Reinforcing the Basic Facts—While Learning New Mathematical Concepts

by Louise Johnson

In recent years much emphasis has been placed on such topics as problem solving, patterns, algebra in middle-school math, geometry throughout the curriculum, and the use of technology in teaching elementary- and secondary-school mathematics. While these are all very important areas that should not be eliminated, the focus on them doesn’t mean you should avoid helping students learn some basic operations.

Students must be fluent in arithmetic computation. It is imperative that they have efficient and accurate methods and understand them. Memorization of basic facts and the ability to use basic processes, coupled with understanding, is important for the future study and application of mathematics. Students should know their basic addition, subtraction, multiplication, and division combinations. Not being competent in these areas can be a great hindrance to someone wanting to use mathematics to solve problems they encounter.

Many recent textbooks for students today do not contain as many drill exercises as were in textbooks used by their parents. The demand for the educated public to have excellence in the broader field of mathematics is greater today than it was when textbook companies were able to use considerable space for drill purposes.

It is important that the math program you select help your student develop a very good understanding of what it means to add, subtract, multiply, or divide numbers. That a program contains only a small number of practice exercises should not necessarily mean it is bad or that drill is not important. It means, rather, that we should look for ways of supplementing the lessons with short, well-planned drill exercises.

Before planning how to supplement a program, consider the student. One student may have the ability to memorize very quickly. Such a student may need only occasional practice. Another student may have more difficulty memorizing or may be older before mastering the basic facts. This student will probably need more frequent practice. One must be careful not to discourage the student who may have great mathematical talent but finds memorization difficult. Most students are capable of engaging in challenging mathematics and a good beginning can be helpful in getting them to pursue it, enjoy it, and be ready for any challenge God may give them in this area.

Drill Suggestions

The following are some suggested ways that drill can be done without disrupting the regular math lessons.

  • An oral drill on basic facts could be done while you and your student are doing other tasks at home. A written drill could be designed so the student could correct her work and keep a record of her own progress. As in other educational tasks, you will want to acknowledge success. Quick, timed drills (approximately five minutes) interspersed at various times during the school week can be very effective. These drills could be on basic facts or on the addition, subtraction, multiplication, and division processes.
  • Flash cards with the correct answers on the back can also be useful. At times you may wish to work with the student. At other times, a student could practice independently or get help from a friend or sibling. Once again it is important to keep a record of the progress.
  • The student who has access to the Internet and likes to use the computer may wish to try a good website for math games (Baseball, Soccer Shoot, Tic Tac Toe, and Math Car Racing).
  • If a student is having difficulty with particular addition, subtraction, or multiplication facts, practice with just one number fact per day. For example, several times during the day have the student repeat “nine times eight equals 72.” Also have him frequently write the product and suggest problems where the product could be used, such as, “ If I bought nine candy bars for my friends and each bar costs 8 cents, the total cost would be 72 cents.”
  • Have the student create an addition or multiplication table by filling in all the facts she knows. Help her recognize the patterns in the charts such as 7 x 6 = 6 x 7. As a new one is memorized have her write the sum or product in the chart. When the entire chart is filled in, have a special recognition day.
  • Instead of having the student fill in the addition or multiplication table as each fact is learned, have the table filled out and allow the student to black out each fact as it is learned. You may wish to have him repeat the fact at different intervals during the day before blacking it out. The thrill of visually seeing the learning progress and knowing he can practice those not known can be great motivating factors.
  • Ordinary tasks done in a home can provide excellent practice opportunities. Ask your student to calculate the amount of money needed to purchase groceries or to determine the number of plates needed when nine guests are sharing lunch with your family. If a double recipe is needed, ask for help to calculate the required ingredients.


Many games provide an excellent opportunity for practicing the basic addition facts. Determining the score for games such as Dominoes, Children’s Scrabble, Racko®, Ten Thousand, Phase 10®, Yahtzee®, or Rummy requires knowledge of addition facts.

For the purpose of memorization, gradually discourage students from counting on their fingers or from using other objects to help them get the answers.

You and your student can do this simple activity together. Have your student make cards numbered 1 to 25. Put the cards face down on any flat surface. After the student chooses two cards, decide whether he should add, subtract, or multiply the two numbers selected. If the solution is correct, the student keeps those cards. The game can continue for as long as you have time. Have the student count the number of cards collected. (Note: You may wish to add larger numbered cards.)

Sum of What Dice Game

The Sum of What Dice provides practice in both basic addition facts and mental arithmetic. The tools needed for the game are two dice, a playing strip for each player, markers, pencil, and paper. To make the playing strips, have each student write the numerals 1 through 12 on a strip of paper. Each player uses one strip.

Players take turns rolling the dice. On each turn the player may cover either the sum rolled on the dice or any two numbers that are still uncovered that add to the sum rolled. For example, if the sum 7 is rolled first, the player may cover a 7 or 1 and 6 or 2 and 5 or 3 and 4. A number can-not be used more than once, so if the 7 is covered early in the game and a 7 is rolled again, two other numbers with the sum of seven would have to be covered. If the player cannot play, she is out of the game and scores the sum of the numbers still uncovered on her playing strip.

Play continues until everyone is out. The person with the lowest score wins. Variations: 1. Use the sum of three dice and make the strip with numerals 1 through 18. The player covers one or two numerals as before. 2. Use two dice, number strips from 1 through 25, and both multiplication facts and addition facts. Use more numbers and bigger numbers to add when finding individual scores.

Problems of the Day

The following are some short problems of the day that can be given orally while you are fixing dinner or can be used to start a math lesson:

  1. How many potatoes are there in this pan? How many carrots are on the counter? How many potatoes and carrots are in all?
  2. There are six people in our family. Your friend Josh and his family are coming to dinner. How many are in Josh’s family? How many plates do we need to put on the table for the two families?
  3. Uncle Bob has three children, Uncle Paul has five children, and Uncle Norman has seven children. How many cousins do you have?
  4. How many miles did we travel today? How many miles did we travel yesterday? How many miles did we travel yesterday and today?
  5. John has 18 candies. In what ways can he share them with his two friends? Which ways would be equal shares?
  6. Suppose I baked 18 cookies yesterday, and you ate three, Mary ate one, and Dad ate five. How many cookies would be left?
  7. How many pairs of numbers can you give with the sum of 16?
  8. How would you make 25 cents if you had only nickels? How would you make 50 cents if you had only nickels? …only dimes?
  9. Sometimes students benefit from seeing relationship between numbers or patterns such as:
    • If 4 x 5 = 20, what is 8 x 5? If 4 x 6 = 24, what is 8 x 6?
    • If 10 x 7 = 70, what is 9 x 7?
    • If 8 x 7 = 56, what is 9 x 7?
    • If you know that 6 x 7 = 42, what is 7 x 6?
    • What is true about the sum of the numerals in the multiples of 9?9 x 1 = 99 x 2 = 18 (1 + 8 = ?)9 x 3 = 27 (2 + 7 = ?)9 x 5 = 45 (4 + 5 = ?) etc.

These are but a few of many ways to give your student needed practice in the basic arithmetic facts. You may wish to select one or more of these or others that work for your student. The important thing is that he or she gains those skills that are necessary to be successful and to enjoy the future study of mathematics.

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