Solving basic math problems as an adult may seem like a breeze (especially with readily available calculators), but for young learners, understanding basic math operations can be a challenge. Younger students can grasp such ideas much more successfully with visual and conceptual explanations. Such understanding leads to higher retention of the material, quicker computation based on this understanding, and mental math strategies that will follow a child through their education.

Though potentially time-consuming at first, these key math strategies ensure that students gain the long-term benefits of a deep conceptual understanding that informs their math studies for years to come.

## Number Bonds

Number bonds are different pairs of numbers that add up to your original number, which we can use to change a challenging addition problem into a much more manageable one. The goal is to break the number down into its tens and ones. You can then add up the tens and ones separately to find your answer.

For example, a student may be asked to add 27 and 44. If they were to use the standard algorithm, it would look like the image below.

However, a young student solving this problem may just “memorize the steps” and not truly understand why they are “carrying the one.” The below figure shows how the student could use a number bond to solve this same equation.

## Open Number Lines

Young students are often asked to master subtraction with regrouping before gaining a conceptual understanding. To help students learn this skill, we turn to an open number line. Students build on to the “subtrahend” (the number being subtracted) with the goal of ending with the original amount.

If a student were asked to solve 94 – 37, the standard algorithm may look something like the image below.

Instead, a student can use an open number line that starts with 37 and then use tens and ones to build up to 94.

## Base Ten Blocks

Base ten blocks are another fantastic way to conceptually demonstrate addition and subtraction. Don’t worry, you don’t need actual blocks! Simply draw the base ten rods and singles to get the same effect. See two examples below of how they can be used for addition and subtraction.

*Base Ten Blocks (Addition)*

*Base Ten Blocks (subtraction)*

## Using the Distributive Property for Mental Math

Older students will face more challenging computation. As we saw with number bonds, any number can be broken down into more manageable numbers. Older students can use the distributive property to do more complex multiplication. For example, a student may be asked to do 87 x 6.

These are just some of the many creative and conceptual strategies students can use to solve traditional math questions! We encourage parents to help their kids practice their new and developing math skills with these key strategies.

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