Fun Ways to Build Numeracy with Number Lines

A recently published study has got us thinking about number lines. German researchers taught first graders to walk along an unmarked number line on the floor to show where certain numbers (78, 15, etc.) would be. Compared with a group that learned simply to point to the right place on a smaller number line, the group that used gross motor movements performed better on various addition tasks afterward.

Used creatively, number lines certainly have a lot of potential.

Number lines are often used in classrooms, particularly with young children learning early math skills or middle school students working on negative numbers for the first time. But number lines’ potential for helping students develop numeracy skills (sometimes called “number sense”) is vast, and we think they deserve to be a bigger part of math education for learners of all ages. Here are some fresh ideas that will help unleash the power of number lines:

• Want a simple way to make number line use more tactile? Draw a number line in permanent marker just under the closure of a slider Ziplock bag. Students can move the slider from one number to another as they use the line to help them solve problems. Sandwich bags work well for lines showing 0-10, and gallon-sized bags can be used for longer lines with more numbers.

• Help a younger child draw a number line on the sidewalk using chalk, or on a big whiteboard or butcher paper with markers. Show him how to make the distance between numbers uniform by using the length of his foot or the width of his hand to measure.

As the study above shows, movement can help lots of young children grasp concepts. Engage an energetic child by making a giant number line to use on the floor. Write the numbers with sidewalk chalk or write on separate pieces of paper that can be taped down. (Plan to use this a lot? Get a scrap of carpet or an inexpensive carpet runner and make the number line with duct tape or paint, then roll up your reusable number line between uses.) There are almost endless ways to use this; here are a few ideas:

• Ask the child to hop along the line in a pattern: land on odd numbers with one foot and land with two feet on even numbers.

• Show/say a simple number sentence (e.g. 5+2 or 7-4) and ask her to “jump it out” or “stomp it out” by starting on the correct number and hopping or stepping to the next number in the equation. She should count aloud as she moves along the line to find the answer. Note that this will require some pre-teaching.

• Ask student to jump along the line while counting by 1’s, 3’s, etc. Help her to recognize that she has to make bigger and bigger jumps as she counts by bigger and bigger numbers. 

A tailor’s measuring tape makes a great number line. Unroll it and ask the student to place paper clips along it at intervals as he skip counts. Colored paper clips can be used for different skip counting intervals (e.g. 2’s vs. 4’s). Ask the child to remark on how the different intervals look and, through questioning, try to help him make generalizations. For example, he might notice that the spaces between the paper clips are larger when he skip counts by bigger numbers. Or he might see that the space between clips when he counts by 4’s is twice as wide as the spaces when he counts by 2’s, and 4 is twice as big as 2. Keep a record of these observations. There are also commercially available number lines.

Give a student a blank number line with only the first and last numbers labeled. The scale can be varied according to the student’s experience with number lines. Ask her to estimate the placement of various numbers by drawing a dot and labeling it. She can check her own work with a master number line drawn or printed on a transparency that she can lay over her work; punch and label holes in the transparency so that she can mark the correct placement on her paper.

Help a student see the relationship between a pictorial fraction (e.g. a “pie” with some of the slices shaded in) and a fraction on a number line. Present a student with a shape shaded to show the fraction 1/2 and a number line that goes from 0 to 1, and ask him to estimate where to place the fraction on the line. Help him to understand that half of the shape means he should move halfway along the line. Try the same exercise with other pictorial representations of different fractions.

Students often understand fractions more readily than decimals. A number line can be used to harness a child’s understanding of fractional quantities to help her grasp the correlation between fractions and decimals. Help her construct a number line that goes from 0 to 1 with important benchmarks written as fractions above the line, like 1/3, 1/2, 3/4, etc. Underneath each benchmark, ask her to write the corresponding decimal (0.33, 0.5, .75, etc.). Help her to notice trends; for example, the number closest to the decimal point gets larger as the decimal gets closer to 1. Keep the number line to use as a tool for homework assignments.

Number line at top from Wikkispaces Classroom

Build Number Sense with Native Numbers App

Ever heard someone say that they're just not a math person? Native Brain's Dr. Michael Connell, developer of an innovative app called Native Numbers, doesn't buy it. Connell believes the idea that there are people who simply understand math and those who never will is not only false, it is damaging. His app, Native Numbers, is designed to teach any child aged four and up to intuitively understand numbers deeply enough to succeed in math in kindergarten, first grade, and beyond.

 

Before a child can easily crunch numbers in elementary school, a skill known as computational fluency, he must develop a solid number sense. The National Council for Teachers of Mathematics (NCTM) defines number sense as the knowledge that allows students to understand numbers and ways of representing them, appreciate relationships among numbers, and comprehend number systems.

Sound abstract? Much of it is, and it's precisely those abstract aspects of number sense that Connell worries are being left out of young children's early math education. Memorizing number symbols and learning to count in preschool is only a fraction of the number sense young children need to learn to be successful in math, according to Connell. The rote memorization that allows many kids to learn to count fluently is misleading; many of those kids don't possess a deep understanding about quantity and number relations. And as a result, they're not arriving in elementary school ready to learn computation. This leaves them with a flimsy foundation on which to build higher math skills, a worrying status for a subject as cumulative as math.

