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Unit 2 Section B Goals and Expected Skills 

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Unit 2 Section B Goals and Expected Skills 

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Use same-sized wholes to show equivalent fractions.

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Mixed Numbers and Improper Fractions on the Number Line

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Unit 2 Section C Goals and Expected Skills

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Unit 2 Section C Goals and Expected Skills

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Unit 3 Section B Goals and Expected Skills 

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Unit 3 Section B Goals and Expected Skills 

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Unit 3 Section B Goals and Expected Skills 

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Unit 3 Section B Goals and Expected Skills 

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Unit 2 Section A Goals and Expected Skills 

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Unit 2 Section A Goals and Expected Skills 

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Unit 3 Section A Goals and expected skills

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Unit 3 Section A Goals and expected skills

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Section A Main ideas and expected skills 

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Section A Main ideas and expected skills 

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Section B main ideas and expected skills  

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Section B main ideas and expected skills  

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What we're going to talk about in this video is the idea of a fraction. And we'll see there's many ways to think about a fraction. But first, we'll think about the most fundamental. So let's say that I have this square. And we can consider this a whole. So let me write that down. This is a whole. It is a complete square. Now, what I'm going to do is divide this into 4 equal parts. So with one cut like that, I've divided it into 2 equal parts, and then with another cut like this, I could divide it into 4 equal parts. So there are 4 equal parts. And now what I'm going to do is I'm going to select one of those equal parts, so let's say this part right over here. I am going to select that. So the question is, what fraction of the whole is the part that I have shaded in red? Well, it is 1 out of the 4 equal parts, right? I've shaded in 1 out of 1, 2, 3, 4 equal parts. So we write this as this fraction. This piece represents 1/4 of the whole. And there's two ways that you can think about this. You could view this as 1 of the 4 equal parts, or you could view this as a whole divided by 4 would get you exactly this much. Now let's do another one. And this time, let's think about how we could represent 1 over 8, so 1 over 8. Well, we could divide this whole, in this case, the whole is this rectangle-looking thing. We could divide the whole into 8 equal parts. So let's do that. So here I've divided into 2 equal parts. That looks pretty good. And now I can divide each of those into 2 equal parts to get me 4 equal parts. And then if I were to divide each of those into 2 equal parts, I will have 8 equal parts. And it's not exact. Obviously, I've drawn it by hand, but hopefully this gets you a sense. So now I have 8 equal parts. And now I'm going to select exactly one of them. And that'll represent 1/8. And I could select any one of these, but I'll just do this one to show you it does not have to be necessarily the first one. So once again, this square right over here that I'm shading in red represents 1/8 of the whole. Now, let's look at a few more examples where I've shaded them in ahead of time. And what I want you to do right now is pause the video, and either in your head or a piece of paper write down if you consider this purple thing, the whole, what fraction does this red part represent? If you consider this blue part the whole, what fraction does this red part represent? If you view this yellow triangle as a whole, what fraction does this red part represent? And so I encourage you to pause the video now. Well, let's look at each of these. So in this case, for this rectangle, we have 3 equal parts, and we've shaded in one of them. So this red rectangle right over here represents 1/3 of the whole. Now, Over here, in this kind of pie-looking thing, this circle-looking thing, we have 1, 2, 3, 4, 5 equal parts. And we have shaded in 1 of those 5 equal parts. So this little slice of the pie, this represents 1/5. This right over here is 1/5 of the entire pie. Now, this one's interesting. You might be tempted to say, well, I've got 5 parts, and then I've shaded in 1. That must represent 1/4. But remember, it needs to be 4 equal parts. And it's pretty clear looking at this that this part right over here is not equal in size to this part right over here or this part right over here. These are not 4 equal parts. So we cannot say that this is 1/4 of the triangle. So you cannot say that.

