Transcript Operations spring 12 - Math-4326

Helping Children Master
the Basic Facts
•
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
Copyright © Allyn and Bacon
2010
Using Problem
Structures
• P. 146
Reasoning Strategies
ADDITION
SUBTRACTION
• One more than and • Subtraction as
two more than
think-addition
• Adding zero
• Down Over 10
• Using 5 as an
• Take from the 10
anchor
• 10 facts
• Up Over 10
• Doubles
• Near-doubles
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 + 7
What 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 + 199
What are some other strategies for
solving these problems?
CROSS OUT SINGLES
1. 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.
2.
3.
4.
5.
35-18 =
140–35 =
298-99 =
1000–5 =
312-20=
Mastering the Basic Facts
(Effective Drill)
What to Do:
• Ask students to selfmonitor
• 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
Copyright © Allyn and Bacon
2010
Multiplication
• Arrays
Fact Remediation
1. 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.
Copyright © Allyn and Bacon
2010
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?