Maximizing Math Mentality – Sarasota County Schools
Correct Shares
Provide children with regions showing examples and non examples of fractional parts. Have the children identify the wholes that are correctly divided into requested fractional parts and those that are not.
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
Finding Fair Shares
Give the children dot paper and have them find halves, quarters, or other fractional parts of an enclosed region.
The activity is especially interesting when different shapes represent equivalent areas.
Resources
Dot paper with regions identified
More, Less or Equal to One Whole
Give the children a collection of fractional parts ( all the same size pieces) and indicate the kind of fractional part they have. Parts can be drawn on a worksheet or physical models can be placed in plastic bags with an identifying card.
For example, if done with Cuisenaire rods or fraction strips, the collection might have seven light green rods with a caption or note indicating “each piece is one third”. The task is to decide if the collection is less than one whole, equal to one whole, or more than one whole.
Ask children to draw pictures or use symbols to explain their answer
Materials
Sets of fraction pieces with labels.
Dot paper
Fraction strips.
MM master- fraction circles
Mystery Stars?
Mixed Number Names
Give the children a mixed number such as 3[pic]. Their task is to find a single fraction that names the same amount. They may use any familiar materials or make drawings, but they must be able to give an explanation for their result.
Similarly, have children start with a fraction greater than one, such as [pic], and have them determine the mixed number and provide a justification for their result.
When the children become skilled at explaining the fractions challenge them to figure out the new name without the use of materials.
Look for an explanations like the following for 3[pic] : there are four quarters in one whole, so there are 8 quarters in two wholes and 12 quarters in 3 wholes. The extra quarter makes 13. Note the iteration concept. There is no need to provide the children with any rules.
Materials:
Mixed numbers, fraction pieces, improper fractions.
Zero, One Half, or One
Provide the children with fraction cards ( or write 8 – 10 fractions on the board) with some values greater than one, with others between 0 and 1.
The children are to sort the fractions into three groups: close to 0, close to half or close to zero. For those fractions close to half ask the children to decide if the fraction is more or less than half.
The difficulty of the task depends on the fractions. For the first time use fractions that are close to the benchmarks
[pic], [pic] or [pic]. On other occasions use fractions with 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
Close Fractions
Have the children name a fraction that is close to 1 but not more than one. Next have them name another fraction that is even closer to 1 than that. For the second fraction have them explain why they believe the fraction is closer to 1 than the previous. Continue for several fractions in the same manner with each one being closer to 1 than the previous fraction.
Try close to 0 or close to half (either over or under). Initially let the children use models to help with their thinking. Later see how well they do using imaging. Focus discussions on the relative size of the fractional parts.
About How Much?
Draw some number lines on the board. Ask the children to name the fraction they think is a good estimate of the number indicated on the number line.
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 coming up with an estimate, ask if they think the amount is closer to 0, [pic], or 1.
A good activity to follow Dotty Pairs, Book 7 page 22
Ordering Unit Fractions
Give the children a set of unit fractions and ask them to put the fractions in order from the least to the most.
Challenge the children to defend the way they order the fractions. Initially allow the children to use materials or models to explain their thinking.
For children at Level One use fraction words initially.
Materials
Fraction cards – words and symbols
Choose, Explain, Test
Give children two or three pairs of fractions. Their task is to decide which fraction is greater (choose), to explain why they think this is so (explain), and then to test their choice using any model they wish.
They should explain (or write a description of how they made their test) and whether or not it agreed with their choice. If their choice was incorrect, they should try to say what they would change in their thinking.
Materials
Pairs of Fractions
Line ‘Em Up
Give the children four or five fractions to put in order from smallest to biggest. Have them indicate where each one belongs on a number line labeled with 0, [pic], and 1.
The children should give an explanation of how they decided to put their fractions in order.
Material
Fraction cards
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.
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