Mathematical Thinking - Lake Washington School District

Mathematical Thinking at Grade 3

Introduction to Mathematics

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
Exploring materials that will be used throughout this curriculum as problem-solving tools
Communicating about mathematical thinking through written and spoken language

Investigation 2—Doubles and Halves

Reviewing coin values and finding the values of collections of coins
Exploring which numbers can be divided in half evenly

Investigation 3—Data and Handfuls

Sorting and classifying information
Collecting, recording, and representing data
Describing data presented in tallies and graphs
Using grouping to count tallies or objects
Developing strategies to combine and compare quantities

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

Your child will have assignments to work on at home this year. Sometimes he or she will ask for your participation. Play games sent home with units; allow your child to teach the game to you. Your child will be figuring out ways to make $1.00. Have him/her count change and work with money at home.
Often children will work out number problems using real objects. When working at home, it helps to have a collection of small objects (like beans, pennies or buttons) that can be used as counters.

Vocabulary Terms

100 Chart: 10 by 10 grid of the numbers from 1 to 100. Children use the 100 chart to look for number patterns.
Bar Graph: Data representation using the height of bars to show the amount of data being represented
Coins: Coins used in this unit include pennies, nickels, dimes, and quarters
Line Plots: Data is arranged on a horizontal axis with each piece of data represented with an X
Representation: A graph, picture or chart showing the data that was collected
Skip Counting: Counting up by multiples of a number (10, 20, 30, 40…)

Mathematics Vocabulary Web site

Mathematics Strategy—Patterns on a Hundred Chart

Patterns on a 100 Chart lead children to develop a deeper understanding of our number system and the relationships among numbers. Using a 100 chart, children will see a variety of patterns. A few examples of patterns include:

The numbers in every horizontal row increase by ones
The numbers in every vertical column increase by tens
The value of the ones in each vertical column is the same
The value of the tens in each horizontal row is the same until you read the last square
When you mark multiples of 2, every other vertical column is marked
When you mark multiples of 5, two vertical columns are marked
When marking multiples, you can use patterns to check your accuracy.

Source: Investigations in Number, Data, and Space: Mathematical Thinking at Grade 3. Dale Seymour, 1998.

Mathematics Game—Addition Subtraction BINGO

Materials

100 chart for each player

Deck of numeral cards

Markers

Playing the Game

Each player uses a 100 chart as a BINGO board. The goal is to mark five numbers in one row—up, down, or diagonal--like in BINGO.

Put numeral cards in a pile in the middle; players take turns drawing two cards from the deck, the first card is the tens digit and the second card is the ones digit. A wild card can be used as any numeral.

Once the two-digit-number is built, the player chooses to add 10, subtract 10, or stay with the original number. This is marked on his/her 100 chart.

The next player draws two new cards, builds a two-digit number and chooses to add 10, subtract 10 or stay with the number. This number is marked on the second player’s 100 chart.