At kindergarten level it is very easy to help your child learn arithmetic without using a textbook or program. You might continue to work without a text or program through first or second grade.
In The Three R's, Dr. Ruth Beechick outlines arithmetic courses without texts for first through third grades, although by third grade, most parents find it easier to use a text or program. (A chart that comes in The Three R's has a math side with a "Hundred Chart" and describes both easy and advanced activities to be used with it.)
I include here my own outline of how you might cover first grade without a text as an example.
First Grade Math without a Textbook
If we know our goals, we can put together our own program with learning materials and games. If you are inexperienced this might sound a bit overwhelming, so I have included an example here of how to do this.
Following is the list of educational goals for first grade with suggestions for teaching each concept. There is space to offer only one suggestion for each goal, but the ideas themselves should suggest other ideas to you.
• Counts backwards from 10 to 0—Use a number line or 100's chart (chart numbered 1-10 across, 11-20 second row, etc., to 100).
• Add numbers 0 to 10—Use objects such as beans, blocks, LEGOS, etc.
• Matches set with numbers 0 to 20—Write numbers on a large number line. Glue beans to popsicle sticks to represent each number. Match popsicle sticks to the number line.
• Add numbers 0 to 20—Use objects.
• Subtract numbers 0 to 10—Use objects or a one hundred chart or board.
• Subtract numbers 0 to 20—Use objects.
• Count, read, write numbers to 100—Count houses on your street, leaves on a branch, etc. Use chalkboard for writing.
• Recognize smaller/larger numbers to 100—Play war with card deck.
• Count backwards from 20 to 0 using objects.
• Recall addition facts to 10—Make or buy triangle flash cards. (Triangle Flash Cards have addends of one color in the bottom two corners, the sum in a different color in the third (top) corner. Cover the number to be answered.)
• Recognize that 2 + 4 is the same as 4 + 2 (commutative property)—Do with objects.
• Recognize addition and subtraction in various formats- horizontal and vertical—Show on whiteboard.
• Recall subtraction facts for numbers 10 or less—Use Triangle Flash Cards. Covering an addend rather than the sum changes the problem from addition to subtraction.
• Recognize quarters (money)—Use real money.
• Count coins to $.25—Use real money.
• Recognize time to the hour and half hour—Use a play clock with movable hands that has minute markings. The Judy Company makes small (approx. 4") clocks that sell for a dollar or two at most teacher supply stores.
• Recognize fraction shapes 1/2 and 1/4—Cut bologna, pizza, sandwiches, etc.
• Count by 10s to 100—Use dimes, or 100's chart.
• Represent two-digit numbers in place value form as tens and ones—String beads in groups of tens, keeping some as singles. Show how much easier it is to handle one group of ten that is strung together than ten single beads. Place value is one of the most crucial concepts!
• Read, write, and use expanded notation (60 + 9 for 69)—Using your beads, show numbers as separate groups of tens and ones.
• Perform two-digit addition and subtraction without carrying—Use the beads.
• Name the days of the week—Read the calendar every day.
• Select correct operation for problem solving (addition/subtraction)—Give oral word problems that apply to real-life situations. Ask them to explain how they arrive at their answer. Discuss the process.
• Find practical applications of arithmetic—Explain how math helps you in the grocery store, in making other types of purchases, or in building projects.
• Identify and continue simple patterns—Play a "What comes next?" game—Give numbers such as 2,4,6,8, and ask, "What comes next?"
• Select, collect, record, or organize data using tallies, charts, graphs, tables—Record weather on chart and tally in chart form how many leaves each child collects.
Whether you use a text or not, at younger levels you should be using lots of hands-on activity and experience. Sometimes common items you have around the house will work as well or better than specially designed "math manipulatives." Some such items might include:
• money—real money or a cash box of play money
• household items (especially in the kitchen) e.g., beans, measuring cups, ruler
Games and other learning "tools" that you should consider using might be:
• chalkboard or whiteboard
• Triominoes (3-sided dominoes game available at toy and game stores)
• games that involve counting, number recognition, sequences, simple addition, money, and number relationships (e.g., Yahtzee® and old favorite board games such as Life and Monopoly.
At older levels, a text can serve as a guideline to help you cover all the concepts for the grade level. You can supplement with manipulatives (objects for learning math concepts), games, and activities. If you have a wiggly child with a short attention span, at all levels you should try to substitute experience and activity for workbooks whenever possible. Whatever their learning style, all children can experience the usefulness of math through such activities as budgeting and grocery shopping; planning, measuring, and building a project out of wood; or keeping records of their own income and expenditures.
® copyright 2005 Cathy Duffy