Our children love math! It hides in their sandwiches, seasons their spaghetti, and sweetens their apple pie. From the time our children peek over the table edge or push a chair up to the kitchen counter, they investigate, predict, collect data, and discover. The result: they understand. In the Bastian home, math instruction is multi-sensory, hands-on, and delicious, keeping young ones asking for more.
Can children really like math? Yes! Placing concepts into children’s open hands invites them to learn. As they weigh objects, measure ingredients, estimate quantities, and calculate numbers, they internalize concepts which, for some children, are nothing more than symbols on a page. Math becomes a part of life, real and useful.
The kitchen is a perfect place to teach and reinforce math concepts. Cups of water and corn syrup, measured, weighed, and compared, can be heated and transformed into a tasty pound of peanut brittle. Folded, deli-sliced cheese demonstrates equivalent fractions. The weight of a bag of flour can be estimated and confirmed with a kitchen scale. Concepts presented in digestible, practical, and relevant chunks dispel common math fears and anxiety.
Eliminating a parent’s fear of math is the first step in building math confidence in children. These fears often linger from negative personal experiences or a lack of understanding what, when, and how math can be taught. Knowledge complemented by useful tools—scales, measuring cups, tape measures, thermometers—makes math fun and relevant. Empowered and confident, parents often grasp math for the first time in their lives, and their contagious excitement invites children to enthusiastically embrace math.
Pre-number concepts are vital to understanding the value of numbers and include patterning, seriation, comparing and classifying, graphing, and introductory geometry. Each skill adds flavor to the number stew simmering in a child’s mind.
Patterns surround us. A newborn’s eyes focus on color, shape, and design. Young children recognize patterned stripes in candy canes and colorful arrays on dessert trays. Recognizing patterns in the world, and eventually in numbers, is foundational to math. Opportunities to describe, reproduce, and create patterns expand understanding and prepare children for numeration, prediction, and reasoning.
• Make lasagna, patterning ingredients: sauce, pasta, cheese, sauce, pasta, cheese. Draw a visual representation.
• Pattern fruit, cheese cube, or veggie kabobs.
• Open a package of Starburst chews on the seam. Notice the pattern. Extend and incorporate additional skills for multi-level learning: sort and graph flavors, add colors (4 orange and 4 cherry equal 8 candies), write a multiplication equation to represent the package (4 groups of 3 candies equals 12 total candies), label each flavor as a fraction of the whole package (orange is 4/12), and discuss equivalent fractions (4/12 equals 1/3).
Seriation is the ability to order objects in a series. Instruction begins with arranging objects according to one characteristic, generally length or size, and is reinforced with attributes of weight, color, amount, or cost. Seriation is a stepping-stone to comparison and classification.
• Build Cheez-It towers. The first tower is made of one cracker, the second of two and so on.
• Arrange the carrots from a 1-pound bag according to length. Weigh carrots on a kitchen scale and order according to weight.
Comparing and Classifying
Comparison, the ability to observe and analyze two or more objects based upon their differences, is the converse skill of classification (sometimes referred to as sorting), which focuses on the similarities of objects. When introducing comparison and classification, focus on a familiar feature, likely color, size, or length. From this foundation, two or more attributes can be considered, perhaps color and weight, texture and taste, size and origin, or length and use. The ability to discover and express similarities and differences in two or more objects is the first step toward comprehending set notation and computation.
• 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.
• 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.
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.
• 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.
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.
• 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.
• Add two sets of stick pretzels. Write the equation (symbolic expression).
• Cut an apple into eight slices. Eat one slice and write the corresponding equation. Continue, reinforcing the subtraction concept.
• Place ten cookies on a plate; divide evenly among the people at the table. Discuss remainders, if necessary.
• Add to find the number of pints in a gallon. Multiply to find the number of pints in two, four, or six gallons.
How many jellybeans in a handful? Children learn estimation skills once they comprehend quantity. Introduced with amounts smaller than twenty, estimation skills build quickly to collections of one hundred and beyond. Familiar, appealing objects, ideal for beginning estimation work, create a framework for intermediate problem-solving strategies.
• Estimate contents of a given package: baby carrots, radishes, raviolis, oranges, etc. Write the estimations of each family member. Count. Whose estimate was closest?
• Hand a child three baking potatoes and ask him to estimate the weight. Record the estimate. Weigh potatoes on a kitchen scale. Subtract to find the difference.
What child isn’t fascinated with tape measures, kitchen scales, and turkey basters? Fascinating tools make math memorable. Exploration and experimentation are integral components of a child’s first attempts at measurement, which begins with non-standard units—candy bars, saltine crackers, spoons, and Twizzlers—and inches toward standard units—inches, feet, and yards, as well as millimeters, centimeters, and meters. Measurement concepts include time (elapsed and actual), weight, capacity, and area.
• Compare 1 pound of several items: 1 pound of rice, 1 pound of lima beans, 1 pound of potatoes, 1 pound of cream cheese. Discuss.
• Measure the square area of the kitchen table with saltine crackers.
• Bake and cook. Double and half recipes.
Instruction for place value in a base ten number system begins when a child counts ten objects in a set, identifies a quantity of ten, and combines groups of ten to create larger sets. Real-life experiences with multiple sets of ten are a prerequisite for learning addition with carrying and subtraction with regrouping.
• Beans, pasta, crackers, and small candies make excellent teaching tools. Place a handful on the table and help the child make groups of ten. Extras are placed in a separate set. The parent reinforces the concept by stating, “Make ten and count extras.” Together, parent and child count by tens and then add the extras.
Fractions, Decimals, and Percentages
The kitchen fosters opportunities for learning, practicing, and applying fraction, decimal, and percentage concepts. Exploration and part-whole vocabulary internalizes piece and portion skills. As children progress to the symbolic stage, reading fractions, decimals, and percentages, they easily associate parts and pieces to the numbers they represent.
• Cut sandwiches into equal parts.
• Measure and prepare ingredients for a cherry pie. Bake, slice, and discuss in fractional terms.
• Describe a box of assorted popsicles in terms of which a portion of the box is represented by each flavor. Draw pictorial representation.
Mouth-watering math feeds a child’s natural curiosity. A learning laboratory, the kitchen provides a rich environment for children to measure and pour, divide and cut, estimate and portion. The kitchen, the heart of the home, invites learning, encourages sharing, and promotes thinking—a perfect place to be immersed in math with the ones we love.
Cheryl Bastian and her husband Mike have six children, aged 21 to 4, and anticipate the birth of another blessing in February 2011. Homeschooling since 1993, Cheryl organized and led a Central Florida support group, mentors current leaders, and remains active in the homeschooling community. As an author and speaker, Cheryl encourages parents to embrace the education and training of their children. Her books and resources are available at www.cherylbastian.com.
Copyright, 2011. Used with permission. All rights reserved by author. Originally appeared in The Old Schoolhouse®Magazine, Spring 2011.
Visit The Old Schoolhouse® at www.TheHomeschoolMagazine.com to view a full-length sample copy of the print magazine especially for homeschoolers. Click the graphic of the moving computer monitor on the left. Email the Publisher at Publisher@TheHomeschoolMagazine.com.