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Transitioning Students from Concrete to Abstract Addition and Subtraction - tips and freebie!

Updated: Jun 30, 2023

How to support your students moving from concrete to abstract understandings in addition and subtraction.

Explore effective strategies for transitioning students from concrete to abstract thinking in addition and subtraction. Discover engaging activities using vertical number lines, ideal for 1st to 3rd grade learning.

Guiding children through the transformational journey from using tangible counting aids to adopting abstract mental strategies for addition and subtraction is a monumental task. This leap is most palpable when learners face larger numerical values, and concrete resources are no longer practical. In such scenarios, scaffolding efficient mental strategies, like adding 10, can prove challenging.

Students using vertical addition / subtraction line to practice their maths skills.

The most effective technique I've discovered for reinforcing their understanding of larger number addition is the deployment of vertical number lines. Students are tasked with crafting their number lines up to 100, using pegs for counting or adding 10. Through color-coding, the children can visualize the addition of more significant numbers physically and mentally.


Students using vertical addition / subtraction line to practice their maths skills.

One engaging application of these vertical number lines is the 'Race to 100' game. In this, learners start from 0 and roll dice to move their peg up the line, aiming to reach 100 first. Alternatively, the 'Race to 0' game provides an enjoyable method for honing subtraction skills.


I've repeatedly implemented this strategy to practice counting on, adding 10, reaching to 10, and counting back. Students soon become familiar with deploying the lines as a tool to aid in addition and subtraction calculations. These techniques are exceptionally beneficial for learners from 1st to 3rd grade.



Vertical addition and subtraction line - resource to support students from moving from concrete to abstract operations
Vertical addition and subtraction line - resource to support students from moving from concrete to abstract operations

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