Ruler Games for 3rd Graders

A Dutch proverb says “Measure thrice before you cut once”, this explains the importance of any type of measurements in one’s life. One can measure time, weight, length, capacity etc. Time can be measured in seconds, minutes and hours. For measuring weights, capacity, and length, there are mainly two types of units: metric units and customary units. Metric units for weight include milligram, gram, kilogram etc while customary units are ounces, pound, ton etc. For measuring lengths the metric units are millimeter, centimeter, meter, kilometer etc. Customary units for length include inches, feet, yards, miles etc. Capacity can also be measured and the customary units are ounces, pints, cups, quarts, gallon etc. Customary units are widely used in the United States of America.

Lengths are more important than many other measurements in the fields of geometry, technical drawing, civil engineering etc. Rulers are mainly used for three purposes: to measure, to draw straight lines and as a straight guide for cutting with a blade.

Different Types of Rulers

In mathematics, children need to measure many things like a line segment, angles, sector etc. There are many types of rulers serving different purposes. Line segments can be measured using scale rulers.  The below picture is of a centimeter ruler that measures up to 20 cm.

Triangular scale rulers have different units on each of the sides. Triangular rulers are less likely to use in lower grades compared to scale rulers.

An angle, an important mathematical concept that would be introduced to children in higher grades, can be measured using a protractor.

Math Manipulatives and Activities

A first-hand experience of measuring the things around them using actual rulers would be an interesting activity for kids. They should be introduced to measuring objects using different types of metric rulers and inch rulers. Children should be taught how to read a ruler in inches or centimeters using these manipulatives. The ruler reading is something that kids learn in 2nd grade. Teachers can provide the children different types of rulers explaining about reading a ruler and ask the children to measure the object they see around and note down the ruler measurements. A 12 inch ruler would be adequate for measuring a black board or a desk. A 6 inch ruler can be used to find the lengths of pencils, pencil box etc.

There are many online rulers available which can be resized to a real size ruler. By doing this, these can be made to printable rulers.

There are many online math activities that allow kids to get practice in estimating and measuring the length of a given object. Measuring the familiar images that they see around can be fun math games for kids.

Or the ruler game for measuring a line segment shown using the ruler provided can also be very effective.

Online ruler games are available in metric and customary units. The difficulty level can be adjusted by choosing the appropriate units as well as the division of each whole.

SplashLearn feature practice problems for measuring the lengths of objects to the nearest inch/ half an inch and a quarter inch.

Measuring Halves and Fourths of a Whole

In second grade, kids measured lengths in whole units using metric and U.S. customary units. In third grade more accurate rulers, marking halves and quarters are introduced to kids.

Children in grade 3 have a basic knowledge of fractions which can be applied here. They already know that two halves or four fourths make a whole. They are familiar with the equivalence between fractions and fraction models to represent the fractions. Children have already learned how to plot or read fractions on a number line. This would help them relate the ruler markings with the number line.

When measurements on a ruler are till the half of a whole, each whole is equally divided into two. In an online 12 inch ruler, the first mark after 0 would be at ½, the second one at 1, the fourth one at 1½  and so on. There would be 24 marks on the 12-inch ruler.

When measurements on a ruler are till the quarter of a whole, each whole is equally divided into four. In a one inch ruler, the first mark after 0 would be at ¼, the second one at ½, the third one at ¾, and the fourth one at 1. In a similar way, each whole is divided into 4.

The below ruler measures halves and fourths of an inch:

Usually, 1/4 on a ruler is marked with equal heights but shorter than the ½ mark.

To measure an object, the child should make sure that one end of the object to be measured is at 0. To read a ruler, find the mark closest to the other end of the ruler.

In metric units, a millimeter ruler would divide each centimeter into 10 equal parts. A mm ruler is useful in measuring things which are less than one centimeter in length.

In most of the scale rulers available in the market, one side of ruler would be marked in centimeters and the other side in inches as shown.

Activity 1: Children can be asked to measure the heights of their classmates, correct to the quarter of an inch and list the measurements. The listed measurements can be plotted in line plot using a number line.

Let the heights in inches of 16 kids be as listed:

To make a line plot from the above list of heights, the children can determine the greatest and least value in the data. Here the least value is   and the greatest value is 51.

Children can draw a segment of a number line diagram that includes these extremes, say from 47 to 51, with each whole divided equally into 4 and marking up to the quarter of an inch. Note that it is not necessary to arrange the whole data from the least to greatest.

Now, the children can record each observation(height, in this case) by plotting a mark like a dot or a tick mark. If a data occurs more than once in the data set, it will pile up above that value.

So, the line plot of the above data can be done as:

Further, this line plot can be used to ask questions about the data collected.

For example, how many kids have the heights between 48 inches and 50 inches?

By counting the number of marks between 48 and 50, it can easily be found that the number of kids is 7.

What is the height that occurs the most?

The number of marks just above 50, 4, is the highest. Thus, the 50 occurs the most.

What is the height of the kid who is shortest?

As the number line increases from left to right, the shortest kids height would be marked on the left most. The mark on the left most occurs just above the number 47½. So, the shortest kid has a height of 47½ inches.

SplashLearn has similar practice problems for reading as well as representing data on a line plot.

Similarly, the heights measured in centimeters also can be tabulated and plotted. Since the kids have not been introduced to decimal numbers it is recommended not to use the metric unit for measuring up to the quarter of a centimeter.

Activity 2: Children can be supplied with real rulers that measure up to a quarter of an inch that can be printed from internet and seeds of various plants. They can be asked to make saplings at home and note down the measurements on every alternate day.

After two weeks, the measurements can be brought to class. Each of them can make line plots for the set of saplings for each measurement day. The questions analyzing the growth of the saplings can be discussed in the class.

Evaluation:

1. The left over chalk pieces after the previous class can be distributed among the kids and asked to measure the lengths correct to the quarter of an inch. What is the length of the longest piece? What is the length of the shortest piece?
2. Use a measuring ruler to find the length of a sandwich to the half of an inch.
3. A fidget spinner is kept on a paper ruler centered at 2. When it is spun, the circle formed touches the marks ¼ on one side 3¾ on the other side. What is the length covered by the spinner on the ruler?

Ans: The length covered by the spinner is from ¼ to 3¾. There are 14 marks between ¼ and 3¾ at a distance of a quarter of an inch. Each 4 marks would make a whole. So, 14 marks would make 2 and a half ruler inches. That is, the spinner covers 2½ inches.

1.  Use a digital ruler to measure an image of a ladder.