Multiplicative Comparison: Comparing quantities by showing how many times larger one quantity is than another
- Identify the larger quantity (Sarah: 24 stickers)
- Identify the smaller quantity (Tom: 6 stickers)
- Divide the larger quantity by the smaller quantity
- State the result as "times more"
Sarah has 24 stickers, Tom has 6 stickers
To find how many times more, divide Sarah's stickers by Tom's stickers: 24 ÷ 6
24 ÷ 6 = 4
Sarah has 4 times more stickers than Tom
Sarah has 4 times more stickers than Tom because 24 ÷ 6 = 4
• To find how many times larger one quantity is than another, divide the larger by the smaller
• "Times more" means multiplication relationship
Measurement Division: Finding how many groups of a certain size can be made from a total amount
The rope is 36 feet long
Each piece is 4 feet long
Total length ÷ Length of each piece = Number of pieces
36 ÷ 4 = 9
We will have 9 pieces because 36 ÷ 4 = 9
• Measurement division: Total ÷ Size of each group = Number of groups
• This tells us how many equal parts we can make
Partitive Division: Dividing a total amount into equal groups to find how many items are in each group
There are 48 students in total
They are divided into 6 equal groups
Total students ÷ Number of groups = Students per group
48 ÷ 6 = 8
There are 8 students in each group because 48 ÷ 6 = 8
• Partitive division: Total ÷ Number of groups = Items per group
• This tells us how many items go in each equal group
Division: The operation of splitting a number into equal parts or groups
Multiplicative Comparison: Showing how many times larger one quantity is than another
Measurement Division: Finding how many groups of a certain size can be made
Partitive Division: Dividing into equal groups to find how many in each group
Quotient: The answer to a division problem
Remainder: What's left over when division doesn't come out evenly
- Read the problem carefully and identify what is being asked
- Identify the total amount and the number of groups or size of each group
- Determine which type of division problem it is (multiplicative comparison, measurement, or partitive)
- Set up the division equation with the appropriate numbers
- Calculate the quotient using division facts or algorithms
- Check your answer by multiplying to see if you get the original total
- State your answer in the context of the problem
• Division is the inverse of multiplication
• Dividend ÷ Divisor = Quotient
• If Dividend ÷ Divisor = Quotient, then Quotient × Divisor = Dividend
• You cannot divide by zero
• Any number divided by itself equals 1
• Any number divided by 1 equals itself
Definition: Problems that ask how many times larger one quantity is than another
Keywords: "times more," "times as many," "how many times," "multiplied by"
Formula: Larger quantity ÷ Smaller quantity = Times more
Example: "John has 20 marbles. Mary has 5 marbles. How many times more marbles does John have?"
Solution: 20 ÷ 5 = 4, so John has 4 times more marbles
Definition: Problems that ask how many groups of a certain size can be made
Keywords: "how many groups," "cut into pieces," "packaged into," "divided into"
Formula: Total amount ÷ Size of each group = Number of groups
Example: "A ribbon is 24 inches long. If cut into pieces of 6 inches each, how many pieces?"
Solution: 24 ÷ 6 = 4, so 4 pieces can be made
Definition: Problems that ask how many items are in each group when divided equally
Keywords: "each group," "per person," "in each," "divided equally"
Formula: Total amount ÷ Number of groups = Amount per group
Example: "There are 18 cookies shared equally among 3 children. How many cookies per child?"
Solution: 18 ÷ 3 = 6, so each child gets 6 cookies
Problem 1: "Tom has 35 books. Jane has 7 books. How many times more books does Tom have?"
Type: Multiplicative comparison
Solution: 35 ÷ 7 = 5, so Tom has 5 times more books
Problem 2: "A farmer has 42 apples to pack into boxes of 6 apples each. How many boxes does he need?"
Type: Measurement division
Solution: 42 ÷ 6 = 7, so he needs 7 boxes
Problem 3: "A teacher has 24 pencils to share equally among 8 students. How many pencils does each student get?"
Type: Partitive division
Solution: 24 ÷ 8 = 3, so each student gets 3 pencils
Manipulative Practice: Use counters, blocks, or other objects to model division problems
Word Problem Creation: Write your own division word problems based on real-life situations
Picture Drawing: Draw diagrams to represent division problems visually
Group Games: Play division fact games with classmates or family members
Real-Life Scenarios: Practice with actual situations like sharing snacks or organizing items
- Practice basic division facts regularly to build fluency
- Read word problems multiple times to understand what is being asked
- Circle or underline key information in word problems
- Check your work by multiplying your answer by the divisor
- Use estimation to check if your answer is reasonable
- Work with a partner to discuss problem-solving strategies
• Always identify what the problem is asking for
• Look for clue words that indicate the type of division problem
• Check your answer by multiplying to verify it's correct
• Make sure your answer makes sense in the context of the problem
• Practice regularly to build fluency with division facts
Questions & Answers
Question: How do I know if a word problem is multiplication or division? They seem similar.
Answer: Great question! Here's how to tell the difference:
- Multiplication problems: Usually ask for a total when you know the number of groups and how many in each group. Look for words like "each," "total," "altogether," or "product."
- Division problems: Usually ask for either the number of groups or how many in each group when you know the total. Look for words like "shared equally," "how many in each," "how many groups," or "divided by."
For example: "There are 5 boxes with 8 apples in each box. How many apples altogether?" (Multiplication: 5 × 8 = 40)
Vs: "There are 40 apples shared equally among 5 boxes. How many apples in each box?" (Division: 40 ÷ 5 = 8)
Question: My child struggles with word problems. How can I help them understand division word problems better?
Answer: Here are some effective strategies:
- Act it out: Use real objects like toys, blocks, or food items to model the problem
- Draw pictures: Sketch the situation described in the problem
- Highlight key words: Circle or underline important information and clue words
- Read multiple times: Have your child read the problem at least twice before attempting to solve
- Ask questions: "What do you know? What are you trying to find?"
- Make it personal: Change the names in the problem to include your child or family members
Consistent practice with visual aids and real objects helps build understanding.
Question: What if the division doesn't come out evenly? What do I do with the remainder?
Answer: Good question! What to do with the remainder depends on the problem:
- If it's about sharing: The remainder is what's left over that can't be shared equally
- If it's about making groups: You might need an extra group for the remainder
- If it's about materials: You might need to round up to ensure you have enough
Example: "If you have 17 cookies and want to put 5 in each bag, how many bags do you need?"
17 ÷ 5 = 3 R2, so you need 4 bags (3 full bags and 1 more for the 2 remaining cookies)
Always consider the context of the problem when dealing with remainders!