Introductory Activity 4: A fractional part is always based on a whole. Big Ideas page 3 Interactions and Quest activities Fractions with Counters activity
Introductory Activity 5: Renaming Fractions John ate 4/6 of a pie and his sister ate another 2/3 of the pie. What fraction of pies did they eat altogether? A problem such as this necessitates that we add 4/6 and 2/3. How can we add sixths and thirds? We can do this by renaming them as the same denominator. Let’s say we rename 4/6. This one is easy because it can be renamed as 2/3. How do we know that 2/3 can be renamed as 4/6? This is also worded that 2/3 is equivalent to 4/6.
Introductory Activity 6: Renaming Fractions What are EQUIVALENT FRACTIONS? Equivalent fractions are fractions that share the same space in a whole or a set. In the above diagrams, ½ is an equivalent fraction to 2/4. We renamed ½ as 2/4.
What are some manipulative materials we can use in the classroom to rename fractions to show equivalent fractions?
Introductory Activity 7: Models for Renaming Fractions. Counters Model – Making a New Arrangement: Lay out 6 counters. Flip 4 to red. What fraction of the counters is red? To rename this, place the counters in another arrangement: Into 3 groups, with YY RR RR. Now you can see that 2/3 of the counters are red. This demonstration shows that 4/6 is equivalent to 2/3 or 4/6 can be renamed as 2/3.
Introductory Activity 8: Models for Renaming Fractions. Counters Model – Making a New Arrangement: Lay out 6 counters. Do this with 6/8 with 6 of 8 counters being red. What other way could you arrange the counters into similar groups? You could make four groups of YY RR RR RR. What fraction of the counters is red? 3 fourths so 6-eighths can be renamed as 3 fourths.
Introductory Activity 9: Models for Renaming Fractions. Let’s Practise: Rename 3/6 by placing the counters in another arrangement. Rename 10/12 by placing the counters in another arrangement. Rename 10/20 by placing the counters in another arrangement. Rename 5/15 by placing the counters in another arrangement.
Introductory Activity 10: Models for Renaming Fractions. Counters Model – Duplicating Groups: We can also rename fractions by adding one or more similar groups. Lay out 6 counters with 4 red and 2 yellow. Make a new group identical to the one you just made. This causes the total red counters to double and the total yellow counters to double. There are now 12 counters so the red counters make up 8 twelfths of the counters. So 4/6 is equivalent or can be renamed as 8 twelfths.
Introductory Activity 11: Models for Renaming Fractions. Counters Model: Lay out 6 red and 2 yellow counters. Instead of one group in which there are 6 red and 2 yellow counters, we could have 3 groups like this. RRRRRR YYRRRRRR YY RRRRRR YY We now have how many counters? How many of these are red? What fraction of the total counters is red? Therefore, we just renamed 6/8 as 18/24
Introductory Activity 12: Models for Renaming Fractions. Now let’s look at the symbolic representation of what we just did. 4/6 = 8/12 6/8 = 18/24 Let’s Practise: Rename ¾ by making more groups. Rename 4/5 by making more groups. Rename 3/5 by making more groups.
Introductory Activity 13: Models for Renaming Fractions. Fraction Factory Model: First, let’s practise to review/learn the identity of the various pieces. Demonstrate your knowledge of the pieces by answering the teacher’s questions
Introductory Activity 14: Models for Renaming Fractions. Fraction Factory Model: Use the pieces to find all the fractions equivalent to ½. This means that the area of the ½ piece can be exactly covered by several same-colour pieces. One orange can be covered by 3 red, 4 brown, 5 yellow, 6 beige. What about green? Now find fractions equivalent to 1/3. Can you rename 1/3 as any other fraction using the pieces? Rename 1/4. Rename 3/4. Now write the symbolic representations of these answers. Investigate the patterns involved.
Introductory Activity 15: Models for Renaming Fractions. Rectangle Model: A rectangle or circle can be subdivided into different sized but equal pieces. Complete the sheet EQUIVALENT FRACTIONS from the Fraction Factory book. In number 1, the rectangle that is first divided into two equal parts is renamed by dividing it into four equal parts and seeing that 2 out of the 4 are shaded.
Introductory Activity 16: Models for Renaming Fractions. Paper Folding Model: ½ can be renamed by folding paper. Fold in half and shade one-half. Then fold in half again. See how many fourths are shaded. Then fold again to see eighths and then 16ths, etc. ½ can be renamed as 2/4, 4/8, or 8/16. These would be just some of the answers.
Introductory Activity 17: Models for Renaming Fractions Dot Paper (Geoboard) Model: Make a rectangle equal 1 whole (12 dots). Shade in ½ of the dots. This would be 6 twelfths, etc. Practise with the teacher.
Introductory Activity 18: Models for Renaming Fractions Fraction Circles Model: Let’s use the fraction circles to rename fractions. Subdivide each part of a 6 th fraction circle into two equal parts. We just renamed 6 th s as 12 th s by halving each sixth. Shade in 2 sixths and rename these as twelfths. 2-sixths can be renamed as 4 twelfths. Now complete Renaming Twelfths (have copies) by shading and renaming fractions by subdividing in a different way.
Introductory Activity 19: Types of Fractions A proper fraction has a numerator that is smaller than its denominator. An improper fraction has a numerator that is greater than its denominator. A mixed number is a combination of a whole number and a fractional part.
Let’s Practise!: What kind of fraction am I? 8/9 (eight-ninths) 13/12 (thirteen-twelfths) ½ (one-half) 4 and ¾ (four and three-fourths) 16/18 (sixteen-eighteenths) 5/4 (five-fourths) 9 and ¼ (nine and one-fourth)
Introductory Activity 20: Mixed numbers are numbers that contain a whole and a fractional part. Which of the following are mixed numbers? 6 ½ 7.89 3 ¾
Introductory Activity 21: Renaming Fractions Greater Than 1 Combine your fraction factory pieces with a partner and listen to the teacher’s instructions. Big Ideas booklet page 5 Interactions and Quest activities
Student Activities A3.1: Use your fingers and hands to show that ½ and 5/10 are equivalent fractions. Choose another concrete material to show this pair of equivalent fractions. Choose another pair of equivalent fractions and use a model to show they are equivalent.
Student Activities A3.2: Work with a partner and use Fraction Factory to show that 1 and 2/3 = 5/3. Use Fraction Factory to show that 1 and ¾ is equivalent to 7/4.
Student Activities A3.3: Draw a circle and subdivide it through its centre into 3 equal sections. Next, use your circle to find 2/3 of 18.
Student Activities A3.4: Imagine that you have a pan of brownies represented by a geoboard. Use the geoboard to explain how ½, 2/4, and 4/8 are equivalent fractions. In your explanation, make a connection to the pan of brownies. Choose another concrete material to show this pair of equivalent fractions.
Student Activities A3.6: Fold the circular coffee filter through the centre to make 8 equal sections. Draw lines on the fold lines. Now shade in 6 of the sections so that consecutive sections are shaded. What fraction represents the shaded part? Explain how 6/8 can be renamed as ¾ using ‘clumping’. Next, make a diagram and identify the ‘clump size’ that should be used to show that 10/15 can be renamed as 2/3. How might you predict the ‘clump size’ without drawing the diagram?
Student Activities A3.7: With a partner prepare a display showing all of the equivalent fractions you can find using a set of no more than 30 pattern blocks.