Different Shapes, Equal Pieces

Different Shapes, Equal Pieces
Fractions and Area

Mathematical Emphasis
Investigation 1—Parts of Squares, Halves, fourths, and Eighths

Understanding that equal fractions of a whole have the same area
Understanding that equal parts of shapes are not necessarily congruent—that is, they may have different shapes
Understanding that cutting and pasting shapes conserves their area
Becoming familiar with relationships among halves, fourths, and eighths

Investigation 2—Parts of Rectangles: Thirds, Sixths, and Twelfths

Knowing that equal fractions of different-sized wholes will be different in area
Becoming familiar with relationships among thirds, sixths, and twelfths
Using different combinations to make a whole
Comparing fractions that have “one piece missing”
Working with fractions that have numerators larger than one

Investigation 3—Ordering fractions

Using both numerical reasoning and area to order fractions
Using the size of the numerator to compare fractions that have the same denominator
Using the size of the denominator to compare fractions that have the same numerator
Comparing fractions greater than 1 with fractions less than or equal to 1
Identifying equivalent fractions

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 solve a simpler version of the problem?
What have you already tried? What steps did you take?
Did you show all of your work?
Does the answer make sense?
How do you know your answer is correct?

Activities at Home

Look for opportunities to have your child help you divide things up in different way—cutting a cake, slicing the pizza.
Play Investigations games sent home in this unit: “Fraction Fish”
Help your child come up with unusual ways to divide things and have him/her prove that everyone gets the same amount.

Vocabulary Terms

Area
The size of a surface measured in square units


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


Equivalent
Having the same value or amount


Fraction
Any part of a group, number, or whole


Numerator
The number of parts of the whole; the number above the line of a fraction


Perimeter
The distance around the outside edge of a figure