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Solving Word Problems Using Block Models
Heuristic Approach to Problem-Solving
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Problem Solving Strategies

Join My Free group 👈👈👈 Follow this link to join my WhatsApp group: this is my first video for math's trick s. Math word problems are packed full of words and every word means something to about the intent and the mathematics in the problem, especially in middle school and high school. Reading has to be done both at the literal and inferential levels to actually correctly determine what needs to be done and execute the proper mathematics.

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

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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?

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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:

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:

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

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.

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)

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:

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.

Math Problem Solving Sheets

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Problem Solving

Problem solving and competition-style math plays an interesting role at Mathcamp: it can be a big piece of your mathematical experience, or play little to no role at all. (It's not the central focus of our curriculum, though, so if you're looking for a full schedule of contest math preparation, then this probably isn't the right fit for you.) As with all subjects, our goal is to make problem-solving resources and activities available to students and invite students to choose what interests them most.

We run two weekly competitions and teach one or two classes each day on problem solving (some at a beginner/intermediate level, others at the Olympiad level). Among both students and staff, you will find people who have won medals at the IMO and people who have never done a problem-solving competition in their lives. And of course, in the Mathcamp library, you'll find lots of books on problem solving (and people who want to talk about problems with you!).

Team Problem Solving is an olympiad-style competition held weekly throughout camp at Virtual Mathcamp on Friday afternoons from 1pm to 3pm PT (during the regular TAU time). Campers can opt to participate in advance of camp and can choose between two types of teams:

Math Problems Solving

• Hardcore teams are competing to win! Team members are encouraged not to quit mid way through camp (because they would be letting their team down). Team members cannot be shuffled and teams cannot merge.
• Mellow teams are solving just for fun (although the problems are the same). Team members may choose to skip one or various weeks without feeling guilty. With staff permission, teams can merge if they have lost too many members.

The results of the five weeks are added, and prizes for the winning teams are awarded at the final assembly.

'Relays' are a fun, light-hearted Saturday afternoon activity at Virtual Mathcamp, and most of camp participates: it's a chance to run around outside in the sunshine and solve quick math problems. Campers organize themselves into teams of 5-7 people and again opt for 'mellow' (we're just here to relax) or 'hardcore' (we're in it to win it) and spend an hour solving problems as a team: logic problems, games, 'traditional' contest problems -- you name it. (The prize for winning may involve candy.)

We teach one or two Problem-Solving Classes, at beginner and Olympiad levels, each day. Recent topics have included ARML Power Rounds, Diophantine Equations, Inequalities, and Geometric Transformations. The topics change from year to year, so both new campers and returning alumni can dive into problem-solving techniques together.