Mathematical Emphasis
Investigation 1—Things That Come in Groups
- Finding things that come in groups
- Using multiplication notation
- Using multiplication to mean groups of groups
- Writing and illustrating multiplication sentences
Investigation 2—Skip Counting and 100 Charts
- Recognizing that skip counting represents multiples of the same number and has a connection to multiplication
- Finding patterns in multiples of 2, 3, 4, 5, 6, 9, 10, 11, and 12 on the 100 chart
- Understanding that the patterns numbers make can help us multiply those numbers
Investigation 3—Arrays and Skip Counting
- Recognizing that finding the area of a rectangle is one situation where multiplication is used
- Using arrays with skip counting to multiply and divide
- Finding factor pairs
- Making connections between number and shape
Investigation 4—The Language of Multiplication and Division
- Understanding the relationships between multiplication and division
- Identifying whether word problems can be solved using division and/or multiplication
- Using multiplication and division notation to write number sentences
Investigation 5—Problems with Larger Numbers
- Using patterns to solve multiplication and division problems
- Sorting out complex problems that require both multiplication and division
- Making up division and multiplication story problems from real data
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
- Play the games sent home during the unit including array games like “Count and Compare” and “Multiplication Pairs.”
- Through class activities children will be learning lots of multiplication pairs and combinations (facts). Skip counting is an excellent way to practice and learn these multiplication relationships. Practice skip counting at home.
- Your child will be bringing home activities using 100 charts. Have your child teach you about the patterns on 100 charts.
Vocabulary Terms
- Array
- Rectangular arrangement of squares; the length and width of the array are factors, the area is the product of a multiplication problem
- Factor
- A whole number that can be multiplied by another factor to get a product
- Multiple
- Mathematical operation where a number is added to itself a number of times
- Repeated Addition
- A way of showing a multiplication problem using the addition of groups (4 x 2 = 2 + 2 + 2 + 2)
- Skip Counting
- Counting up by multiples of a number (2, 4, 6, 8…)
Mathematics Vocabulary Web site
Mathematics Strategy—The Relationship Between Division and Multiplication
Multiplication and division are related operations and are taught together in Investigations. Both involve two factors and the multiple that is created when those factors are multiplied. These related sets of problems are sometimes called “Fact Families.” Here is a set of linked multiplication and division problems:
Many problems children encounter can be described using either multiplication or division. For example:
I bought a package of 24 treats for my dog. If I give her 3 treats every day, how many days will
this package last?
This problem could be written in standard notation as either division or multiplication:
Understanding the relationship between multiplication and division gives students the tools to solve problems in multiple ways.
Source: Investigations in Number, Data, and Space: Things That Come in Groups. Dale Seymour, 1998, Page 15.
Mathematics Game—Multiple Cover-Up
Materials
100 chart for game board
Number cards from 2-50 (cut up a second 100 chart to use as number cards)
Playing the Game
- The game board is placed in the middle of the players. The number squares are placed in a box or bag.
- Each player draws ten number squares and arranges them face up so everyone can see the numbers.
- The player with the smallest number starts the play by calling out any factor.
- All players find any of their number squares that are multiples of the factor that was called. These number squares are placed on the matching number on the game board.
- Players take turns calling out factors. All players get to find multiples of the factor and place number squares on the board.
- The object of the game is to get rid of all your number squares by placing them on the board. The game ends when a player has no more number squares.
Variation: Use number cards from 2-100. This is more difficult!
Get to 100 Chart (for printing)