helping children master the basic facts copyright © allyn and bacon 2010

Helping Children Master

the Basic Facts

• Copyright © Allyn and Bacon 2010

Copyright © Allyn and Bacon 2010

Developmental Nature of Basic Fact Development

• Phase 1: Counting Strategies—using object counting

• Phase 2: Reasoning Strategies—using known information to logically determine an unknown combination

• Phase 3: Mastery—efficient production of answers

Copyright © Allyn and Bacon 2010

Guiding Strategy Development

• Story problems• Reasoning strategies

Using Problem Structures

• P. 146

Reasoning StrategiesADDITION•One more than and two more than•Adding zero•Using 5 as an anchor•10 facts•Up Over 10•Doubles•Near-doubles

SUBTRACTION•Subtraction as think-addition•Down Over 10•Take from the 10

Number Sense, Mental Math, and Addition:

1. Use making and breaking apart numbers to find the sums.

A. 9 + 5 B. 4 + 8 C. 7 + 6

D. 9 + 7What are some other strategies for

solving these problems?

Number Sense, Mental Math, and Addition:

Find the sums. Use as many different methods as you can.A. 68 + 14 B. 27 + 49 C. 46 + 38 D. 92 + 14• Did you try these?

– Add tens, add ones, then combine– Move some to make tens– Add on tens then add ones (Number line)– Use a nice number and compensate

Number Sense, Mental Math, and Addition:

1. Use making and breaking apart numbers to find the sums.

A. 398 + 99 B. 89 + 298 C. 425 + 199What are some other strategies for

solving these problems?

CROSS OUT SINGLES1. Make a 3 x 3 grid.2. Roll a die nine times. 3. Each time a number is rolled all players write that number

in a square on their chart. 4. When nine squares are filled in, players find the sums of

the rows, columns, and diagonal, and record these sums in the circles outside the grid.

5. If a sum appears in only one circle it must be crossed out.6. The total of the sums that are not crossed out is the

player’s score for that round.

3 4 2

2 3 4

6 3 5

© Math Solutions (Burns)

How Would You Solve?1. 35-18 =2. 140–35 =3. 298-99 =4. 1000–5 =5. 312-20=

Copyright © Allyn and Bacon 2010

Mastering the Basic Facts (Effective Drill)

What to Do:• Ask students to self-monitor• Focus on self-improvement• Drill in short segments• Work on facts over time• Involve families• Make drill enjoyable• Use technology• Emphasize the importance of quick recall of

facts

What Not to Do:• Use lengthy timed tests• Use public comparisons

of mastery• Proceed through facts

in order from 0 to 9• Move to memorization

too soon• Use facts as a barrier to

good mathematics

Copyright © Allyn and Bacon 2010

Reasoning Strategies(Multiplication)

• Doubles• Zeros and ones• Nifty nines• Using known facts to derive other facts

Multiplication• Arrays

Copyright © Allyn and Bacon 2010

Fact Remediation1. Recognize that more drill will not work.2. Provide hope.3. Inventory the known and unknown

facts for each student in need.4. Diagnose strengths and weaknesses.5. Focus on reasoning strategies.6. Build in success.7. Provide engaging activities for drill.

Contextual Division Problems

• Ms. Wright has 28 students in her class. She wants to divide them into groups with 4 students in each group. How many groups will she have?

• Ms. Wright has 28 students in her class. She wants to divide them into 4 groups. How many students will be in each group?

Contextual Division Problems

• How could you distribute 231 M&Ms evenly among 5 containers?

• How could you evenly distribute 231 gum balls into packages of 5? How many packages could be filled?