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Intro to fractions (video) | Fractions intro | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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We're asked to identify the numerator and denominator in the fraction 3 over 4, or 3/4. So let's rewrite this just so it's nice and big. So let me just write the fraction. So we have 3 over 4, 3/4. Now, they want us to identify the numerator and the denominator. So the numerator is just the number on top, so the numerator is the 3 right there. And then they want us to find the denominator. The denominator is just the number on the bottom. It's the 4. So if they say what's the numerator? 3. What's the denominator? It's 4, just the number on the bottom. They could've just called this the number on the bottom. They could've just called this the number on top. Now to think about what this represents, what this fraction represents, you can think of it as three out of four pieces of a pie. That's how I think about it. So you can imagine, the denominator tells us, what are we taking a fraction out of or how many pieces are there? So let's imagine a pie like this. So we could draw like a square pie. So this is what the denominator represents. This is what the number on the bottom represents. And then 3 says, we are representing three of those four pieces. So this 3 tells us that out of 4 possible ones, I guess you could think of it, we are using three, or maybe we're eating three. So you can imagine if someone says I ate three-fourths of a pie-- this would be read as three-fourths-- they're eating the blue portion of the pie if we cut it this way. If we imagine a round pie, it would look like this. Let me draw a round pie. So that is my round pie. Let me cut it into four equal pieces or roughly equal pieces. And if someone says I ate three-fourths of this pie, where the 3 is the numerator, and then the 4, and you'd read that as three-fourths, the 4 is the denominator, they would eat this much of the pie. They would eat 3 of the 4 pieces. So this is is one piece, this is two pieces, and this is three pieces. So you could imagine the 4, the denominator represents the total number of pieces in the pie, and then the 3 represents how many of those we ate.

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Identifying numerators and denominators | Fractions | Math (video) | Khan Academy

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We're asked to identify the numerator and denominator in the fraction 3 over 4, or 3/4. So let's rewrite this just so it's nice and big. So let me just write the fraction. So we have 3 over 4, 3/4. Now, they want us to identify the numerator and the denominator.

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Fractions on a Number Line Song | 3rd Grade & 4th Grade

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Factors and Multiples made easy |Prime Factorization| Find factors of all numbers| Class 1 to 5 |

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What are Multiples of a Number? How are Factors and Multiples related? | Don't Memorise

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Finding factors of a number | Factors and multiples | Pre-Algebra | Khan Academy

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Perimeter and area are basic concepts in geometry. Yet, to master them, students need plenty of practice. Our free online interactive area and perimeter game is perfect for helping your students master these concepts.

Using the interactive area and perimeter game is intuitive and easy. Click and drag the colored blocks onto the grid to create rectangles or irregular shapes. The tool will automatically show students the totals of the perimeter and area in the upper left hand corner of shapes of the same color. Perimeter sums also appear along the edge of the shape. You can toggle these features on and off using the "Hide Totals" and "Hide Perimeter" buttons in the top right hand corner. If you create several shapes, you can click on them to show the perimeter and area of each one. Clear the grid using the trash can button.

Offer students a given perimeter or area and see how many different ways they can achieve those totals with the blocks.

Visit classplayground.com for more resources and printables related to perimeter and area. For more interactives on geometry visit mathmine.com..

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Area Perimeter Explorer | Geometry for Kids | Toy Theater

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This online interactive area and perimeter game is perfect for helping students practice and master these essential geometry concepts.

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Prime and Composite Numbers: StudyJams! Math | Scholastic.com

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In the world of factors, there are two kinds of numbers: prime and composite. This activity will teach students to identify prime and composite numbers.

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A prime number is a whole number that only has two factors which are itself and one. A composite number has factors in addition to one and itself.

The numbers 0 and 1 are neither prime nor composite.

All even numbers are divisible by two and so all even numbers greater than two are composite numbers.

All numbers that end in five are divisible by five. Therefore all numbers that end with five and are greater than five are composite numbers.

The prime numbers between 2 and 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.

Is the number prime or composite?

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A prime number is a whole number that only has two factors which are itself and one. A composite number has factors in addition to one and itself. The numbers 0 and 1 are neither prime nor composite. All even numbers are divisible by two and so all even numbers greater than two are composite numbers.

