Teaching font for thought using. Give your students food for thought – and opportunities – to learn outside of the classroom. Not everything in life can be found on a sheet of paper. Lessons in life from a 16 year old. Use this template. The act of making a change – to the world, a student or a school – takes no time at all, you just have to take action.
Anyone who has taught maths for any length of time will know how difficult it can be to teach pupils to solve maths problems out of context. Present pupils with a familiar setting or a sum that they've tackled before then they're usually fine, but turn it into an unfamiliar problem then it's a different matter. However, in the same ways that we teach strategies for other areas of maths, we can also teach strategies to solve maths problems.
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- Math Problem Solving Problems
- Solving Math Word Problems Free
- Math Problem Solving Strategies Poster Pdf
The Identification of Mathematics Students' Characteristic and Metacognitive Level in Mathematical Problem Solving State University of Medan Article Full-text available. The augmented matrix is used to 'solve' for x1 and x2, it is not 'equal' to x1 and x2. In the example, this gives x1 = b1 + 3x2, while x2 = x2 (free variable). Then the vector x is written in terms of its components. X = x1,x2 = (b1 + 3x2),x2 = (b1 + 3x2), (0 + 1x2) = b1,0 + 3x2,1x2 = b1,0 + x2 (3,1) in your notation. Solving the Math Problem. The students who attended youcubed summer camp describe the power of mindset math in their own words!
When solving maths problems, students should be encouraged to follow a general problem solving procedure. This is summed up as follows:
1. Read the problem carefully. The first and most important step is to read the problem carefully to understand what you're asked to find out and what information you have been given. Underlining the important information is also useful so you have all the important numbers/facts to hand.
2. Choose a strategy and make a plan.
3. Carry out the plan and solve the problem.
4. Check the working out and make sure that your solution is actually answering the question.
There are a number of strategies that can be used to solve maths problems, as follows:
Create a diagram
Creating a diagram can help mathematicians to picture the problem and find the solution. To create a diagram, the problem must be read carefully and the information that has been given to them in the question drawn into the diagram. They can then work out the solution from the diagram that has been drawn.
Guess and check
The guess and check strategy can be helpful for many types of problems. When students use this strategy, they will make a reasonable guess, based on the information that they have been given and then check to see if their guess is correct The guesses should get closer and closer to the answer, until the correct answer is found.
Use a table or make a list
Using a table is a good way to sort out and organise the information that has been given in the question. The information that has been set out in the table will hopefully lead students to the correct solution.
From the 'Littafin Wakoki' hymnbook as well as other songs, chorus and chants that are sung by Hausa Christians in West Africa and elsewhere. Additionally, the app has URL links to the original. There are no copyright issues with live streaming the videos and music on this site for your church services. Africa) Littafin Wakoki - Hausa (West Africa) Numbers 401-446 are Yan Waƙoƙi (small songs 1- 46) 1 Ubangiji Allah. Just as you would in Church. I have recorded two styles of piano music: Simple Piano (often with midi file) Piano and Organ; SMALL BAND. There recordings are computer generated using the 'Band in a Box' program. Several styles are used, including: Small Band (often with BIAB source file). Hausa (west africa)music for your church services. Littafin Wakoki - Hausa (W. There are no copyright issues with live streaming the videos and music on this site for your church services. This is because all songs are public domain,. Littafin Wakoki - Hausa (West Africa) 301: Alherin Ubangijina abin mamaki ne (Amazing grace).
Making a list is a strategy that will help students sort out the information that has been given in the problem. Once the students can see all of the possibilities for the solution, they can then attempt to solve the problem more easily.
Logical reasoning
This strategy requires students to use the information they have been given in the question to eliminate possible solutions to finally discover the correct solution.
Find a pattern
When students use this strategy they look for a pattern from the information that has been given. Once the pattern has been identified, the students can predict what will happen next and then continue the pattern to find the correct solution.
Working backwards
Working backwards is an excellent strategy to use when the final outcome of the problem has already been given. Students just need to work out what the events were that occurred previously.
Solve an easier version
Sometimes the problem is too difficult to solve in one step. When this happens the students will be able to make the problem more simple by dividing it into smaller and easiest steps, such as rewording the problem using smaller numbers.
These strategies are really useful in helping to solve maths problems. I have used them with the classes that I've worked with in KS2 to great effect. Giving children the experience of using these maths problem solving strategies will provide themv with a really useful toolkit for their maths arsenal as well as making them more confident when presented with a maths problem.
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:
- What do you know?
- What do you need to know?
- 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
- Identify - What is the question?
- Plan - What strategy will I use to solve the problem?
- Solve - Carry out your plan.
- 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.
Math Solving Calculator
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. Blessen ir daruma fields saddlery shop.
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.
Example:
Seven ex-schoolmates had a gathering. Each one of them shook hands with all others once. How many handshakes were there?
The guess and check strategy can be helpful for many types of problems. When students use this strategy, they will make a reasonable guess, based on the information that they have been given and then check to see if their guess is correct The guesses should get closer and closer to the answer, until the correct answer is found.
Use a table or make a list
Using a table is a good way to sort out and organise the information that has been given in the question. The information that has been set out in the table will hopefully lead students to the correct solution.
From the 'Littafin Wakoki' hymnbook as well as other songs, chorus and chants that are sung by Hausa Christians in West Africa and elsewhere. Additionally, the app has URL links to the original. There are no copyright issues with live streaming the videos and music on this site for your church services. Africa) Littafin Wakoki - Hausa (West Africa) Numbers 401-446 are Yan Waƙoƙi (small songs 1- 46) 1 Ubangiji Allah. Just as you would in Church. I have recorded two styles of piano music: Simple Piano (often with midi file) Piano and Organ; SMALL BAND. There recordings are computer generated using the 'Band in a Box' program. Several styles are used, including: Small Band (often with BIAB source file). Hausa (west africa)music for your church services. Littafin Wakoki - Hausa (W. There are no copyright issues with live streaming the videos and music on this site for your church services. This is because all songs are public domain,. Littafin Wakoki - Hausa (West Africa) 301: Alherin Ubangijina abin mamaki ne (Amazing grace).
Making a list is a strategy that will help students sort out the information that has been given in the problem. Once the students can see all of the possibilities for the solution, they can then attempt to solve the problem more easily.
Logical reasoning
This strategy requires students to use the information they have been given in the question to eliminate possible solutions to finally discover the correct solution.
Find a pattern
When students use this strategy they look for a pattern from the information that has been given. Once the pattern has been identified, the students can predict what will happen next and then continue the pattern to find the correct solution.
Working backwards
Working backwards is an excellent strategy to use when the final outcome of the problem has already been given. Students just need to work out what the events were that occurred previously.
Solve an easier version
Sometimes the problem is too difficult to solve in one step. When this happens the students will be able to make the problem more simple by dividing it into smaller and easiest steps, such as rewording the problem using smaller numbers.
These strategies are really useful in helping to solve maths problems. I have used them with the classes that I've worked with in KS2 to great effect. Giving children the experience of using these maths problem solving strategies will provide themv with a really useful toolkit for their maths arsenal as well as making them more confident when presented with a maths problem.
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:
- What do you know?
- What do you need to know?
- 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
- Identify - What is the question?
- Plan - What strategy will I use to solve the problem?
- Solve - Carry out your plan.
- 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.
Math Solving Calculator
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. Blessen ir daruma fields saddlery shop.
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.
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.
Math Problem Solving Problems
- 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.
Solving Math Word Problems Free
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Math Problem Solving Strategies Poster Pdf
