I can understand and explain how multiplying a number by a fraction greater than, less than, or equal to 1 affects its size (scaling/resizing)
This standard helps your child develop important mathematical skills.
Multiplication doesn't always make numbers bigger! When we multiply a number by a fraction, we are "scaling" or resizing it.
Imagine a starting number on a number line.
Draw a rectangle.
Use a tape diagram to represent an original quantity.
Encourage your child to predict! Before calculating 6 x 2/3, ask: "Will the answer be greater than, less than, or equal to 6?" Since 2/3 is less than 1, the product will be less than 6. For 6 x 3/2, the product will be greater than 6 because 3/2 is greater than 1. This builds number sense about scaling.
1. Focus on "Times as Much": Rephrase multiplication as "times as much." For example, 3 x 1/2 means "half times as much as 3" or "half of 3." This helps connect to the idea of resizing.
2. Predict the Outcome: Before multiplying, ask: "Will the answer be bigger or smaller than the number we started with? Why?" This reinforces understanding of scaling up (multiplying by >1) or scaling down (multiplying by <1).
3. Use Concrete Examples: Relate to real-world scaling. "If this recipe makes 12 cookies, and we only want to make 2/3 of the recipe, will we make more or fewer than 12 cookies?" (Fewer, because 2/3 is less than 1).
4. Visual Comparison: Draw two bars. One represents the original number. The other represents the scaled number. For 5 x 3/4, draw a bar for 5, then draw another bar that is 3/4 the length of the first bar. This visually shows the "shrinking."
5. Emphasize "Of" Means Multiply: Remind them that in many contexts, especially with fractions, "of" means multiply. So, "1/2 of 6" is the same as "1/2 x 6." This can make scaling problems more intuitive.
Activity 1: Scaling Sort: Write multiplication problems on cards (e.g., 8 x 3/2, 10 x 1/4, 5 x 4/4). Have your child sort them into three piles: "Makes Bigger," "Makes Smaller," "Stays the Same," without actually calculating.
Activity 2: Scaling Stories: Give a simple multiplication problem like 6 x 1/3. Ask your child to create a short story problem where this multiplication would be used to scale something down (e.g., "A ribbon is 6 inches long. I need a piece that is 1/3 of that length. How long is the piece?").
Activity 3: Greater Than or Less Than?: Call out a number (e.g., 10). Then call out a fraction (e.g., 5/4). Ask your child to quickly say if multiplying 10 by 5/4 will result in a number greater than, less than, or equal to 10. Discuss why.
Activity 4: Real-World Scaling Hunt: Look for examples of scaling in everyday life. "This picture is enlarged by 150% (which is 1 1/2 times). This map is scaled down." Discuss if the scaling factor is greater or less than 1.
Write a whole number (e.g., 12). Then, write a fraction next to it (e.g., 3/4). Ask your child: "If we multiply 12 by 3/4, will the answer be bigger than 12, smaller than 12, or equal to 12? Why?" Repeat with fractions like 5/4 (bigger) and 4/4 (equal).
Write simple scaling scenarios on slips of paper (e.g., "A recipe is doubled," "A photo is shrunk to half its size," "A model car is 1/10th the size of a real car"). On other slips, write corresponding multiplication factors (e.g., x 2, x 1/2, x 1/10). Have your child match the scenario to the scaling factor and explain if it scales up or down.
Show a multiplication problem involving a whole number and a fraction (e.g., 8 x 5/3). Ask your child to quickly state if the product will be greater than, less than, or equal to the whole number. Discuss their reasoning. Focus on the fraction being greater than, less than, or equal to 1.
Use coins or play money. Say, "I have $10. If I multiply this by 1/2 (or find 1/2 of it), will I have more or less money? How much?" Then try, "If I multiply my $10 by 1 1/2 (or 3/2), will I have more or less?" This makes scaling more tangible.
Find a simple recipe (e.g., for cookies or a drink). Ask your child: "What if we want to make 1 1/2 times this recipe? Will we need more or less of each ingredient? How would we find out?" (Multiply each ingredient by 3/2). Then try, "What if we only want to make 2/3 of the recipe?" (Multiply by 2/3). This shows scaling up and down in a practical context.
Look at a map with a scale (e.g., 1 inch = 10 miles). Measure a distance on the map. Ask: "If the real distance is 10 times the map distance, what fraction are we multiplying by to scale up from the map to reality?" (10/1). Then, "If we know the real distance, what fraction would we multiply by to find the map distance?" (1/10). Discuss how map scales work by multiplying.
When you resize a photo on a computer or phone, discuss the scaling. "If we make this photo 200% of its original size, what fraction are we multiplying its dimensions by?" (2/1 or 2). "If we shrink it to 75% of its original size, what fraction is that?" (3/4). Does it get bigger or smaller? Why?
If your child has model cars, trains, or dollhouse furniture, discuss the scale factor. "If this model car is 1/24th the size of a real car, and the real car is 12 feet long, how long is the model?" (12 x 1/24 feet). Is the model scaled up or down from the real thing? By what kind of fraction (greater or less than 1)?
Look at a growth chart. "If you were 3 feet tall last year, and this year you are 1 1/6 times as tall, are you taller or shorter? How can we figure out your new height?" (Multiply 3 by 7/6). This connects scaling to personal growth.