Grade 3
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?
•
Your student will be figuring out ways to make
$1.00 and will be asking to count the change in
your pocket or purse.
•
In class, students will be making a set of
Addi-
tion cards
. You will probably recognize these as
addition facts, although we call them combina-
tions. Your child will be sorting these cards into
“the ones I know” and “ the ones I am working
on.” Speed is not the goal: the goal is for each
child to develop effective strategies for combining
numbers. Sometimes for homework, the children
will choose a few combinations that they are
working on and think about strategies that will
help them remember them. For example, one
strategy a child might use is this:
What ‘s 6 + 7? Well, I know 6 + 6 is 12, and 6 + 7 is
one more than that so it’s 13.
You can help with these combinations by listening
you your child’s strategies or sharing ones that you
use.
Website
http://cms.everett.k12.wa.us/math/Third
Grade
Mathematical Emphasis
Investigation 1—What’s a Hundred
•
Counting and grouping quantities to make 100
•
Becoming familiar with the number patterns on the
100 chart
Investigation 2—Doubles and Halves
•
Constructing symmetrical patterns
•
Learning the addition combinations 1+1 to 10+10
•
Developing and using addition strategies, including
the use of known addition combinations to help
learn others
•
Exploring what happens when 10 or 20 is added or
subtracted
•
Exploring what numbers can be divided in half
evenly
•
Reviewing coin values and finding the values of
collections of coins
Investigation 3—Data and Handfuls
•
Sorting and classifying information
•
Collecting, recording and representing data
•
Describing data presented in tallies and graphs
•
Developing strategies to combine and compare
quantities
Investigation 4 - Exploring Odds and Evens
•
Exploring the characteristics of odd and even num-
bers and examining how they behave when they
are combined
•
Using evidence gathered from examples to make
conjectures about the ways numbers behave
•
Continuing to develop familiarity with addition com-
binations
•
Working with wholes and halves
•
Exploring mathematical tools such as the calcula-
tor
Introduction
7 + 6 =
6 + 7 =
Clue: ______________________
Game
Plus - Minus - Stay the Same
Materials: 100 chart for each player, Deck of numeral
cards ( 0 - 9 plus 4 wild cards), counters to mark on the
chart.
Players: 2
How to Play:
1. Decide who will go first. The first player chooses two
Numeral Cards from the deck to get a base number.
The first card is the tens digit, the second is the ones
digit. A Wild Card can be used as any numeral.
2. Decide whether you want to
add
10 to this number,
subtract
10 from this number, or
stay
with this num-
ber. Cover the resulting number on your 100 chart.
3. The other player now chooses two Numeral Cards
from the deck, determines the number, and decides
whether to
add
10 to that number,
subtract
10 from
that number, or
stay
with that number.
4. Put the cards you use in a discard pile. (if you run out
of cards, mix these up and use them again.)
5. The goal is to cover five numbers on your 100 chart in
a row - across, up and down, or diagonally - before
your partner does. The game continues until one
player has five in a row.
7
Glossary
http://www.amathsdictionaryforkids.com/
Two Powerful Addition Strategies
Most of us who are teaching today learned to add
starting with the ones, then the tens, then the hun-
dreds, and so on, moving from right to left and
“carrying” from one column to another. This algorithm
is certainly efficient once it is mastered. However,
there are many other ways of adding that are just as
efficient, closer to how we naturally think about quan-
tities, connect better with good estimation strategies,
and generally result in fewer errors.
When students rely on memorized rules and proce-
dures that they do not understand, they usually do
not estimate or double-check. They can easily make
mistakes that make no sense. We want students to
think about quantities they are using and what results
to expect. We want them to use their knowledge of
the number system. We want them to break apart
and recombine numbers in ways that make computa-
tion more straightforward and, therefore less prone to
error. Writing problems horizontally rather than verti-
cally is one way to help students focus on the whole
quantities.
Left to Right Addition: Biggest Quantities First
When adding 27+27, a student might say “20 and 20
is 40, then 7 + 7 is 14, so 40 plus 10 more is 50 and
4 more makes 54.” This strategy is both efficient and
accurate. One advantage of this approach is that
when students work with the largest quantities first,
its easier to maintain a good sense of what the final
sum should be. Another advantage is that students
tend to continue seeing two 27’s as whole quantities,
rather than breaking them up into their separate dig-
its and losing track of the whole.
Rounding to Nearby Landmarks
To add 27 and 27, some students might think of the
problem as 30 + 30, then subtract 3 and 3 to give
them the final result. Of course, there are other use-
ful landmarks, too. Another student might think of tis
problem as 25+25+2+2.
Having more than one strategy is a necessary part of
doing computation, and that using what you know
about the numbers to simplify the problem leads to
procedures that make sense.
Russell, S. Investigations in Number, Data, and Space: Mathematical Think-
ing at Grade 3. Dale Seymour Publications, 1998.
4
6
Vocabulary
Odd - a number that is not divisible by 2
5
Even - a number that is divisible by 2
4
Representation - organizing information in a way that
others may understand. This could be in the form of a
picture, graph, chart, or model.
