1. Teach Math Metacognitive Strategies for Solving Computation and Word/Story Problems
DRAW A DD F A S T D R W
STAR
FIND
CAP
ORDER

2. EMIP-SL #4:
☞Students with math learning problems do not naturally employ problem solving strategies like successful mathematics students do...
☞ However they can learn and use them effectively when systematically taught to them by their teacher

3. What Are Math Problem Solving Strategies?
Efficient & learnable processes for:
1) general problem solving
2) solving a particular types of problems
3) developing conceptual understanding of important mathematics concepts
What do they include?
limited number of steps (3 to 7 steps)
accurately reflect the problem/concept
provide cueing
actions & thinking
they are taught

4. The DRAW Strategy for Whole and Rational Number Computations
DRAW (Mercer & Mercer, 1998) – provides students a strategy for solving addition, subtraction, multiplication, & division problems at the representational (by drawing) level or at the abstract level ("in" student’s "head"). Students who don’t need to draw the solution can bypass the draw process and move directly to writing the answer.
D iscover the sign: student finds, circles, and says name of computation sign.
R ead the problem: student reads equation.
A nswer, or draw tallies and/or circles and check your answer: see draw examples for each operation below.
W rite the answer: student writes answer to problem.

5. “Four times four…” or “Four groups of four is…”4
This means I need to multiply
“Four times four…” or “Four groups of four is…” 16

6. A nswer, or draw and check.
D iscover the sign.
½ x ¼ =
R ead the problem.
“one-half times one-fourth equals” OR “one half of one-fourth is”
A nswer, or draw and check.
W rite the answer.
½ x ¼ = 1/8
The DRAW Strategy with Operations with Fractions
This means I need to multiply.
Student draws a circle (or box) separated into fourths, chooses one of the four sections and divides it in half (one-half of one-fourth). Then student shades one of the two halves. The shaded in section represents one-eighth of the circle.

7. The DRAW Strategy for Solving Basic Algebraic Expressions and Equations (Allsopp, 1997). Provides students a strategy for independently solving basic algebraic equations involving variables.

11. DRAW for Algebra With Fractions: The following are examples of drawing solutions to algebraic equations and expressions with fractions:
½a =
Student draws a circle (or box) and divides it into two equal parts to represent “1/2a”. Then, student draws 8 tallies to represent “8.”
Student evenly shares the eight tallies among the two one-half sections of the circle. The student represents the value of “a” as the total of tallies in one-half of the circle.
a =

12. DRAW for Algebra With Fractions: The following are examples of drawing solutions to algebraic equations and expressions with fractions:
½a + ¼a =
Student draws two circles (or boxes); divides one circle into two equal parts and shades one part to represent “1/2a”. Then, student divides and shades second circle to represent “1/4a.”
Student combines the shaded areas into one drawing (representing ½ + ¼). Student then evenly shares the four tallies among the four parts of the circle. The student represents the value of “a” as the total of tallies in three-fourths of the circle.
a =

13. Strategy Instruction Solve: 3a + 2a + 5 = 20 C = 5a + 5 = 20
Example: CAP Strategy (for Abstract Application)
C = Combine like terms
A = Ask yourself, “ How can I isolate the variable?”
P = Put the value of the variable in the initial equation, and check if the equation is “balanced”
Solve: 3a + 2a + 5 = 20
C = 5a + 5 = 20
A: “To isolate the variable, I need to subtract 5 from both sides” 5a = ; 5a = 15; a = 3.
P: 5(3) + 5 = 20; 20 = 20 Yes, it checks.

14. Strategies for Solving Word/Story Problems
FASTDRAW
STAR

15. FASTDRAW
FAST
Step 1: F ind what you're solving for.
Underline the information that tells you what you are solving for.
Name the variable with a letter and write it after the question mark.
Step 2: A sk yourself, "What information is given?"
List useful information as you read it.
Step 3: S et up the equation.
Write the equation with the variable and the numbers in the correct order.
Step 4: T ake the equation and solve it.
If you cannot solve it from memory, use "DRAW" or "CAP" to solve it.
DRAW
Step 1: D iscover the variable, the operations, and what the left side of the
equation equals.
Step 2: R ead the equation, and combine like terms on each side of the equation.
Step 3: A nswer the equation, or draw and check.
Step 4: W rite the answer for the variable, and check the equation.
Helps students to determine what information is important and to set up an equation to solve the problem
Students use DRAW or CAP to solve the problem

