Grade 4
Tips for Helping at Home
•
Questions to ask:
What is it that you don’t understand (have
the student be specific)?
What about putting things in order?
Could you try it with simpler numbers?
Can you guess and check?
Does this make sense?
What can you do to explain your answer to
show others what you are thinking?
Does your answer seem reasonable?
•
In this unit, students work on dividing squares in
several different ways. You can help your child by
encouraging him/her to come up with unusual
divisions and to convince you that the squares
are really divided in half (or quarters, eighths,
etc.)
•
Watch for situations at home where similar think-
ing is relevant—for example, how can we split the
driveway in equal amounts for shoveling snow;
what are some different ways we can put cheese
on half of a pizza?
•
Look for opportunities to talk to your children
about comparing fractions like 2/3 or 3/4.
Mathematical Emphasis
Investigation 1—Parts of Squares: Halves, Fourths, and Eighths
•
Understanding that equal fractions of a whole have the same
area
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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
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Becoming familiar with halves, fourths, and eighths
Investigation 2—Parts of Rectangles: Thirds, Sixths, and
Twelfths
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Knowing that equal fractions of different-sized wholes will be
different in area
•
Becoming familiar with relationships among thirds, sixths, and
twelfths
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Using different combinations to make a whole
•
Comparing fractions that have “one piece missing”
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Working with fractions that have numerators larger than one
Investigation 3—Ordering fractions
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Comparing any fraction to the landmarks 0, 1/2, 1, and 2
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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 with the
same numerator
•
Comparing fractions greater than 1 with fractions less than or
equal to 1
•
Understanding that fractions “missing one piece” are ordered
inversely to the size of the missing piece
•
Identifying equivalent fractions
Websites
http://cms.everett.k12.wa.us/math
http://nlvm.usu.edu/en/nav/vlibrary.html
Fractions and
Area
In this unit students are asked to come up with many
different ways to divide a square into fourths and
then eighths. One interesting way to generate fourths
is to start with a simple division into fourths, such as
example A, and to cut a small piece from each
fourth to add to the next fourth, as in example B. As
long as you do the same thing to all four fourths, the
resultant figure with also be divided into equal
fourths.
As students work with these fractions, they soon be-
gin to come up with many creative ways to divide
squares into fourths.
When working with eighths, students will likely first
come up with a picture like Kim’s, then begin to mod-
ify into something like Jesse’s. More unusual eighths,
like Qi Sun’s, may emerge more slowly, as these
eights require a deeper understanding.
Vocabulary
Area:
the size of a two-dimensional figure I
square units
Perimeter:
distance around the outside edge
of a closed figure
Equivalent:
having the same value
Congruent:
having exactly the same shape
and size
<:
less than symbol (4 < 5)
> :
greater than symbol (5 > 4)
Fraction:
a number showing part of a whole
Whole Number:
all counting numbers
including zero
Glossary
http://www.amathsdictionaryforkids.com/
Capture Fractions
Materials:
Deck of fraction cards
Players:
2 or more
How to Play:
1. Divide the deck into equal-sized piles, one for
each player. Players hold their piles upside
down.
2. In each round, each player turns over the top
card in his or her pile. The person with the larg-
est fraction wins, takes the other player’s cards,
and puts them on the bottom of his or her own
pile.
3. If two of the cards show equivalent fractions,
those two players turn over another card. Who-
ever has the larger fraction wins all the other
player’s cards.
4. The person with the most cards wins. The game
can be stopped at any time.
Tierney, C. Investigations in Number, Data, and Space: Different Shapes,
Equal Pieces. Dale Seymour, 1998.
