Mathematical Emphasis
Investigation 1: How Many Hundreds?
- Grouping things for more efficient counting
- Recording numbers for more efficient mental arithmetic
- Estimating how many hundreds in the total of a group of three-digit numbers
- Communicating about mathematical thinking through writing and speaking
- Exploring materials used in this curriculum as problem solving tools
Investigation 2: How Many Dollars?
- Grouping coins for more efficient counting
- Recognizing values of U.S. coins
- Recognizing the decimal point on the calculator
Investigation 4: Geometric Patterns
- Distinguishing between geometric patterns and random designs
- Distinguishing between mirror symmetry and rotational symmetry
- Writing about designs
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 that your answer is correct?
Helping At Home:
- Your child will have assignments to work on at home this year. Sometimes they will involve your participation. For example, your child will be teaching you several games that can be played cooperatively at home.
- During this unit, students will solve problems involving money. It would help them to have an assortment of coins to work with at home. Involve your child in solving problems using money.
Vocabulary Terms
- Coins
- Students need to know the value of pennies, nickels, dimes, quarters, and half dollars as well as dollar bills
- Difference
- The difference between two numbers, the answer to a subtraction problem
- Estimation
- An approximate or rough calculation, rounding is one form of estimation
- Mirror Symmetry
- An object has mirror symmetry when one half is the mirror image of the other half
- Rotational Symmetry
- An object has rotational symmetry if its turned outline has the same shape
- Sum
- The total or whole amount, the answer to an addition problem
Mathematics Vocabulary Web site
Mathematics Strategy: Two Powerful Addition Strategies
Left to Right Addition—Biggest Quantities First
When students develop their own strategies for addition from an early age, they usually move from left to right, starting with bigger parts of the quantities.
For example, when adding 27 + 27, a student might say, “20 and 20 is 40, then 7 and 7 is 14, so 40 plus 10 more is 50 and then 4 more makes 54.”
This strategy is both efficient and accurate. Some people who are extremely good at computation use this strategy as their basic approach to addition, even with large numbers.
Rounding to Nearby Landmarks
Changing a number to a more familiar one that is easier to compute with is another strategy that students should develop. Multiples of 10 and 100 are especially useful landmarks at this age.
For example, in order to add 199 and 149, a student might think of the problem 200 plus 150, find a total of 350, then subtract 2 to compensate for the 2 added at the beginning and get an answer of 348.
There are no rules about which landmarks in the number system are the best to use. It simply depends on whether using nearby landmarks helps a child solve the problem.
Source: Investigations in Number, Data, and Space: Mathematical Thinking at Grade 4. Dale Seymour, 1998. (Pages 21 and 22).
Mathematics Game—Make a Dollar
Materials
Deck of Coin Cards (4 sheets)
Players: 2 or 3
Playing the Game
- Deal out 8 Coin Cards face up between players. Put the rest of the pack in a pile face down.
- Players take turns finding pairs that equal one dollar. When pairs are removed, replace with two new cards from the pile.
- If everyone agrees there are no combinations that make one dollar, all 8 cards are shuffled and put back in the pack. 8 new cards are put out.
- The goal is to collect as many pairs of cards (dollars) as possible.
- The game ends when all the cards have been paired and the player with the most dollars (pairs) wins.
Get to Coin Cards (for printing)