentence stems: “I started at…”, “I jumped back…”, and “I checked by…”.
• Encourage students who need additional support to use the hundreds chart after attempting a mental jump; pair them with a patient mathematical coach and model one jump at a time.
• Provide EAL/D support through visual demonstrations, gestures and the terms “start”, “subtract”, “jump back”, “adjust” and “check”, with opportunities to rehearse explanations orally.
• Extend confident students by asking them to solve the same problem in two ways, compare efficiency and create a subtraction problem where compensating by 10 or 100 is useful.