• Math Problem Solving
• Help Solving Math Word Problems
• Solving Math Equations

Solving the Math Problem. The students who attended youcubed summer camp describe the power of mindset math in their own words! The National Council of Teachers of Mathematics (NCTM, 1980) recommended that problem solving be the focus of mathematics teaching because, they say, it encompasses skills and functions which are an important part of everyday life.

Related Pages
Solving Word Problems Using Block Models
Heuristic Approach to Problem-Solving
Algebra Lessons

Problem Solving Strategies

The strategies used in solving word problems:

1. What do you know?
2. What do you need to know?
3. Draw a diagram/picture

Solution Strategies
Label Variables
Verbal Model or Logical Reasoning
Algebraic Model - Translate Verbal Model to Algebraic Model
Solve and Check.

Solving Word Problems

Step 1: Identify (What is being asked?)
Step 2: Strategize
Step 3: Write the equation(s)
Step 4: Answer the question
Step 5: Check

• Show Video Lesson

Problem Solving Strategy: Guess And Check

Using the guess and check problem solving strategy to help solve math word problems.

Example:
Jamie spent $40 for an outfit. She paid for the items using $10, $5 and $1 bills. If she gave the clerk 10 bills in all, how many of each bill did she use?

Problem Solving : Make A Table And Look For A Pattern

1. Identify - What is the question?
2. Plan - What strategy will I use to solve the problem?
3. Solve - Carry out your plan.
4. Verify - Does my answer make sense?

Example:
Marcus ran a lemonade stand for 5 days. On the first day, he made $5. Every day after that he made $2 more than the previous day. How much money did Marcus made in all after 5 days?

• Show Video Lesson

Find A Pattern Model (Intermediate)

In this lesson, we will look at some intermediate examples of Find a Pattern method of problem-solving strategy.

Example:
The figure shows a series of rectangles where each rectangle is bounded by 10 dots.
a) How many dots are required for 7 rectangles?
b) If the figure has 73 dots, how many rectangles would there be?

Solution:

Rectangles	Pattern	Total dots
1	10	10
2	10 + 7	17
3	10 + 14	24
4	10 + 21	31
5	10 + 28	38
6	10 + 35	45
7	10 + 42	52
8	10 + 49	59
9	10 + 56	66
10	10 + 63	73

a) The number of dots required for 7 rectangles is 52.

b) If the figure has 73 dots, there would be 10 rectangles.

Example:
Each triangle in the figure below has 3 dots. Study the pattern and find the number of dots for 7 layers of triangles.

Solution:

Layers	Pattern	Total dots
1	3	3
2	3 + 3	6
3	3 + 3 + 4	10
4	3 + 3 + 4 + 5	15
5	3 + 3 + 4 + 5 + 6	21
6	3 + 3 + 4 + 5 + 6 + 7	28
7	3 + 3 + 4 + 5 + 6 + 7 + 8	36

The number of dots for 7 layers of triangles is 36.

Example:
The table below shows numbers placed into groups I, II, III, IV, V and VI. In which groups would the following numbers belong?
a) 25
b) 46
c) 269

I	1	7	13	19	25
II	2	8	14	20	26
III	3	9	15	21	27
IV	4	10	16	22
V	5	11	17	23
VI	6	12	18	24

Solution:
The pattern is: The remainder when the number is divided by 6 determines the group.
a) 25 ÷ 6 = 4 remainder 1 (Group I)
b) 46 ÷ 6 = 7 remainder 4 (Group IV)
c) 269 ÷ 6 = 44 remainder 5 (Group V)

Example:
The following figures were formed using matchsticks.

a) Based on the above series of figures, complete the table below.

Number of squares	1	2	3	4	5	6	7	8
Number of triangles	4	6	8	10
Number of matchsticks	12	19	26	33

b) How many triangles are there if the figure in the series has 9 squares?

c) How many matchsticks would be used in the figure in the series with 11 squares?

