Mathematical Emphasis
Investigation 1—Multiples on the 100 Chart
- Using skip counting as a model for multiplication
- Seeing multiplication as an accumulation of groups of a number
- Looking for the multiplication pattern of numbers
- Interpreting standard multiplication and division notation
- Using known multiplication relationships to solve harder problems
Investigation 2—Arrays
- Using an array as a model for multiplication
- Becoming more familiar with multiplication pairs
- Recognizing prime numbers as those that each have only one pair of factors and only one array
- Becoming familiar with a variety of notation used for multiplication and division
- Understanding how division notation represents a variety of division situations
- Determining what to do with “leftovers” in division, depending on the situation
Investigation 3—Multiplication and Division with Two-Digit Numbers
- Becoming fluent in basic multiplication relationships
- Partitioning numbers to multiply them more easily
- Recognizing multiplication and division situations and representing each situation using a mathematical statement
- Learning about patterns that are useful for multiplying by multiples of 10
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 your answer is correct?
Helping At Home
- Play the Array Games that come home as part of this unit.
- Practice skip counting (counting by 2’s, 3’s, etc.). Try skip counting starting at a number other than zero (count by 2’s starting at 17).
- Find real life examples of arrays (floor tiles, stacks of items in a cupboard, cars in a parking lot). Talk about the rows and columns (dimensions) and figure out the total number.
Vocabulary Terms
- Area
- The size of a surface measured in square units
- Array
- A set of objects arranged in rows and columns with equal amounts in each row; a rectangular array is a rectangle whose dimensions equal the factors of a multiplication problem.
- Composite
- A number with more than two factors
- Dimensions
- Length of a side of a figure (like a rectangle)
- Factor
- A whole number that can be divided evenly into another number
- Perimeter
- The distance around the outside edge of a figure
- Prime Number
- A number with only two factors (1 and itself)
- Product
- The result when two numbers are multiplied
Mathematics Vocabulary Web site
Mathematics Strategy—Ways to Solve 36 x 4
Many students see multiplication problems as one of repeated addition although their explanations differ.
Others may know that if two 27’s is equal to 54, then four 27’s is double.
We expect that many students will be able to break apart numbers into smaller, more familiar multiplication problems as one of their strategies. Here are two versions.
Source: Investigations in Number, Data, and Space: Arrays and Shares. Dale Seymour, 1998. (Pages 58-9)
Mathematics Game—Multiples BINGO (from ten minute math)
Materials
100 chart for each player
Factor 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 factor cards in a pile in the middle; players take turns drawing a card for the group.
- When a number is drawn, every player marks one number that is a multiple of the factor card and writes the factor in the square. (If a 2 is drawn, a player can mark any even number on their board.)
- If a wild card is turned over, that player can choose any factor from 1 to 100.
- The game continues until one player colors five numbers in a row and gets BINGO.
Get to 100 Chart (for printing)
Get to Factor Cards (for printing)