16. FASTDRAW
FAST
Step 1: F ind what you're solving for.
Underline the information that tells you what you are solving for.
Name the variable with a letter and write it after the question mark.
Step 2: A sk yourself, "What information is given?"
List useful information as you read it and circle the number phrases.
Step 3: S et up the equation.
Write the equation with the variable and the numbers in the correct order.
Step 4: T ake the equation and solve it.
If you cannot solve it from memory, use "DRAW" or "CAP" to solve it.
Helps students to determine what information is important and to set up an equation to solve the problem
James and Suzette love to play video games. They both made some money at their part time jobs. So, they decided to go to the video store to rent their favorite video games. When they went to the store they found a section where each game could be rented for the same low price. James rented two games and Suzette rented three games. Altogether they paid $15.00 for the five video games. How much did each video game cost?
2a a = 15

17. FASTDRAW Students use DRAW or CAP to solve the problem 2a + 3a = 15
Step 1: D iscover the variable, the operations, and what the left side of the
equation equals.
Step 2: R ead the equation, and combine like terms on each side of the equation.
Step 3: A nswer the equation, or draw and check.
Step 4: W rite the answer for the variable, and check the equation.
Students use DRAW or CAP to solve the problem
2a a =
a = 3

18. STAR (adapted from Macinni & Hughes, 2000)
Example of a Structured Worksheet:
STAR Steps
Answers
Search the word problem
a. Read the problem carefully
b. Ask yourself, “What facts do I know?”“What do I need to find?”
c. Write down facts
____________________________________
Translate the words into an equation in picture form
a. Represent the problem (use Graphic Org.) and draw a picture

19. Strategy Instruction:
Answer the problem
a. Look for patterns:
1) What is the difference
between frames?
2) Look for recursive patterns and write numbers under GO
____________________________________
Review the Solution
a. Reread the problem
b. Ask, “Does the answer make sense? Why?
c. Check answer

20. Scaffolding Explicitness: Algebraic Story Problems
For some students, scaffold-ing the amount of cuing provided as they begin to learn how to set up an equation for solving the problem can be very helpful.
Initially provide structure for equation and phrases from story that represent essential elements of equation.
Then omit word phrases but maintain structure for the equation for solving the problem.
No cuing is provided.

21. General Problem Solving
FIND OUT
Look at the problem.
Have you seen a similar problem before?
If so, how is this problem similar? How is it different?
What facts do you have?
What do you know that is not stated in the problem?
CHOOSE A STRATEGY
How have you solved similar problems in the past?
What strategies do you know?
Try a strategy that seems as if it will work.
If it doesn’t, it may lead you to one that will.
SOLVE IT
Use the strategy you selected and work the problem.
LOOK BACK
Reread the question.
Did you answer the question asked?
Is your answer in the correct units?
Does your answer seem reasonable?
Adapted from MathCounts ( )

22. For Additional Examples of Strategies Visit…
Order of Operations
Basic Operations
Pew Eee, Many Dogs Are Smelly
D iscover the sign
R ead the problem
A nswer or draw and check
W rite the answer
The MathVIDS Website:
Specific problem solving strategies provide struggling learners with more explicit strategies they can use to solve specific types of problems or to use with general problem solving strategies. Specific strategies provide students with memory, attention, and metacognitive thinking deficits with a level of structure and cuing that assists them in becoming more active in their learning and problem solving. In fact, strategy instruction in the form of mnemonics, visuals, and graphic organizers are one of the most powerful instructional approaches for students with learning disabilities and other mild learning difficulties. You can find many more examples of metacognitive strategies by clicking on the link provided on this slide. Always remember though that no strategy in and of itself will solve any particular student’s mathematical difficulties. Students need teachers who are committed to teaching them strategies, how to use them, and provide them ample opportunities to apply them with scaffolded support, corrective feedback, and positive reinforcement.
Place Value
Long Division
F ind the columns.
I nsert the t’s.
N ame the columns.
D etermine the place value of individual numbers.