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Using Math Manipulatives Stage by Stage

No matter where you or your child falls on the love-hate spectrum, teaching math does not have to be an ordeal! One of the best ways to help make math more enjoyable for parent and student alike is to use manipulatives. Consider these tips for incorporating math manipulatives throughout your homeschool journey.

Starting out

PreK - 1st Grade

During this stage, children learn that numbers actually represent objects, that shapes have names, and that patterns are part of life. Their understanding of math is very concrete, meaning they need physical representations of math concepts, otherwise known as manipulatives. But, that doesn’t mean you have to spend a great deal of money on special resources. Everyday items and routines work just as well as designated tools and resource. Here are some examples of math manipulatives for this stage:

  • Make chore time math time. Count plates as you set the table. Count the cups of flour you put in cookies. Count the pairs of socks as you fold laundry.
  • Use snack time for simple addition and subtraction. Say, “Three crackers and three crackers make six crackers.” Then, “You had six crackers, and you ate one. Now you have 1, 2, 3, 4, 5 crackers.”
  • Give your child an egg carton and some small objects like buttons or pompoms. Show him or her how to sort them by color and then count how many of each color there are.
  • Practice writing numbers. For small children, write numbers with dashed lines for them to trace. Writing numbers in a pan of salt, rice, or shaving cream will give a multi-sensory experience.
  • Color-by-number is a great way to teach number recognition. If your child is still a non-reader, color the numbers in the key the correct color so they can visually match numbers and colors.
  • Play games like Chutes and Ladders, Hi-Ho Cherry-O, or number Bingo.
  • Ask your child to draw two houses, three trees, etc.
  • Count beads as you string them. Practice stringing them in patterns.
  • Get some shape stencils and show your child how to make different objects by combining shapes – a circle and a triangle make an ice cream cone.
  • Lay out a pattern of colored objects and ask your child what comes next. Now ask your child to make a pattern for you to complete.
  • Make a store in your kitchen and use play money to go shopping.
  • Use a balance scale to compare the weights of objects.
  • Put two groups of objects on the table and ask your child which one has more or less.
  • Talk about how much coins are worth and practice counting them.
  • Use connectable cubes to make groups of ten and demonstrate place value.
  • Cut shapes into halves and quarters and let your child put them together to make a whole.

Getting Excited

2nd - 4th Grade

At this age, children begin seeing how numbers are applied in real life. They will feel very grown up when they learn to make graphs, measure things, tell time, count money, and write the date. During this stage, it is important for children to start memorizing math facts instead of only relying on fingers or other counters to help them add, subtract, multiply, and divide. Even so, there is no reason to discontinue use of aids, and manipulatives will continue to be very helpful through this stage and beyond!

  • Continue incorporating manipulative suggestions from the Starting Out stage, adjusting as needed. For instance, upgrade shape-related manipulatives to include three-dimensional shapes like spheres, pyramids, etc. This will offer recognition and familiarity that will prepare them for the basic geometry they’ll learn in the next stage of learning.
  • Write three digits on separate pieces of paper. Now ask your child to arrange the numbers to make the biggest number possible and the smallest number possible.
  • Create a daily schedule and give it to your child.
  • Help your child save up for something. Give him or her a jar and draw a meter. Every time he or she adds tooth fairy, birthday, or Christmas money, color in the meter.
  • Play Math Facts War. Instead of one card, put down two. Add, subtract, or multiply the two cards to see who wins.
  • Make something in the kitchen and have your child help you double or halve the recipe.
  • Give your child is or her own ruler, yardstick, and measuring tape. Ask for measurements of different objects.
  • Use a family calendar and let your child add events or cross off days.
  • Create a graph of temperatures, precipitation, favorite fruits, favorite colors, or favorite pets.
  • Teach both English and metric weights and measures with measuring cups and spoons and packages of food.
  • Write fractions and decimals on separate index cards and let your child match the equivalents or put them in order.
  • Make a fraction pizza out of poster board. Cut the pizzas into different fractions and practice finding equivalents.
  • For auditory learners, sing or chant math facts.
  • For kinesthetic learners, do jumping jacks or toe touches while repeating math facts.
  • For visual learners, copy math facts in different colors.
  • Although many manipulatives can be replicated with inexpensive household items, if possible invest in a set of base ten blocks. These can be used all the way through the elementary years and on into early algebra courses, so they’re well worth the expense.

