🔢 MathGrade 2Lesson 12
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Add and Subtract Using Number Lines

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Learning Objectives

  • 1Use a number line to model both addition and subtraction and mark the start
  • 2Draw hops in the correct direction
  • 3Read the landing number
  • 4Split a two-digit number into tens and ones to add or subtract in two stages
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Mini Lesson

A number line is a tool that works for both addition and subtraction. The same three questions guide you every time: Where do I start? Which way do I hop? Where do I land?

The three-step number line method

  • Step 1 — Start: Mark the first number (the starting number) with a dot on the number line.
  • Step 2 — Hop: If adding, draw arcs going right (forward). If subtracting, draw arcs going left (backward). Count the number of hops.
  • Step 3 — Land: Put a star on the number where you land. That is your answer.

Choosing hop size

  • Adding or subtracting ones → hop one at a time (small jumps).
  • Adding or subtracting tens → hop ten at a time (medium jumps).
  • Adding or subtracting hundreds → hop one hundred at a time (large jumps).
  • You can also split a number to hop in two stages — first the tens, then the ones (e.g., +24 = +20 then +4).

Quick rule to remember

  • The + sign → hop right (numbers get bigger).
  • The − sign → hop left (numbers get smaller).
Addition hops right, subtraction hops leftTwo number lines on the same axis from 20 to 70. Top: a blue dot on 30, three +10 hops right, landing on 60. Bottom: a red dot on 60, three -10 hops left, landing on 30.+ goes right − goes left203040506070start+ 10 + 10 + 1030 + 30 = 60start− 10 − 10 − 1060 − 30 = 30
Number line showing both operations — blue arcs hop right (30 + 30 = 60) while orange arcs hop left (60 − 30 = 30).
Two-stage hop: 43 plus 24Number line from 40 to 70. Start at 43. A large +20 hop lands at 63. A small +4 hop lands at 67. Result: 43 + 24 = 67.Two-stage hop: 43 + 244045505560657043+ 2063+ 46743 + 20 = 63 → 63 + 4 = 6743 + 24 = 67
A two-stage hop showing 43 + 24: a large +20 blue arc lands at 63, then a small +4 green arc lands at 67.
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Ask yourself: "What is my start number? Am I adding or subtracting? How many hops, and which way?"

Vocabulary
Number line
A line marked with numbers in ordere.g. I drew a number line from 0 to 100.
Hop
A jump on a number linee.g. I made small hops to add ones.
Forward
Going to the right on a number line, for addinge.g. Adding hops me forward on the number line.
Backward
Going to the left on a number line, for subtractinge.g. Subtracting hops me backward to a smaller number.
Split
To break a number into smaller parts to make adding easiere.g. I split 24 into 20 and 4 to hop in two stages.
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