Solution:
a)

Number of squares	1	2	3	4	5	6	7	8
Number of triangles	4	6	8	10	12	14	16	18
Number of matchsticks	12	19	26	33	40	47	54	61

b) The pattern is +2 for each additional square.
18 + 2 = 20
If the figure in the series has 9 squares, there would be 20 triangles.

c) The pattern is + 7 for each additional square
61 + (3 x 7) = 82
If the figure in the series has 11 squares, there would be 82 matchsticks. Download leawo mp4 converter full version marcus reid free.

Example:
Seven ex-schoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?

Solution:

A	B	C	D	E	F	G
A
B	●
C	●	●
D	●	●	●
E	●	●	●	●
F	●	●	●	●	●
G	●	●	●	●	●	●
HS	6	5	4	3	2	1

Total = 6 + 5 + 4 + 3 + 2 + 1 = 21 handshakes.

The following video shows more examples of using problem solving strategies and models.
Question 1: Approximate your average speed given some information
Question 2: The table shows the number of seats in each of the first four rows in an auditorium. The remaining ten rows follow the same pattern. Find the number of seats in the last row.
Question 3: You are hanging three pictures in the wall of your home that is 16 feet wide. The width of your pictures are 2, 3 and 4 feet. You want space between your pictures to be the same and the space to the left and right to be 6 inches more than between the pictures. How would you place the pictures?

The following are some other examples of problem solving strategies.

• Explore it/Act it/Try it (EAT)

  Explore it/Act it/Try it (EAT) Method (Basic)
  Explore it/Act it/Try it (EAT) Method (Intermediate)
  Explore it/Act it/Try it (EAT) Method (Advanced)

• Finding A Pattern

  Finding A Pattern (Basic)
  Finding A Pattern (Intermediate)
  Finding A Pattern (Advanced)

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Problem-solving missing from maths education — Benjamin

THE country’s leading authority on mathematics education has indicated that one of the major gaps in the teaching and learning of the subject in local classrooms is the lack of focus on problem solving.

National Mathematics Coordinator Dr Tamika Benjamin, who is part of the team implementing the iLead educational leadership programme in schools — an initiative created and implemented by the Jamaica National Building Society (JNBS) Foundation and the Ministry of Education — told maths teachers from Happy Grove and St Thomas Technical high schools at a recent workshop that very often the tasks set by teachers are focused on finding answers to questions that already dictate the algorithm to be used to find the solution. However, she explained, problem solving requires students to find solutions without knowing what method to use.

'You have to allow students to use their own strategies; do not restrict them,' she stressed, noting that while questions may have one answer, problems may have multiple solutions.

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Math Problem Solving

'We stifle their development when we eliminate problem-solving. [That] approach adopted by most teachers encourages passive learning and consequently, students become dependent on instructions, rather than grasping concepts and confidently take on challenges,' she argued.

Using examples, Dr Benjamin challenged the teachers by demonstrating how problem solving tasks were different from questions teachers in general currently set.

'Thirty-five pupils attended a Children’s Day party. At the party, each girl was given five sweets and each boy was given three sweets. If a total of 155 sweets were given out the party, how many more girls than boys were there?' the Mathematics Coordinator asked, in an effort to demonstrate her point.

Dr Benjamin posited that the tasks set must deal with situations that are natural to the students and should centre on core mathematical concepts which they should learn. That approach, she said, shoulld lend itself to students justifying and explaining their answers.

The mathematic coordinator countered claims that students will resist problem solving tasks, insisting that dialogue must be an important part of the teaching and learning environment, in order to engage the students.

Help Solving Math Word Problems

'Teachers have to ask purposeful questions that allow students to explain and reflect. Questions that help them to know what the students know. They must lead to meaningful discussions and ideas,' she emphasised.

In addition, she urged teachers to use a variety of strategies to engage students, including drawing or dramatising to 'bring mathematics to life in the classroom.'

Happy Grove and St Thomas Technical are two of the new participants in the iLead programme, which targets ten schools in Portland, St Mary and St Thomas, given the National Education Inspectorate’s assessment of their needs.

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Solving Math Equations

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