Native Numbers is much lauded by both parents and educators, and for good reason. Its carefully designed, adaptive curriculum provides youngsters with thousands of activities that will help them develop the kind of number sense that both NCTM and the developers of the Common Core Standards for math agree are critical. The app teaches kids number concepts, number relations, number ordering, and counting, and they're required to demonstrate mastery before the app allows them to progress to the next level of difficulty. Each activity has been thoughtfully crafted to discourage mindless jabbing at icons on the screen, and there aren't lots of bells and whistles thrown in simply for the sake of fun. Young children find Native Numbers enjoyable because it is designed to motivate them intrinsically, but it is a serious app without a shred of frivolity.

Both parents and experts have been mightily impressed with Native Numbers. And since this hefty, research-based curriculum is available for free on iTunes, anyone with an iPad and a young child should give it a try.

Help for Developing a Number Sense

When we work with children who struggle with math, we often find that they have not developed a strong "number sense" --  the feel for how numbers work, and such concepts as greater than, less than, and ordering. Since math is a cumulative subject, where each skill builds on knowledge of a another, children who do not internalize a number sense at an early age are at a disadvantage in learning more complex aspects of math.


It is this issue that Dr. Mike Connell sought to address in an app for the iPad called Native Numbers, developed by his company, Native Brain. As noted in the magazine of the Harvard Graduate School of Education, the app is based on extensive research as to how children learn specific skills. If your young child is drawn to playing on an iPad, you may want to consider making her playing time more constructive and check out this app, available on iTunes for under $10.

Get a Sense of Your Number Sense with Panamath

Research suggests that students’ achievement in math class may be related to their innate number sense, and it’s no wonder. Number sense, the intuitive recognition of numbers and numerical relationships, is something that animals—including humans!—throughout the world are born with. Panamath, whose name comes in part from the acronym for the Psychological Assessment of Numerical Ability, is an organization hoping to understand the relationship between in-born number sense and math achievement. Through a grant from the National Science foundation, they’re investigating number sense. And if you’re curious about how yours stacks up, their online test is an interesting (and free) resource.

The test is simple enough for even a young child to take: A series of colored dots flashes across the screen and test-takers must decide whether they saw more blue or yellow ones. Both accuracy and decision speed are measured. When the test is over, one can view one’s results compared with other same-age testers. Individuals may wish to take the test out of curiosity, but teachers and clinicians can download it in order to save students’ results. As more is learned about the relationship between number sense and math instruction, gauging a student’s innate skills could be very useful for shaping lessons.

Results not as high as you’d hoped? Never fear! Number sense, like just about every human ability, can be improved. Here are a few ideas for helping kids sharpen their number sense:

Represent Numbers with Different Objects

Pick a number, starting with a small number like five for very young kids. Ask your child to collect different objects and put them in groups that contain that number. (For example, your child might find five rubber bands, five grains of rice, five cotton swabs, etc.) Write the number on a several paper plates and load them with the objects. Point out that groups of ten marbles, ten pieces of puffed rice cereal, ten large crackers, and ten toy cars may take up different amounts of space, but they still contain the same number of objects. Leave the display out for a few days to help your child create an association between the number symbol and the number of items in the group, then try again with a different number.

Comparison Game

Play a guessing game in which you compare groups of different-sized objects with your child. For example, ask your child to cover her eyes and lay out four wooden blocks and seven beads. Then ask your child to look quickly at both groups and point to the one that has more. Next, count the groups to see if she was right. Make the game more challenging by laying out more objects and objects that are closer in size.

Practicing Estimation

There are infinite ways to do this with children. At the grocery store, ask your child to decide which line has the fewest people in it, then count the people in your line and other lines while you wait for the cashier to determine whether your child’s guess was right. Enjoying a treat of candy? Ask kids to guess how many pieces of each color they see or how many pieces there are altogether. Make the estimation games trickier by introducing proportions: Is your child’s little sister half as tall as he is? A third of the height of her father? Measure everyone to see. Is the area of the living room twice the area of your child’s bedroom? More? Less?

Motion Math Games

Evidence suggests that the digital games developed by Motion Math may help kids improve their number sense. The easiest of the games is appropriate for three- or four-year-olds, while other offerings will challenge and entertain kids through early middle school.

How Much is a Million? by David M. Schwartz

This outstanding picture book was made to help children understand large numbers, which can be difficult to conceptualize. No time to get to the library? The book is (of course) available as a charming video  on YouTube.

For even more ideas, investigate the “Number Sense and Place Value” series by NRICH, which contains a wealth of activities for helping very young and elementary-aged children to improve their number sense



This post contains our own ideas as well as inspiration from Panamath (www.panamath.org) and the National Council of Teachers of Mathematics.