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First grader Sarah is working away on addition problems using math link cubes with no difficulties. But put away the hands-on manipulatives and her understanding seems to disappear with them. Have you ever had this happen with a student?

Manipulatives are awesome, but math students need to learn to visualize what numbers mean in their heads as well. Here are four teaching strategies from experts that teach that important skill.

1. Be Strategic About Using Manipulatives

Manipulatives really help to create a visual representation of a math concept you’re teaching. The next step is to help students store those visual images in their brains. For example, when you’re helping kids learn about where numbers fit on a number line, you can use Unifix cubes to build the number line. Once you’ve set up a number line, ask students to engage with the Unifix cubes in a very specific manner. Ask them to touch numbers on the number line at different intervals. Ask them to find 50. Ask them to count by 10s. As the students engage in these activities, they will build a visual image of the number line and the numerals that are part of the number line. Now, remove the manipulatives and have your students do the same tasks; this time, imagining the numbers and cubes as they count.

Sure, there are number lines in your textbook. But how about one that your students can walk on! With a number line, students see and learn the sequence and pattern of numbers in our number system. They see what number comes after 5 and what number comes before 5. They see what the number 15 has in common with the number 25. Building a number line on the floor gives students the opportunity to interact with the numbers in a tactile way, which helps them visualize the numbers and their values, even when the number line is gone. You can even play number-line-inspired games, like this one where children roll a die to move a butterfly along a flower path.

This principal insisted that a school-size number line be built in her hallway to build her students’ number sense. She encourages teachers to work with students using the giant number line in the hallway.

It might sound surprising, but actually giving kids the answers as you help them learn the facts is a strategy that works well for some children. One way to help fact families “stick” is to teach the family as a unit, including all of the answers. Here’s where it gets different: You can also ask the children to rehearse the fact with the answer visible. Asking the child to create a visual image of a math problem (complete with answer) and then re-create that problem visually, even with your example gone, can help facilitate fact recall.

To do this, show your students the side of the flash card that has the answer. Ask your students to see the card in their imagination. You might even encourage them to verbalize what they see: “Five plus three equals eight.” Then, hide the card and ask the students to try to see the card in their imagination. Ask them questions to help them along if they need it: “What is the first number you see?” You can also help students retain a visual image of the fact by asking students to write the fact in the air with their finger.

4. Introduce Fact Family Cards

A twist on this strategy involves fact family cards. Fact family cards have the facts of the family but not a sign. This way, the cards can be used for both adding and subtracting. Cover the answer for the problem you wish the child to solve with your thumb and then ask them to solve either the addition or subtraction version of the fact family. In the example below, if you cover the 10, then you will be asking the child to solve the addition problem of 3 + 7 or the problem of 7 + 3. On the other hand, if you cover the 7, then you are asking your student to do a subtraction problem. This can be more challenging because students have to recognize that the problem is 10 – 3, not 3 – 10. Seeing a card with the entire fact helps children create a visual image of the fact family.

It’s easy to make a set of these cards yourself. Some teachers even ask the children to make the flash cards as a way of reinforcing the facts. If you make your own fact family cards with your students, you can encourage students to write the facts in traditional form right on the card. This gives students another opportunity to practice visualizing the fact.

This article is adapted from the Lindamood-Bell On Cloud Nine program, which helps students learn to visualize math concepts.

The key to math success for students involves helping them create images that go with the numbers and mathematic principles that they need to understand. You can find more strategies for helping students learn to visualize math concepts and experience math success with On Cloud Nine® Visualizing and Verbalizing® for Math.