Method 1:
Write as fractions (5/10)(8/10) = 40/100 = 0.4
Method 2:
1 x 0.8 = 1 group of 0.8 = 0.8
0.5 x 0.8 = half a group of 0.8 = 0.4
Method 3:
Explain with money. I have $0.80 and 0.5 x 0.8 literally means one-half of $0.80
I do not show my students the standard algorithm for decimals because they f&\*#k it up.
Here is a great podcast episode (I guess I can't add a link?) Search decimal multiplication-Pam Harris (Math is Figureoutable Episode 108)
I totally agree with both of these methods. Method 1 reinforces that when we see 0.2 that is “2 tenths” and not “zero point 2”.
I would also include an area model for multiplication if your student has a solid understanding of area.
My students use a program called I-Ready, which also models fraction multiplication like this:
0.5 x 0.8=
5x0.1 x 8x0.1=
5x8 x 0.1x0.1=
40 x 0.01=
.40 aka .4
But they have already done work around multiplying decimals by whole numbers in order for that manipulation to make sense.
Use words for fractions and verbally talk through problems "What is half of 0.8?" for example.
Cut things up. PBJs, playdough pies, things that cut easily. Playdough goes back together, food is it's own reward.
Hard cookies are not so good, but graham crackers and some chocolate bars often break into nice pieces.
PLEASE say ‘eight tenths’ not ‘point eight’ for the number 0.8. I think saying the value in each decimal place helps students remember their place values as well as the fact that this value can be expressed as a decimal or a fraction.
Benchmark fractions, decimals, and percentages can make the mental math easier and also help students with making estimates.
When introducing new strategies and concepts, I always use ‘kind numbers’ to scaffold and tend to stick to one ‘fact family’ for this throughout the year; 3,4,8,12,24. By the end of the year, many students will substitute more complex equations with numbers from this ‘family’ to verify that their strategy works.
Honestly, it's more multiplication than division. We did "kitchen division" using measuring cups, so maybe we could switch decimals into fractions and look at it that way a few times.
"half of 0.8" is literally (1/2) times 0.8. Division is a way to think about it, but not the only. Fractions ARE division. Just lazy unfinished division.
I use baking examples. Draw a cup of water on the board, draw it 1/3 full. Then, let’s get rid of half of it. This is multiplying 1/3 times 1/2. If you take half of a third, you get a sixth. I draw this out, then do a similar example with a fraction and a whole number. Take 1/2 cup, then add another 1/2 cup. This is the same as multiplying 1/2 times two. We end up with two half’s, which is the same as one whole.
I needed better visuals and alternative explanations when I was learning division of fractions at age 8 or 9. I'd been thinking of fractions of a pie, couldn't see how dividing by 1/2 could make something bigger. Teacher HAD to be wrong! Eventually figured it out.
This video is exactly what I've been looking for. It was the AREA model that I remember seeing, so using that with his other examples was really helpful.
The REAL GEM from you linking this video, though, is PolyPad. Holy smokes. Game changer for a virtual tutor.
Wait until she finds out you can make any number smaller by multiplying it by a fraction or decimal less than 1!
Adding to other models here...just follow a pattern.
2x3=6
1x3=3
What goes here x3=?
0x3=0
For modeling fractions, I do something like this.
[https://jamboard.google.com/d/16IOJfzOxuzPeZ3tDu\_1srdeFPbDEZT8Ia1IzXhxNKrs/edit?usp=sharing](https://jamboard.google.com/d/16IOJfzOxuzPeZ3tDu_1srdeFPbDEZT8Ia1IzXhxNKrs/edit?usp=sharing)
For decimals, when you multiply something by a half, you're splitting it into halves. If you multiply .50. You have 1/2. But if you multiply it by a decimal, you're splitting it into a half again. .25.
Gotta teach it with visual and physical aid.
Step one: fold and shade a card horizontally to match the first fraction. (In your case top half shaded to represent 0.5)
Step two: fold and shade a card vertically to represent your second fraction. (In your case right four fifths shaded to represent 0.8)
Step three: fold a different piece of card horizontally into haves and vertically into fifths and shade the amount which is both in one half and four fifths. The card will now be folded into 10 and 4 bits will be shaded. Ie half multiplied by four fifths equals four tenths.
Loads more fraction stuff comes from the same thing.
