﻿﻿﻿﻿﻿ Teaches via problem solving | Scholastic: Children Book Publishing

## Teaches via problem solving

ALPHA Mathematics teaches via problem solving through the systematic development of problem sets; and by focusing on both aspects of problem solving - the method and the process.

### Focus on the Problem Solving Process

ALPHA Mathematics explicitly teaches an efficient 4-step UPAC problem solving process. This process builds good habits for approaching mathematical problems of all levels of difficulty.

#### 1

###### Understandthe problem
• Can you describe the problem in your own words?
• What information is given?
• What do you need to find?
• Is there information that is missing or not needed?

#### 2

###### Plan what to do
• What can you do to help you solve the problem?
• Here are some things you can do:

- Draw a picture
- Make a list
- Guess and check
- Look for a pattern
- Make suppositions
- Act it out
- Work backwards

#### 3

###### Work out theAnswer
• Solve the problem using your plan in Step 2.
• If you cannot solve the problem, make another plan.
• Show your work clearly.
• Write the answer statement.

#### 4

###### Check
• Read the question again. Did you answer the question?
• Does your answer make sense?
• Is your answer correct?
• If your answer is  not correct, go back to Step 1.

### Focus on the Problem Solving Method

ALPHA Mathematics explicitly teaches different problem solving strategies and how to select, express, categorise and compare these strategies.

#### Problem Solving Strategies

• Draw a Picture
• Make a List
• Choose an Operation
• Guess and Check
• Look for a Pattern
• Make a Supposition
• Act it Out
• Work Backwards
• Solve Part of the Problem

### The Bar Model Method

The Bar Model Method is one of the most powerful strategies for mathematical problem solving. It allows students to solve complex word problems using visual representation.

• The Part-Whole Model enables students to understand the concept of addition (given the parts, find the whole).
• The Comparison Model enables students to compare two quantities and shows the difference in quantities.
• The Bar Model Method enables the students to think conceptually, allowing them to do algebraic thinking without having to do algebra.

Example:

Pearl read 10 pages of a book on Monday. She read 1/3 of the remainder on Tuesday. If she still had 24 pages to read, how many pages were in the book?

### Varied Problem Sets

Students progress through different types of problem sets including word problems and non-routine problems.

#### Word Problems

• Enable students to apply knowledge learned and make mathematics relevant to daily life.
• Assess students’ ability to apply knowledge learned.

#### Non-routine Problems

• Provide opportunities for students to apply knowledge to unusual or complex problem situations.
• Develop higher order thinking skills.

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