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Teaching Math 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! Consider these tips for teaching math 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. Here are some ways to offer those representations.

  • 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.
  • Count numbers forward and backward out loud. Hearing, saying, and repeating will solidify the numbers sequences.
  • 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.
  • Go over number “families.” 0+4=4, 1+3=4, 2+2=4, 3+1=4, 4+0=4

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. Although manipulatives will continue to be very helpful, it is important for children to start memorizing math facts instead of relying on fingers or other counters to help them add, subtract, multiply, and divide.

  • 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.
  • When you notice that you are using math yourself, explain what you are doing and ask for your child’s help.
  • 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.
  • Practice writing numbers in Roman numerals.
  • 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.

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.

  • Next time you take a road trip, tell your student the mileage you have to travel and the speed at which you will travel. Ask him or her to calculate how long it 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, let your child calculate the tip.
  • Let your child calculate the sales tax on your next bill of groceries.
  • Take each digit in today’s date and square and cube each one.
  • Find different objects around the house and let your child find the surface area and volume of them.
  • Shop the sales racks and have your child calculate how much the discount is and how much the sale price is.
  • Record daily temperatures. Now find the mean, median, and mode of your temperatures.
  • 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?
  • Let your student make a pie chart of your monthly budget.

Learning to Reason

9th - 12th Grade

In high school, math is much more abstract. Your student will begin studying algebra, analytical geometry, 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.

  • Let your student watch Khan Academy or other online videos to explain difficult math concepts.
  • Ask a friend or family member to help your student with assignments.
  • Try to look for practical applications of math. 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.
  • Give your student his or her own ruler, protractor, and compass.
  • Invest in a good scientific or graphing calculator for your  student.
  • If your student decides he or she does not want to take higher math classes, find out what your state’s requirements are. Then, choose classes like computer math, consumer math, fundamentals of math, integrated math, math applications, practical math, pre-algebra, probability, or statistics.

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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