Mathematics Chapter 5

Fractions, Decimals, and Percentages

By Angie Kellner and Callie Gower

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Mathematics

Chapter 5

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Introduction

Chapter 5 is a dive into the world of fractions, decimals, and percentages!Numbers are essential for counting and measuring in our daily lives. Let's explore!

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• Fractions are among the most difficult mathematical concepts that children come across at primary school.

• Children have difficulty applying the knowledge of fractions to problem-solving situations because they are more familiar with whole numbers.
• The terminology used in fractions like numerator and denominator can be hard to understand.
• Visualizing fractions is another challenge

Introduction to Fractions

Learning Fractions in Key Stages

Key Stage 1 (Years 1-2):

• Students learn simple fractions using objects

(e.g., 1/2 of an apple). Lower Key Stage 2 (Years 3-4):

• Introduction to solving problems with fractions and understanding decimal place value.

Upper Key Stage 2 (Years 5-6):

• Students deepen their understanding and make connections between fractions, decimals, percentages, and ratios.

Common misconceptions about fractions

• The bigger numerator means it is a bigger fraction (e.g., 3/4 vs. 2/3)

Fractions can be understood in various contexts:

• Part of a Whole: e.g., 1/8 of a cake.

• Part of a Set: e.g., 3 out of 8 apples.

• Number Line Representation: Visualizing fractions on a number line.
• Operator Concept: Using fractions in calculations.

• Ratio Comparison: Understanding relationships between different fractions.

• Understanding fractions is crucial for problem-solving in mathematics.

• Research shows that teaching for understanding is more effective than rote memorization.

• Different interpretations of fractions should be introduced gradually to enhance comprehension.

Teaching Fractions Effectively

• Decimals extend the whole-number place-value system to represent fractions.

• The historical significance of decimal notation has made it a universal tool for representing numbers.

• Decimals are rational numbers that can be expressed as fractions.

• Many students find decimals challenging, especially when transitioning from whole numbers.

Introduction to Decimals

The word "percent" means "for every hundred," which is key to understanding its use. Percentages relate closely to fractions (e.g., 50% is equivalent to 1/2). Real-life examples include discounts in stores and statistics in reports. Emphasize understanding percentages through their fractional equivalents. Focus on conceptual understanding. Explain the phrases "of" and "out of" when calculating percentages.

Introduction to Percentages

Ratio and Proportion

• A ratio compares two quantities (e.g., 3:4 indicates a relationship).

• Proportion helps us understand how one quantity affects another when scaled.

• Real-life applications include cooking (adjusting recipes) and scale drawings in art.

• repeated practice of basic math concepts, such as counting and addition (Flash Cards)
• segmenting subject material into smaller units to make it easier to digest information
• use of small groups of other children for math instruction (realizing you are not alone is helpful)
• repeated review of basic math concepts in hands-on, tangible demonstrations (Counting manipulatives)

As a child, I struggled with word problems along with seeing number patterns. I had difficulty making sense of number lines and place values.

Disabilities in Math

Understanding fractions, decimals, percentages, ratios, and proportions is vital in mathematics and everyday life. However, a condition can make this challenging. Dyscalculia is a learning disorder affecting a person’s math ability. Much like dyslexia disrupts areas of the brain related to reading, dyscalculia affects brain areas that handle math- and number-related skills and understanding.

Selected Homework Errors

Learning situation:

Selected Homework Errors

Learning situation:

Kids believe that a fraction is a number smaller than one.

Selected Homework Errors

Learning situation:

Learning situation:

Selected Homework Errors

Selected Homework Errors

Learning situation:

Selected Homework Errors

Learning situation:

Learning situation:

Selected Homework Errors