Lesson Notes By Weeks and Term v5 - Grade 2
Fractions: halves and quarters – Week 4 focus
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Fractions: halves and quarters – Week 4 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 2
Term: 2nd Term
Week: 4
Theme: General lesson support
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Introduction This week, we explore the exciting world of fractions! Fractions are a way of talking about parts of a whole. In South Africa, we share things all the time. We might share a loaf of bread with our family, a bag of oranges with our friends, or a chocolate bar with a sibling. Fractions help us to make sure we are sharing fairly so that everyone gets an equal piece.
What is a Fraction? A fraction is a part of a whole. The most important word to remember is EQUA
L. When we break a whole into fractions, every part must be the exact same size.
The Whole: This is the complete object or the total number of items you start with. It could be one whole pizza, one whole piece of paper, or a whole group of 12 marbles. Imagine you have one vetkoek. That is your whole. ``` ( O ) <-- One whole vetkoek ``` If you cut it to share, you are making fractions. But it's only fair if the pieces are equal.
This is NOT a fair share (not fractions): One piece is big, one is small. ``` ( o | O ) ``` This IS a fair share (fractions): Both pieces are the same size. ``` ( O | O ) ``` Understanding Halves (1/2) When we cut or divide a whole into two equal parts, each part is called a half.
We write a half as a fraction like this: 1/2 The bottom number (2) tells us how many equal pieces the whole is cut into. The top number (1) tells us how many of those pieces we are talking about.
Example 1: Half of a Shape Let's take a whole chocolate bar. ``` [===============] <-- 1 whole ``` To find half, we break it into 2 equal pieces. ``` [=======|=======] ``` One of these pieces is one half (1/2) of the chocolate bar. The other piece is also one half (1/2). Two halves make one whole.
Example 2: Half of a Number (a Collection) Jabu has 8 sweets. He wants to give half to his friend Sipho. How many sweets does Sipho get?
Start with the whole: The whole is 8 sweets. `o o o o o o o o` Share into 2 equal groups: We need to make two groups with the same number of sweets in each. We can share them out one by one.
Group 1: `o o o o` Group 2: `o o o o` Count one group: Each group has 4 sweets. So, half of 8 is
4. Jabu gives Sipho 4 sweets. Understanding Quarters (1/4) When we cut or divide a whole into four equal parts, each part is called a quarter. A quarter is also sometimes called a fourth. We write a quarter as a fraction like this: 1/4 The bottom number (4) tells us the whole is cut into four equal pieces. The top number (1) tells us we are talking about one of those pieces.
Example 1: A Quarter of a Shape Let's take a square loaf of bread for making sandwiches. ``` +-------+ | | <-- 1 whole loaf | | +-------+ ``` To find quarters, we cut it into 4 equal pieces. We can cut it in half, and then cut the halves in half again. ``` +---+---+ | 1 | 2 | +---+---+ | 3 | 4 | +---+---+ ``` Each piece is one quarter (1/4) of the whole loaf. Four quarters make one whole.
Example 2: A Quarter of a Number (a Collection) Mama has 12 eggs. She needs to use one quarter of the eggs to bake a cake. How many eggs does she use?
Start with the whole: The whole is 12 eggs. `O O O O O O O O O O O O` Share into 4 equal groups: We need to make four groups with the same number of eggs in each.
Group 1: `O O O` Group 2: `O O O` Group 3: `O O O` Group 4: `O O O` Count one group: Each group has 3 eggs. So, one quarter of 12 is
3. Mama uses 3 eggs for her cake. Guided Practice (With Solutions) Here are some problems we can solve together as a class.
Question 1: Colour in one half (1/2) of the circle below. ``` / \ / \ | | \ / \ / ``` Wait, this shape is not divided equally. Let's fix it. ``` +-----+ / \ / \ |-----------| \ / \ / +-----+ ``` Solution 1: Step 1 (Think): The word "half" means I need to find 2 equal parts. The line in the middle of the circle cuts it into two parts that are the same size.
Step 2 (Do): I need to colour one of those two parts. It doesn't matter if I colour the top part or the bottom part.
Answer: ``` +-----+ /#######\ <-- This part is coloured in. /#########\ |-----------| \ / \ / +-----+ ```
Commentary: We have coloured in 1 out of 2 equal parts, which shows one half.
Question 2: Circle one quarter (1/4) of the triangles. ``` △ △ △ △ △ △ △ △ ``` Solution 2: Step 1 (Think): The word "quarter" means I need to make 4 equal groups. First, I count the total number of triangles. There are 8 triangles.
Step 2 (Do): I need to share the 8 triangles into 4 equal groups. I can draw circles and share the triangles out. Group 1 gets a triangle. Group 2 gets a triangle. Group 3 gets a triangle. Group 4 gets a triangle. (4 used) Group 1 gets another triangle. Group 2 gets another. Group 3 gets another. Group 4 gets another. (8 used) Each of my 4 groups has 2 triangles in it.
Step 3 (Answer): Now I circle just one of those groups. ``` (△ △) △ △ △ △ △ △ ```
Commentary: One quarter of 8 is
2. By circling two triangles, we are showing one of the four equal groups.
Question 3: Themba has 10 marbles. He loses half of them on the playground. How many marbles does he have left?
Solution 3: Step 1 (Think): The problem asks about "half of 10". This means I need to find out what 10 shared into 2 equal groups is.
Step 2 (Do): I can draw 10 marbles and then share them into two circles.
Marbles: `o o o o o o o o o o` Group A: `o o o o o` Group B: `o o o o o` Step 3 (Answer): Each group has 5 marbles. So, half of 10 is 5.