Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Convert fractions (denominators 10, 100, 1000) to decimals, and decimals to fractions.
• Compare and order decimals up to two decimal places.
• Add and subtract decimals up to two decimal places.
• Identify the place value of digits in decimals.

Lesson summary

This week, we will delve deeper into the fascinating world of fractions and decimals, building upon what you learned in previous grades. Understanding fractions and decimals is crucial in everyday life, from sharing a koeksister with friends to measuring ingredients for your grandmother's potjie recipe, or even calculating discounts at the local spaza shop. This knowledge allows you to make informed decisions and solve practical problems. We will focus on converting fractions to decimals and vice versa, comparing and ordering them, and performing simple calculations involving decimals.

Lesson notes

What are Fractions? A fraction represents a part of a whole. It's written as one number over another, separated by a line. The number on top is the numerator (how many parts you have), and the number on the bottom is the denominator (how many parts the whole is divided into).

Example: 1/4 means 1 part out of 4 equal parts. What are Decimal Fractions (Decimals)? A decimal is another way of representing a fraction, but using the base-ten system. It uses a decimal point (.) to separate the whole number part from the fractional part. The numbers after the decimal point represent tenths, hundredths, thousandths, and so on.

Place Value in Decimals: Understanding place value is crucial. Consider the number 12.34: 1 is in the tens place (1 x 10 = 10) 2 is in the units place (2 x 1 = 2) 3 is in the tenths place (3 x 1/10 = 0.3) 4 is in the hundredths place (4 x 1/100 = 0.04) Converting Fractions to Decimals (and Vice-Versa) (Denominators 10, 100, 1000): Fractions to Decimals: If the denominator is 10, 100, or 1000, the conversion is simple.

Example 1: 7/10 = 0.7 (7 tenths)

Example 2: 23/100 = 0.23 (23 hundredths)

Example 3: 145/1000 = 0.145 (145 thousandths)

Decimals to Fractions: Identify the place value of the last digit after the decimal point. That determines the denominator.

Example 1: 0.4 = 4/10 (4 tenths)

Example 2: 0.65 = 65/100 (65 hundredths)

Example 3: 0.089 = 89/1000 (89 thousandths)

Comparing and Ordering Decimals: Compare the whole number parts: If the whole numbers are different, the larger whole number represents the larger decimal. For example, 3.5 > 2.

8. If the whole number parts are the same: Compare the digits in the tenths place, then the hundredths place, and so on.

Example: Compare 0.65 and 0.

6

2. Both have 0 in the units place and 6 in the tenths place.

However, 0.65 has 5 in the hundredths place, while 0.62 has

2. Since 5 > 2, 0.65 > 0.

6

2. When comparing, it can sometimes be helpful to add a zero at the end of one number, to make sure both numbers have the same number of digits after the decimal point. 0.5 compared to 0.55 can be considered 0.50 compared to 0.

5

5. Adding and Subtracting Decimals: The most important thing is to align the decimal points vertically. Add or subtract as you would with whole numbers, and then bring the decimal point straight down into the answer.

Example 1: 2.35 + 1.42 ``` 2.35 + 1.42 3.77 ``` Example 2: 5.6 - 2.13 ``` 5.60 (Adding a zero to make subtraction easier) 2.13 3.47 ``` Guided Practice (With Solutions)

Question 1: Convert 0.8 into a fraction.

Solution: 0.8 is 8 tenths.

Therefore, 0.8 = 8/

1

0. Commentary: This question reinforces the basic conversion from decimal to fraction. The student must identify the place value (tenths) to correctly form the fraction.

Question 2: Arrange the following decimal fractions in ascending order: 0.45, 0.6, 0.23, 0.

5. Solution: First, compare the whole number parts (all are 0). Then, compare the tenths place: 0.23 has the smallest tenths place (2), followed by 0.45 (4), 0.5 (5, implied 0.50) and 0.6 (6, implied 0.60). So, the ascending order is: 0.23, 0.45, 0.5, 0.

6. Commentary: This question tests the understanding of decimal place values and the ability to compare them. Converting 0.5 and 0.6 into 0.50 and 0.60 might help some learners.

Question 3: Calculate 3.2 + 1.56 Solution: ``` 3.20 (Adding a zero for alignment) + 1.56 4.76 ``` Therefore, 3.2 + 1.56 = 4.76

Commentary: This question emphasizes the importance of aligning decimal points before adding. Adding the implied zero to 3.2 helps avoid mistakes.

Question 4: What is the value of the digit 7 in the number 4.72?

Solution: The digit 7 is in the tenths place.

Therefore, its value is 7/10 or 0.

7. Commentary: Focuses on place value identification, directly linked to decimal fraction understanding. Independent Practice (Questions Only) Convert 3/100 into a decimal. Convert 0.9 into a fraction. Arrange the following decimal fractions in descending order: 0.7, 0.34, 0.89, 0.

1. Calculate 6.54 - 2.3 Calculate 1.8 + 0.

2

5. What is the value of the digit 2 in the number 1.32? Sipho spent R5.75 on sweets and R2.20 on a cool drink. How much did he spend in total? A piece of wood is 1.5 metres long. If you cut off 0.4 metres, how long is the remaining piece? Write 56/10 as a decimal. Which is larger, 0.6 or 0.58? Explain your answer.