Beginning to Understand

5th - 8th Grade

Now your student should be moving from concrete numbers that can be easily represented by objects to more abstract numbers that require the imagination. Students will move from simple shapes to 3D solids and will begin finding perimeter, area, surface area, and volume. Math problems become more complex and sometimes include unknowns (x). These are the foundations for algebra. Your child will become better at working with ratios, decimals, and percentages.

Real life offers great manipulative usage! Here are some ways to take life experiences and utilize them as manipulatives, of a sort, to make abstract concepts more tangible.

  • Next time you take a road trip, tell your student the mileage you have to travel and the speed at which you will travel. Walk him or her through the processes needed to mentally estimate how long the trip will take you.
  • Choose a wall to paint. Calculate the square footage of the wall and how much paint will be required.
  • When you eat out, help your child calculate the tip.
  • Help your child calculate the sales tax on your next bill of groceries.
  • Find different objects around the house and let your child find the surface area and volume of them.
  • Pick a room to rearrange, even if just “on paper.” Measure the room and the objects and create a scale of each on graph paper. Then use the pieces to rearrange and see how each item might fit into the room. Be sure to account for windows and doors!
  • Shop the sales racks and help your child calculate how much the discount is and how much the sale price is.
  • Record daily temperatures. Each month, find the mean, median, and mode of your temperatures.

Although your middle schooler will probably feel like he or she has outgrown many of the manipulatives that have been staples throughout the years, there are still several great options for progressing into higher math. Here are some ideas:

  • Buy your student his or her own compass, protractor, and ruler. A pack of graph paper would also be handy.
  • Use dice to calculate the odds of rolling a certain number. What numbers are most likely to be rolled?
  • Use fraction and pie graph manipulatives to work out concepts such as budgets. This will also help demonstrate the correlation between fractions, percentages, and decimals and how those concepts work in real life (like budgeting!).
  • Square patty paper is an incredibly inexpensive resource that can help with introducing geometry concepts. Cut and fold the paper to help demonstrate angles, sides, and other foundational geometry concepts in a hands-on manner.
  • Continue to base ten blocks as you deal more with abstract concepts such as negative numbers, squares, ratios, etc.
  • Add a set of algebra inserts to your base ten blocks to help you introduce the concept of unknown numbers. Show that the flat surfaces indicate that you might know what place the number holds (ones, tens, hundreds, etc), but not the exact number.

Learning to Reason

9th - 12th Grade

In high school, the abstract nature of math becomes the full focus. Your student will begin studying algebra and analytical geometry, then possibly move on to trigonometry and calculus. Depending on your goals for your student, your student’s talents, and your student’s personal goals, you may decide not to pursue the highest math level possible. But, the continued use of manipulatives can potentially be a deciding factor when it comes to your student’s ability to grasp abstract math.

  • Let your student watch Khan Academy or other online videos to explain difficult math concepts.
  • If you haven’t already, make sure your student has his or her own ruler, protractor, and compass. Encourage your student to draw and create, utilizing hands-on activities to reinforce abstract ideas.
  • Utilize the base ten blocks as long as possible. Even in higher math, starting with a tangible, visual foundation can help the abstract building blocks make more sense.
  • Invest in a good scientific or graphing calculator.
  • Continue to utilize some of the practical applications of math that were explored in the Beginning to Understand stage. Algebra can be used to make conversions while cooking. Trigonometry can be used during land navigation. Geometry can be used in woodworking. Calculus can be used in engineering, medicine, or statistics. Real life use of math not only helps cement concepts, but also reminds you and your student that upper level math really is worth the investment!

Tiffany Ivie Orthman, M.Ed., is a second-generation homeschooler and Curriculum Coordinator for Well Planned Gal. She received her Masters of Education in Curriculum and Instruction from American InterContinental University Online in May, 2011. She is married to the man God chose for her, David, and is a work-at-home mom with four boys aged 8 years, 6 years, 4 years, and 2 year. She also serves as a Trustee for the Christian County Library located in Ozark, MO. Her passions are researching anything, participating in motorcycle ministry with her husband, listening to theological podcasts, and ruling the world through rocking cradles.

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