---
title: "Addition & Subtraction"
description: "53 topics in Mathematics, in the order they build on each other."
canonical: https://lightmysky.com/learn/mathematics/areas/addition-and-subtraction
source: https://lightmysky.com/learn/mathematics/areas/addition-and-subtraction.md
retrieved: 2026-10-19
---

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# Addition & Subtraction

53 topics in Mathematics, in the order they build on each other.

Page: https://lightmysky.com/learn/mathematics/areas/addition-and-subtraction

- [Addition as combining or putting together two groups](https://lightmysky.com/learn/mathematics/addition-as-combining-or-putting-together-two-groups-mt_OvyoRo47K-): Understand addition as combining or putting together two groups to find the total
- [Numbers up to 10 into pairs](https://lightmysky.com/learn/mathematics/numbers-up-to-10-into-pairs-mt_7XcCG43ZZW): Decompose numbers up to 10 into pairs in more than one way (part-part-whole)
- [Number bonds to 10](https://lightmysky.com/learn/mathematics/number-bonds-to-10-mt_e8CZ7E5qW7): Find the number that makes 10 when added to a given number from 1 to 9 (number bonds to 10)
- [Subtraction as taking away or separating](https://lightmysky.com/learn/mathematics/subtraction-as-taking-away-or-separating-mt_zuKAX6lcYR): Understand subtraction as taking away or separating from a group to find how many remain
- [Representing Addition and Subtraction](https://lightmysky.com/learn/mathematics/representing-addition-and-subtraction-mt_PgsHGYJMH-): Represent addition and subtraction using objects, drawings, and mental images
- [Addition and subtraction word problems](https://lightmysky.com/learn/mathematics/addition-and-subtraction-word-problems-mt_yJmvUCCym7): Solve addition and subtraction word problems within 10 using objects or drawings
- [Fluent adding and subtracting within 5](https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-5-mt_ghF3Vv6taM): Fluently add and subtract within 5
- [Number bonds](https://lightmysky.com/learn/mathematics/number-bonds-mt_s2mfRBoTal): Recall number bonds (addition and related subtraction facts) within 20
- [Adding and subtracting](https://lightmysky.com/learn/mathematics/adding-and-subtracting-mt_mr_Vk7FGzK): Add and subtract one-digit and two-digit numbers to 20, including zero
- [Early Word Problems](https://lightmysky.com/learn/mathematics/early-word-problems-mt_VAWV_l7J0D): Solve one-step word problems involving addition and subtraction to 20, including missing-number problems
- [Addition and subtraction strategies](https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-mt_PpWSHA-0kv): Use counting on and counting back as strategies for addition and subtraction
- [Addition in any order](https://lightmysky.com/learn/mathematics/addition-in-any-order-mt_QCgbiVrwnp): Understand and apply the commutative property of addition: addends can be added in any order
- [Finding a missing number in addition](https://lightmysky.com/learn/mathematics/finding-a-missing-number-in-addition-mt_ezc2m_0dzN): Understand subtraction as finding an unknown addend (e.g. 10 − 8 = ? is the same as 8 + ? = 10)
- [Fluent adding and subtracting within 10](https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-10-mt__we2TDqnJx): Fluently add and subtract within 10
- [Addition and subtraction within 20](https://lightmysky.com/learn/mathematics/addition-and-subtraction-within-20-mt_m1W6nTQJ2b): Add and subtract within 20 using strategies such as making ten, decomposing a number leading to ten, and using known facts
- [Grouping numbers to add](https://lightmysky.com/learn/mathematics/grouping-numbers-to-add-mt_T76hKqXf0z): Understand and apply the associative property of addition: when adding three numbers, any two can be added first
- [Adding Three Small Numbers](https://lightmysky.com/learn/mathematics/adding-three-small-numbers-mt_Zx1xZM-RbX): Add three one-digit numbers using strategies including looking for pairs that make 10
- [Inverse: addition undoes subtraction](https://lightmysky.com/learn/mathematics/inverse-addition-undoes-subtraction-mt_ehGS_uVSJv): Recognise and use the inverse relationship between addition and subtraction to check calculations and solve missing-number problems
- [Fluent adding and subtracting within 20](https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-20-mt__t4afSyZRm): Fluently add and subtract within 20 using mental strategies and recall single-digit addition facts.
- [Reading +, −, and = symbols](https://lightmysky.com/learn/mathematics/reading-and-symbols-mt_8RmpkDxT9L): Read, write, and interpret the symbols +, −, and = in number sentences
- [What the equals sign means](https://lightmysky.com/learn/mathematics/what-the-equals-sign-means-mt_oIzycTBeE4): Understand the meaning of the equal sign as 'is the same as' and determine if equations are true or false
- [Unknown in Addition & Subtraction](https://lightmysky.com/learn/mathematics/unknown-in-addition-and-subtraction-mt_3JgrHY221M): Determine the unknown whole number in an addition or subtraction equation relating three whole numbers
- [Subtracting multiples of 10](https://lightmysky.com/learn/mathematics/subtracting-multiples-of-10-mt_HJTuIGHvcR): Subtract multiples of 10 (10–90) from multiples of 10 using place value strategies
- [Adding within 100](https://lightmysky.com/learn/mathematics/adding-within-100-mt_glPPG-kTQY): Add within 100 using strategies based on place value, including adding a two-digit and one-digit number, and a two-digit and a multiple of 10
- [Fluent addition and subtraction](https://lightmysky.com/learn/mathematics/fluent-addition-and-subtraction-mt_3e_PQxwC12): Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
- [Mental addition and subtraction (age 6+)](https://lightmysky.com/learn/mathematics/mental-addition-and-subtraction-age-6-mt_AKAtWEwpcj): Add and subtract a two-digit number and ones mentally and using concrete/pictorial representations
