Using Number Lines to Connect Math & Science Sandra Brodney, Ph.D., NBCT

Session Purpose To familiarize teachers with ways to link math and science in productive ways using number lines To provide examples from classroom based strategies that work

So….What’s the problem? There’s a disconnect between the math class and the science class when it comes to teaching scale. Relating multiples (skip counting) to scale Relating patterns to scale Relating midpoints to scale Not thinking of scale as a number line Not using both horizontal and vertical number lines. Put out three or four graduated cylinders. Why do kids struggle with measuring volume?

Scale vs Scalar for our purposes today The count-by number that is taught using number lines The unit of measure being used like centimeters, liters, degrees, time, et.

What are some examples of Number Lines Used In Science

For Linear Measurement What scales do you see? What scalars are being used?

For Temperature What scales do you see? What scalars are being used?

For Measuring Volume & Capacity What scales do you see? What scalars are being used?

For Measuring Weight & Mass What scales do you see? What scalars are being used? Scales

For Measuring many other things… Meters

For Measuring Time Time keepers

For Measuring Degrees (or direction) In location and space…

For Sharing Data In Data Applications

What are the implications? All number lines have some things in common… Even increments (or roughly equal for open lines) The increments vary with the tool, purpose, and design of the line but within a line the increments should be consistent. Right (or up) means increase and Left (or down) means decrease. Any other way builds misconceptions. Determining increments must be taught. Number sense is essential to the process. Figuring out the increment means being able to count by different numbers until the correct one is found. Handout

Misconceptions with Equal Increments And how we are responsible for them… Failing to teach the concept of equal increments in any number line application Failing to use number lines with varying increments (aka scale) Free handing a number line to explain something quickly a graph with a vertical number line because you don’t have graph paper handy or a document camera Failing to have kids build their own number lines

Midpoints Extends the idea of equal increments to include fractional parts “Half” always means two equal parts or a point that is equidistant from two points on the line segment. Builds concepts of Odd and Even further than just “ends with 0, 2, 4, 6, or 8” (more info in a minute)

Activity: Midpoint Fun Sierpinski Triangles Fold and mark the midpoint of each side of your equilateral triangle. Connect the midpoints to create a new, downward facing triangle. Repeat the process for each of the three upward facing triangles.

Sierpinski Triangles With Midpoints Without Midpoints

Perfect Hearts Midpoint Fun Use a compass to find a midpoint by drawing arcs and connecting them.

Odd & Even from Midpoints Use a number line to determine whether a number is odd or even. What happens when I find the midpoint of an even number? What happens when I find the midpoint of an odd number? Activity: Number Sense on the Open Number Line

Scale Finding the “count by” increment Every number line is unique because each has its own scale. Improper scaling or never having been taught scaling is the number one reason why kids struggle with measurement, graphing, number lines…..SO Job 1 for every closed number line is determining scale or finding the “count by” increment. This must be reviewed and linked every time a new type of number line is introduced.

Activity: What’s the Scale? Determine the “count by” increment and fill in the missing numbers for the first 4 number lines. Discussion: What skills did you use?

Take aways… Math and Science are connected through number lines Number lines can be both horizontal, vertical or curved Number lines are connected to all kinds of measurement Think of measurement scales as a number line that counts by a multiple Use midpoints to help students learn scale