Level 4 NZ Curriculum Achievement Objectives for Number 2
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-4: Apply simple linear proportions, including ordering fractions.
NA4-5: Know the equivalent decimal and percentage forms for everyday fractions.
NA4-2: Understand addition and subtraction of fractions, decimals, and integers.
NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
NA4-4: Apply simple linear proportions, including ordering fractions.
NA4-5: Know the equivalent decimal and percentage forms for everyday fractions.
In this unit you will revise:
1) What is a fraction 2) Equivalent fractions and comparing fractions 3) Adding and subtracting fractions 4) Percentages |
In this unit you will learn:
5) Multiplying Fractions 6) Dividing Fractions 7) Converting fractions to decimals and vice versa 8) Increasing and decreasing by a percentage 9) Inverse perecentage |
1) Naming Fractions
WHAT IS A FRACTION?
Check out this video about what fractions are
https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-fractions-topic/cc-3rd-fractions-intro/v/fraction-basics
- A quantity that is part of a whole is a fraction.
- Naming parts of a fraction ...the top number is the NUMERATOR and the bottom number is the DENOMINATOR
- 3/8 is three-eights. There are 8 parts in one whole and there are three of them.
- The numerator is less than (<) the denominator in a proper fraction: e.g. 3/8, 3 < 8
- The numerator is greater than (>) the denominator in an improper fraction: e.g. in 11/8, 11 > 8
Check out this video about what fractions are
https://www.khanacademy.org/math/cc-third-grade-math/cc-3rd-fractions-topic/cc-3rd-fractions-intro/v/fraction-basics
2) Equivalent Fractions and Comparing Fractions
Equivalent Fractions
Equivalent fractions are equal - they indicate the same share of a whole. A fraction wall like the one shown here can be used to find equivalent fractions. Each row is divided into the number of parts represented by the fraction. The 1/4 brick is the same length as two 1/8 bricks, so 2/8 is equivalent to 1/4.
Here are some fun websites to visit to consolidate your Equivalent Fractions knowledge. Click on the images and go for it!
Comparing Fractions
- A fraction can also be used to compare sizes of fractions. If the numerators of two fractions are 1, the fraction with the larger denominator is the smaller value : e.g. 1/6 < 1/3.
- When comparing two fractions, benchmark each on a number line. It may be necessary to first change the fractions to equivalent fractions with the same denominator. Fractions with the same denominator are said to have common denominators. The smallest denominator is called the lowest common denominator or LCD.
- The lowest common multiple or LCM is the smallest common number that is a multiple of two or more numbers: e.g. 24 is the LCM for 3,4 and 8.
3) Adding and Subtracting Fractions
Common Denominators
Different Denominators
- Change fractions to equivalent fractions with the same denominator before adding or subtracting.
- Add or subtract the numerators.
- If possible write the answer in its simplest form or as a mixed number.
Have a look at this video to see how it is done.
4) Percentages
In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". A percentage is a dimensionless number (pure number)
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5) Multiplying Fractions
Multiplying Fraction Games |
Click on these images and you will be taken to a fun world of multiplying fraction games. Enjoy and good luck!
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Visit this website: http://www.math-aids.com/Fractions/ It has printable worksheets for you to practice your fractions.
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6) Dividing Fractions
- When dividing a whole number by a fraction, the result is an even bigger number, because we are finding out how many 'lots of' the fraction there are in the whole number.
- When dividing a fraction by a whole number gives an even smaller fraction, because we are dividing that fraction part into even smaller pieces.
7) Converting fractions to decimals and vice versa
Fractions to Decimals
Decimals to Fractions
8) Percentage Increase and Percentage Decrease
PERCENTAGE INCREASE
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PERCENTAGE DECREASE
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8) Inverse Percentage
Visit this site for more on INVERSE percentages http://www.onlinemathlearning.com/reverse-percentage.html |
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