The meaning of addition
Students need to know more than just how to solve addition problems. If they are to generalize this skill to other settings and utilize addition in a variety of applications they need to understand addition including what addition is, what the + symbol means, and when to apply the skill.
The 5 examples listed are certainly not an exhaustive list of tools and lessons that could be used to teach this skill.
They are rather a sample progression from hands-on to abstract thinking!
Which step represents your students’ current level of understanding?
Consider introducing the meaning of addition without numbers at all! Adding a “scoop” to a “cone” creates and ice cream cone! Your students can practice putting these pictures into number bonds and equations to solidify their understanding of addition and the plus sign as meaning “put together”.
It is critical to use math vocabulary including the words “part” and “whole” as your students begin to understand addition!
Together with your students, explore sets of linking cubes to make the number 5.
Have towers of 1 blue, 2 red, 3 green, 4 yellow and 5 black available for your students to experiement with.
Record your students findings in number bonds and as equations. This will help your students to understand addition in hands-on, representational and written forms.
Provide your students with a variety of hands-on materials such as linking cubes or mini erasers and ask them to solve simple word problems with a put-together context.
As your students explore the context of the story problem, model the action of the problem in number bonds and record an equation that matches the context.
Continue to emphasis the language of “part” and “whole” as you put parts together!
If you take away the hands-on support, are your students still solid in their understanding of addition?
Continue to explore word problems. As you do, ask your students to model with math materials such as linking cubes or mini erasers.
Ask students to draw a picture that matches their math materials. This will support the transition from concrete to representational.
Given an addition equation with a missing total with sums to 10, can your students solve to find the total?
Before leaving this unit of study, be sure that your students know what an addition equation means (put together) and, given a problem, they have strategies (either hands-on, drawing or otherwise) to solve to find the total.
To connect the equation to your previous work, consider asking your students if they could tell you a story about a given topic that matches the equation!