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

Make Your Own Word Problem Activity

At The Yellin Center, we often work with students who struggle with word problems. The difficulty can come from not being able to identify the salient information that is required to solve the problem. Other times, it can be difficult for a student to understand the language of a word problem, and to decide what “how many more” means in terms of mathematical concepts. Selecting the appropriate algorithm (sequence of steps) to use can also be challenging for some students. Regardless of the challenges, getting an in-depth understanding of how a word problem is constructed and how the language of the problem translates into mathematical concepts is important for students. One way to expose students to the structure of word problems is by having them construct their own. This is an activity I would usually give to primary students, and they would be required to select some of the information to create and solve a story (or word) problem of their own.

My Animal Story Problems activity always followed a lesson with guided modeling on how to create word problems. We would construct several word problems together as an entire class, being sure to clearly define terminology like “how many more”, “how many”, “how much more” and “all together” meant. I would then have students create word problems in small groups or with partners, and provide the opportunity for students to create their own on the board. It was only then that I would give students this activity to try their hand at independently creating word problems.

I have found that this activity gave me a great deal of insight into what areas my students were finding most difficult about word problems. It was often easy to determine if it was the phrasing of a word problem or selecting the right algorithms based on the given information that the student found challenging.

Note that the examples that follow use the metric system. This incorporates the Common Core standards for elementary grades, which incorporate metric measurements as early as grade two.

• Grade 2: “Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes and Estimate lengths using units of inches, feet, centimeters, and meters.”
• Grade 3: “Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).”
• Grade 4: “Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec.”

An example of a properly constructed addition word problem using the Animal Story Problems handout would be:

If a turtle is 8cm and a pig is 55cm tall, how tall are they all together?

8 + 55 = 63

Materials Needed

One Animal Story Problem Handout

Game Play Steps

1. Model how to construct story problems.
2. Explain activity rules to the students:

• Each student will select some of the information from the Information Section of the handout.
• They will then create and solve one addition problem.
• They will select two different pieces of information.
• They will then create and solve one subtraction problem.

      3. Allow students time to create their word problems.
      4. Gather handouts for assessment of their understanding of how a word problem is constructed.

Extension Activities

• Have your students create more than one addition and one subtraction by giving them multiple handouts.
• Have students create word problems in small groups or pairs to promote mathematical conversation skills.
• Have students create problems but not solve them. Then have students trade their handouts with other students and solve their friend’s equations.
• Have students extend their word problems to include distraction information. 

          For Example:
         If a turtle is 8cm, an own is 13 cm tall and a pig is 55cm tall, how tall are the pig and the turtle all together?   8 + 55 = 63


A PDF Version of the game can be downloaded for free.