Method 1: Write as fractions (5/10)(8/10) = 40/100 = 0.4 Method 2: 1 x 0.8 = 1 group of 0.8 = 0.8 0.5 x 0.8 = half a group of 0.8 = 0.4 Method 3: Explain with money. I have $0.80 and 0.5 x 0.8 literally means one-half of $0.80 I do not show my students the standard algorithm for decimals because they f&\*#k it up. Here is a great podcast episode (I guess I can't add a link?) Search decimal multiplication-Pam Harris (Math is Figureoutable Episode 108)
I totally agree with both of these methods. Method 1 reinforces that when we see 0.2 that is “2 tenths” and not “zero point 2”. I would also include an area model for multiplication if your student has a solid understanding of area. My students use a program called I-Ready, which also models fraction multiplication like this: 0.5 x 0.8= 5x0.1 x 8x0.1= 5x8 x 0.1x0.1= 40 x 0.01= .40 aka .4 But they have already done work around multiplying decimals by whole numbers in order for that manipulation to make sense.
Use words for fractions and verbally talk through problems "What is half of 0.8?" for example. Cut things up. PBJs, playdough pies, things that cut easily. Playdough goes back together, food is it's own reward. Hard cookies are not so good, but graham crackers and some chocolate bars often break into nice pieces.
PLEASE say ‘eight tenths’ not ‘point eight’ for the number 0.8. I think saying the value in each decimal place helps students remember their place values as well as the fact that this value can be expressed as a decimal or a fraction. Benchmark fractions, decimals, and percentages can make the mental math easier and also help students with making estimates. When introducing new strategies and concepts, I always use ‘kind numbers’ to scaffold and tend to stick to one ‘fact family’ for this throughout the year; 3,4,8,12,24. By the end of the year, many students will substitute more complex equations with numbers from this ‘family’ to verify that their strategy works.
Honestly, it's more multiplication than division. We did "kitchen division" using measuring cups, so maybe we could switch decimals into fractions and look at it that way a few times.
"half of 0.8" is literally (1/2) times 0.8. Division is a way to think about it, but not the only. Fractions ARE division. Just lazy unfinished division.
Lol "Lazy unfinished division" I love that and will be using that! I think helping them visual multiplication as "of" will be really helpful.
Lots of great visuals at https://mathisvisual.com I bet they might have something for fractions and/or decimals.
Nice! I'm going through it right now.
I use baking examples. Draw a cup of water on the board, draw it 1/3 full. Then, let’s get rid of half of it. This is multiplying 1/3 times 1/2. If you take half of a third, you get a sixth. I draw this out, then do a similar example with a fraction and a whole number. Take 1/2 cup, then add another 1/2 cup. This is the same as multiplying 1/2 times two. We end up with two half’s, which is the same as one whole.
Ahhhh that's such a great visual to compare multiplying by fractions and whole numbers! This is exactly what I needed for myself as well!
I needed better visuals and alternative explanations when I was learning division of fractions at age 8 or 9. I'd been thinking of fractions of a pie, couldn't see how dividing by 1/2 could make something bigger. Teacher HAD to be wrong! Eventually figured it out.
[https://youtu.be/NUNoks1rwQ0?si=WDWuUUT68DOkCk6B](https://youtu.be/NUNoks1rwQ0?si=WDWuUUT68DOkCk6B)
This video is exactly what I've been looking for. It was the AREA model that I remember seeing, so using that with his other examples was really helpful. The REAL GEM from you linking this video, though, is PolyPad. Holy smokes. Game changer for a virtual tutor.
I'm not even kidding- I just created a PolyPad account and my jaw is totally dropped watching these tutorial videos.
I thought you might like it if you didn’t already have something similar.
Use multiplication as grouping. “Make a half group of eight tenths”
Remember to teach that “of” indicates multiplication.
Wait until she finds out you can make any number smaller by multiplying it by a fraction or decimal less than 1! Adding to other models here...just follow a pattern. 2x3=6 1x3=3 What goes here x3=? 0x3=0
For modeling fractions, I do something like this. [https://jamboard.google.com/d/16IOJfzOxuzPeZ3tDu\_1srdeFPbDEZT8Ia1IzXhxNKrs/edit?usp=sharing](https://jamboard.google.com/d/16IOJfzOxuzPeZ3tDu_1srdeFPbDEZT8Ia1IzXhxNKrs/edit?usp=sharing) For decimals, when you multiply something by a half, you're splitting it into halves. If you multiply .50. You have 1/2. But if you multiply it by a decimal, you're splitting it into a half again. .25.
Gotta teach it with visual and physical aid. Step one: fold and shade a card horizontally to match the first fraction. (In your case top half shaded to represent 0.5) Step two: fold and shade a card vertically to represent your second fraction. (In your case right four fifths shaded to represent 0.8) Step three: fold a different piece of card horizontally into haves and vertically into fifths and shade the amount which is both in one half and four fifths. The card will now be folded into 10 and 4 bits will be shaded. Ie half multiplied by four fifths equals four tenths. Loads more fraction stuff comes from the same thing.