Mathematical Emphasis
Investigation 1—Sharing Brownies

• Realizing that fractional parts must be equal (for example, that one-third is not just one of three parts but one of three equal parts)
• Developing familiarity with conventional fraction words and notation
• Becoming familiar with grouping unit fractions, those that have a numerator of 1

Investigation 2—Pattern-Block Cookies

• Developing familiarity with common equivalent fractions, especially relationships among halves, thirds, and sixths
• Understanding that what occurs between 0 and 1 also occurs between 1 and 2 and between any consecutive whole numbers
  For example,

Tips For Helping At Home
Questions To Ask:

• What is the problem about? Tell me in your own words.
• What did you do in class to get started?
• Can you make a drawing (model) to help you figure out the problem?
• Can you solve a simpler version of the problem?
• What have you already tried? What steps did you take?
• Does your answer make sense?
• How do you know your answer is correct?
• Did you show all of your work?

Helping At Home

• When your family really is sharing food, talk about “fair shares” and help your child name fractions. If you want to split the pizza among five people, how can you split it fairly? How much does each person get?
• Cooking is another great way to learn about fractions. How can we measure ¾ cup? Look together at how the fractions appear on a measuring cup. Doubling recipes, or cutting them in half, can help your child understand how to make new numbers with fractions.
• Throughout the unit, look over your child’s work. Ask about the fraction work the class is doing and encourage your child to explain some of the problems to you. Early on, you’ll make a set of Fraction Cards together. Later your child will learn a game you can play with these cards.

Vocabulary Terms

Denominator

The bottom number of a fraction, the number of parts the whole is divided into

Equivalent

Representing the same amount; of equal value

Mixed Number

A number that is a combination of whole numbers and fractions

Numerator

The top number of a fraction, the number naming the parts of the whole

Mathematics Vocabulary Web site

Mathematics Strategy—Different Shapes, Equal Pieces
Many younger children believe that if you split a rectangle into two equivalent rectangles and then split the same rectangle into two equivalent triangles, the smaller rectangle is not equal to the smaller triangle. By third grade most children are able to see that the rectangle and the triangle are equal because both are half of the larger rectangle.

This understanding of the constancy of halves is developmental and comes after experiences with composing (putting together) and decomposing (taking apart) shapes. Most third graders in this unit will come to understand that the pieces are the same size because they are both half of a constant amount. Children show a good understanding of the concept when they can show that the pieces are the same by cutting and moving parts of one shape to make the other shape.

Source: Investigations in Number, Data, and Space: Fair Shares. Dale Seymour, 1998. (Page 12)

Mathematics Activity—Making Fraction Cards
Materials

5 sheets of paper that are all the same size

Marker or crayon

Scissors

Envelope or resealable bag for storage

Directions

1. Fold and label sheets of paper as shown. Write the fraction on one side only. Draw the fold lines and cut on the lines.



2. Halves: Fold the sheet in the middle.



3. Thirds: Fold the sheet into 3 equal pieces.



4. Fourths: Fold the sheet in half one way and then fold it in half the other way to make 4 equal pieces.



5. Sixths: Fold the sheet the way you did to make thirds. Cut apart the thirds. Fold two of the thirds in half the long, skinny way and cut to make long, skinny sixths. Fold the other third in half the fat way to make shorter, chunky sixths.



6. Eighths: Fold the sheet into fourths. Cut part the fourths. Fold each fourth in half and cut into eighths

Mathematics Game—Fraction Challenge
A math game that is similar to the traditional game of “War”

Materials

Two sets of fraction cards

Directions

1. You need space on a table or the floor for this game. Each player needs a set of fractions cards that are mixed up. The fraction labels need to be face down.



2. Both players turn up one card at a time and show the fraction label.



3. The player with the biggest fraction takes both cards.



4. If the cards show fractions that are the same, both players turn over a second card and the player with the biggest fraction takes all four cards.



5. The player with the most fraction cards at the end of the game wins.

Variations

1. As players get cards, they try to combine fractions to make a whole (1). Wholes are laid out on the table.



2. At the end of the game, the player with the most wholes wins the game.