Correct Shares

Correct Shares Finding Fair Shares

Provide children with regions showing examples and non examples Give the children dot paper and have them find halves, quarters, or of fractional parts. Have the children identify the wholes that are other fractional parts of an enclosed region. correctly divided into requested fractional parts and those that are not. The activity is especially interesting when different shapes represent equivalent areas. For each response, have the children explain their reasoning. This should be done with a variety of models, including discrete and continuous.

Resources:

MM Fraction Circles

Resources Dot paper with regions identified

Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon, Chapter 15 Boston: Allyn & Bacon, Chapter 15. More, Less or Equal to One Whole Mixed Number Names

Give the children a collection of fractional parts ( all the same size 2 Give the children a mixed number such as 3 . Their task is to find a pieces) and indicate the kind of fractional part they have. Parts can 5 be drawn on a worksheet or physical models can be placed in plastic single fraction that names the same amount. They may use any bags with an identifying card. familiar materials or make drawings, but they must be able to give an explanation for their result. For example, if done with Cuisenaire rods or fraction strips, the collection might have seven light green rods with a caption or note Similarly, have children start with a fraction greater than one, such indicating “each piece is one third”. The task is to decide if the 17 as , and have them determine the mixed number and provide a collection is less than one whole, equal to one whole, or more than 4 one whole. justification for their result.

Ask children to draw pictures or use symbols to explain their answer When the children become skilled at explaining the fractions challenge them to figure out the new name without the use of Materials materials.

Sets of fraction pieces with labels. 1 Look for an explanations like the following for 3 : there are four Dot paper 4 Fraction strips. quarters in one whole, so there are 8 quarters in two wholes and 12 MM master- fraction circles quarters in 3 wholes. The extra quarter makes 13. Note the iteration Mystery Stars? concept. There is no need to provide the children with any rules.

Materials: Mixed numbers, fraction pieces, improper fractions.

Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon, Chapter 15 Boston: Allyn & Bacon, Chapter 15. Zero, One Half, or One Close Fractions

Provide the children with fraction cards ( or write 8 – 10 Have the children name a fraction that is close to 1 but not fractions on the board) with some values greater than one, more than one. Next have them name another fraction that with others between 0 and 1. is even closer to 1 than that. For the second fraction have them explain why they believe the fraction is closer to 1 The children are to sort the fractions into three groups: close to 0, close to half or close to zero. For those fractions than the previous. Continue for several fractions in the close to half ask the children to decide if the fraction is same manner with each one being closer to 1 than the more or less than half. previous fraction.

The difficulty of the task depends on the fractions. For the Try close to 0 or close to half (either over or under). first time use fractions that are close to the benchmarks Initially let the children use models to help with their 1 53 9 , or . On other occasions use fractions with thinking. Later see how well they do using imaging. Focus 20 100 10 discussions on the relative size of the fractional parts. denominators less than 20. Use some fractions that are exactly in between the benchmarks.

As the children to explain their choices using drawings or materials.

Materials Fraction pieces Fraction cards Number lines

Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon, Chapter 15 Boston: Allyn & Bacon, Chapter 15. About How Much? Ordering Unit Fractions

Give the children a set of unit fractions and ask them to 0 1 put the fractions in order from the least to the most.

Draw some number lines on the board. Ask the children to name the fraction they think is a good estimate of the Challenge the children to defend the way they order the number indicated on the number line. fractions. Initially allow the children to use materials or models to explain their thinking. Get the children to discuss the estimates that have been made. There is no single correct answer but children’s estimates should be reasonable. If they have difficulty For children at Level One use fraction words initially. coming up with an estimate, ask if they think the amount 1 is closer to 0, , or 1. 2 Materials A good activity to follow Dotty Pairs, Book 7 page 22 Fraction cards – words and symbols

Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon, Chapter 15 Boston: Allyn & Bacon, Chapter 15. Choose, Explain, Test Line ‘Em Up

Give children two or three pairs of fractions. Their task is Give the children four or five fractions to put in order from to decide which fraction is greater (choose), to explain smallest to biggest. Have them indicate where each one 1 why they think this is so (explain), and then to test their belongs on a number line labeled with 0, , and 1. choice using any model they wish. 2

They should explain (or write a description of how they The children should give an explanation of how they made their test) and whether or not it agreed with their decided to put their fractions in order. choice. If their choice was incorrect, they should try to say what they would change in their thinking. Material

Materials Fraction cards Pairs of Fractions

Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon, Chapter 15 Boston: Allyn & Bacon, Chapter 15. Group the counters, Find the Names

Have the children set out a specific number of counters in two colours e.g 24 counters 16 red, 8 yellow. The 24 make up the whole.

The task is for the children to group the counters into different fractional parts of the whole and use the parts to create fraction names for the red and the yellow counters.

Children should record their different groupings and explain how they found the fraction names.

Extension: challenge the children to find other numbers that work well.

Materials Counters

Exploration of equivalent fractions.

Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Van de Walle, J. A., Karp, Karen. S., Bay-Williams, Jennifer, M. (2010). Elementary and middle school mathematics: teaching developmentally (7th ed.). Elementary and middle school mathematics: teaching developmentally (7th ed.). Boston: Allyn & Bacon, Chapter 15 Boston: Allyn & Bacon, Chapter 15.