- [Fluent adding and subtracting within 100](https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-100-mt_cChv2j_-Da): Fluently add and subtract within 100 using strategies based on place value, properties of operations, and the relationship between addition and subtraction
- [Adding several two-digit numbers](https://lightmysky.com/learn/mathematics/adding-several-two-digit-numbers-mt_TiQbi027PE): Add up to four two-digit numbers using strategies based on place value and properties of operations
- [Two-Step Word Problems](https://lightmysky.com/learn/mathematics/two-step-word-problems-mt_yTWxkzzoOZ): Solve one- and two-step word problems within 100 using addition and subtraction, with unknowns in all positions
- [Adding and subtracting tens mentally](https://lightmysky.com/learn/mathematics/adding-and-subtracting-tens-mentally-mt_I5j1ZWo2cn): Add and subtract a two-digit number and tens mentally and using concrete/pictorial representations
- [Adding and subtracting two two-digit numbers](https://lightmysky.com/learn/mathematics/adding-and-subtracting-two-two-digit-numbers-mt_UQnAFPs83F): Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods
- [Mental and written addition and subtraction](https://lightmysky.com/learn/mathematics/mental-and-written-addition-and-subtraction-mt_wzAZ8qFDc4): Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures
- [Addition and subtraction strategies (age 7+)](https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-age-7-mt_zxST3MarI9): Explain why addition and subtraction strategies work, using place value and the properties of operations
- [Addition and subtraction within 1000](https://lightmysky.com/learn/mathematics/addition-and-subtraction-within-1000-mt_ewmuMMPAzP): Add and subtract within 1000 using concrete models, drawings, and strategies based on place value; understand composing and decomposing tens and hundreds
- [Adding and subtracting (age 7+)](https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-7-mt_SrrsLiJkr3): Add and subtract numbers with up to three digits using formal written methods of columnar addition and subtraction
- [Mentally adding and subtracting ones with 3-digit numbers](https://lightmysky.com/learn/mathematics/mentally-adding-and-subtracting-ones-with-3-digit-numbers-mt_oDU_8zMZjp): Mentally add and subtract a three-digit number and ones
- [Missing number problems (age 7+)](https://lightmysky.com/learn/mathematics/missing-number-problems-age-7-mt_XuHmIn2xje): Solve addition and subtraction problems including missing-number problems, using number facts, place value, and more complex methods
- [Fluent adding and subtracting within 1000](https://lightmysky.com/learn/mathematics/fluent-adding-and-subtracting-within-1000-mt_HFRYjTb-Z5): Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and the relationship between addition and subtraction
- [Numbers on a number line](https://lightmysky.com/learn/mathematics/numbers-on-a-number-line-mt_19j_5AuuQI): Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagram
- [Mentally adding hundreds to 3-digit numbers](https://lightmysky.com/learn/mathematics/mentally-adding-hundreds-to-3-digit-numbers-mt_xPqczp7zPX): Mentally add and subtract a three-digit number and hundreds
- [Mentally adding tens to 3-digit numbers](https://lightmysky.com/learn/mathematics/mentally-adding-tens-to-3-digit-numbers-mt_aHQ9kNt3is): Mentally add and subtract a three-digit number and tens
- [Adding and subtracting (age 8+)](https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-8-mt_mpS-JK_p_m): Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction
- [Two-step addition and subtraction problems](https://lightmysky.com/learn/mathematics/two-step-addition-and-subtraction-problems-mt_CDa5AVakLE): Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
- [Fluent addition and subtraction (age 9+)](https://lightmysky.com/learn/mathematics/fluent-addition-and-subtraction-age-9-mt_Yw1_4Nfsql): Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm
- [Estimating by rounding](https://lightmysky.com/learn/mathematics/estimating-by-rounding-mt_QaYfeVL-0C): Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning
- [Two-Step Equations](https://lightmysky.com/learn/mathematics/two-step-equations-mt_anAe11HAEH): Solve two-step word problems using the four operations; represent problems using equations with a letter standing for the unknown quantity
- [Mental addition and subtraction (age 9+)](https://lightmysky.com/learn/mathematics/mental-addition-and-subtraction-age-9-mt_MWXPiaTnEu): Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts
- [Adding and subtracting (age 9+)](https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-9-mt_-F_Lv_apzH): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
- [Checking Answers by Rounding](https://lightmysky.com/learn/mathematics/checking-answers-by-rounding-mt_G3sVFQNCme): Use rounding to check answers to calculations and determine appropriate levels of accuracy in context
- [Addition and subtraction strategies (age 10+)](https://lightmysky.com/learn/mathematics/addition-and-subtraction-strategies-age-10-mt_JH_6RpNWjr): Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning
- [Adding and subtracting (age 10+)](https://lightmysky.com/learn/mathematics/adding-and-subtracting-age-10-mt_M1tnXqmYbn): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals
- [Positive and Negative Numbers](https://lightmysky.com/learn/mathematics/positive-and-negative-numbers-mt_9QzSnn8m80): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances
- [Adding and Subtracting Negative Numbers](https://lightmysky.com/learn/mathematics/adding-and-subtracting-negative-numbers-mt_qX7X7uMzsY): Add and subtract with negative integers, reading each move as a direction on the number line, and settle what subtracting a negative does.