Making Math

• Purchase celery (stalk/stem), carrots (roots), cucumber (fruit), broccoli (flowers), cauliflower (flowers), lettuce (leaves), snap peas (seeds), onions (bulbs), radish (roots), tomatoes (fruit), and spinach (leaves). Compare size and shape. Sort fruits and vegetables. Sort according to part of plant. Wash, cut, chop, and enjoy the salad.

• Empty contents of one bag of 18-bean soup. Sort beans. Compare sizes. Make soup.


Graphs provide visual representations of comparisons and classifications. Young children need concrete experiences creating and interpreting many types of graphs: pictographs, symbolic graphs, real graphs, and bar graphs. Pictographs use actual pictures of objects (photographs of people), symbolic graphs use symbols to represent objects (paper cookies), real graphs use real objects (hats or shoes), and bar graphs use columns to represent a quantity.

Making Math

• Ask family members if they prefer grape, cranberry, or orange juice. Graph results. Other graph possibilities include favorite cookies, ideal lunches, preferred pizza toppings, and favored yogurt flavors.

• While shelling peanuts, graph the number of peanuts in each shell.

Introductory Geometry

Circle, square, triangle. Shape recognition is one of the first geometric skills a child learns, paving the way for intermediate skills including symmetry, fractional parts, perimeter, area, and volume. Directional skills—the ability to determine left, right, north, south, east, and west—set a foundation for following directions, navigation, and grid work.

Making Math

• Discover symmetry in an orange slice, a hard-boiled egg, an onion, or a candy bar.

• Measure the circumference of pita bread with a string. Use a ruler to measure the string, and discuss the concept of inches. Introduce diameter and radius. Measure both. Cut the bread to make a semi-circle. Make a sandwich for lunch.

A diverse exposure to pre-number skills enables children to comprehend number concepts. Repetition and life application solidify a pre-number foundation to fortify intermediate and advanced equations and postulates.

Number Skills


Children walk through the toddler and preschool years identifying and reciting numbers. Parents beam with pride. Their children have embarked on the counting adventure.

There are two types of counting: rote and rational. Memorizing and reciting the numbers in order without associating a number with a group of objects is defined as rote counting. This stage varies in length from child to child. With repeated hands-on activities, children initiate rational counting, assigning one number to one object. This is called one-to-one correspondence. Assigning the correct number to a group of objects, first with groups of one to five items and moving rapidly to sets up to ten, is the last major milestone in the counting process. Along the journey, children learn to count backward and determine if numbers precede or follow other numbers. Rote and rational counting provide the foundation for number computation skills.

Making Math

• Model counting whenever possible. Count scoops of flour, strawberries in a quart container, blueberries in a muffin, or silver-dollar pancakes on a plate.

• Count M&M’s in groups of ten. Count by tens to find out how many M&M’s were in the bag.


Once a child has moved past the conceptual level of number and into the symbolic stage, computation—addition, subtraction, multiplication, and division—can be taught. Instruction should include opportunities to represent equations concretely (with objects), verbally (with words), and visually (with symbols). Oral word problems encourage auditory processing.