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Determine whether the following numbers are prime, composite, or neither. So just as a bit of review, a prime number is a natural number-- so one of the counting numbers, 1, 2, 3, 4, 5, 6, so on and so forth-- that has exactly two factors. So its factors are 1 and itself. So an example of a prime factor is 3. There's only two natural numbers that are divisible into 3-- 1 and 3. Or another way to think about it is, the only way to get 3 as a product of other natural numbers is 1 times 3. So it only has 1 and itself. A composite number is a natural number that has more than just 1 and itself as factors. And we'll see examples of that and neither-- we'll see an interesting case of that in this problem. So first let's think about 24. So let's think about all of the-- I guess you could think of it as the natural numbers or the whole numbers, although 0 is also included in whole numbers. Let's think of all of the natural counting numbers that we can actually divide into 24 without having any remainder. We'd consider those the factors. Well, clearly it is divisible by 1 and 24. In fact, 1 times 24 is equal to 24. But it's also divisible by 2. 2 times 12 is 24. So it's also divisible by 12. And it is also divisible by 3. 3 times 8 is also equal to 24. And even at this point, we don't actually have to find all of the factors to realize that it's not prime. It clearly has more factors than just 1 and itself. So then it is clearly going to be composite. This is going to be composite. Now, let's just finish factoring it just since we started it. It's also divisible by 4. And 4 times 6-- had just enough space to do that. 4 times 6 is also 24. So these are all of the factors of 24, clearly more than just one and 24. Now let's think about 2. Well, the non-zero whole numbers that are divisible into 2, well, 1 times 2 definitely works, 1 and 2. But there really aren't any others that are divisible into 2. And so it only has two factors, 1 and itself, and that's the definition of a prime number. So 2 is prime. And 2 is interesting because it is the only even prime number. And that might be common sense you. Because by definition, an even number is divisible by 2. So 2 is clearly divisible by 2. That's what makes it even. But it's only divisible by 2 and 1. So that's what makes it prime. But anything else that's even is going to be divisible by 1, itself, and 2. Any other number that is even is going to be divisible by 1, itself, and 2. So by definition, it's going to have 1 and itself and something else. So it's going to be composite. So 2 is prime. Every other even number other than 2 is composite. Now, here is an interesting case. 1-- 1 is only divisible by 1. So it is not prime, technically, because it only has 1 as a factor. It does not have two factors. 1 is itself. But in order to be prime, you have to have exactly two factors. 1 has only one factor. In order to be composite, you have to have more than two factors. You have to have 1, yourself, and some other things. So it's not composite. So 1 is neither prime nor composite. And then finally we get to 17. 17 Is divisible by 1 and 17. It's not divisible by 2, not divisible by 3, 4, 5, 6. 7, 8, 9 10, 11, 12, 13, 14, 15, or 16. So it has exactly two factors-- 1 and itself. So 17 is once again-- 17 is prime.

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Recognizing prime and composite numbers (video) | Khan Academy

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Determine whether the following numbers are prime, composite, or neither. So just as a bit of review, a prime number is a natural number-- so one of the counting numbers, 1, 2, 3, 4, 5, 6, so on and so forth-- that has exactly two factors. So its factors are 1 and itself.

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Prime and Composite Numbers | Maths | EasyTeaching

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Written explanation of how to solve

FIND THE FACTORS is a logic puzzle based on the multiplication table. In this table, the numbers 1 - 12 in the top row and first column are factors of the products listed on the inside of the table.

Since several of the products are listed more than once, the chart below can be very helpful. It shows every product in the multiplication table and the factors from the table that make those products. (Since multiplication is commutative, 3 x 5 = 15 and 5 x 3 = 15. To save space both facts are simply listed as 5 x 3 with the greater factor listed first.)

Most people can fill out a multiplication table even if it looks like this:

FIND THE FACTORS challenges you to complete a similar looking multiplication table except NONE of the factors are given! Only a few of the products are given as clues. To help you solve the puzzles, here are step by step instructions to solve a level 5 puzzle that includes most types of situations you may encounter trying to solve any of the puzzles

1. FIND THE FACTORS 1-10 is a logic puzzle. The object is to write each of the numbers 1 - 10 in both the top row (the factor row) and the first column (the factor column) so that those written numbers are the factors of the given clues. There is only one solution. Here is a sample puzzle:

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2. First look for the following perfect squares: 1, 25, 49, 64, 81, or 100 because there is only one way to factor each of those numbers so that both factors are not greater than ten. In this puzzle, the 1 must be 1 x 1 and the 25 must be 5 x 5. Note that perfect squares 16 and 36 both have more than one way to factor them using only factors less than 10, so deal with those clues later. (If you were trying to solve FIND THE FACTORS 1 - 12, you would also look for perfect squares 121 and 144.)

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3. Next look for a row or a column with at least 2 clues so that you can find a factor for both clues. This puzzle has one column and one row that qualify. However, the clues, 36 & 24, are not helpful yet because 2 different numbers (4 and 6) will factor into both 36 & 24. On the other hand, the column containing 24 and 72 is very useful because 8 × 3 = 24 and 8 × 9 = 72, and all of those factors are not greater than 10. Since 8 is the ONLY common factor meeting that condition, write 8 above that column and write 3 and 9 in the corresponding cells.

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4. Since you have found the 3 in the factor column, try to find the 3 in the factor row. Because the only way to factor 21 is 3 × 7, that has to be where the other 3 belongs. Likewise, since 42 = 7 × 6, you know where to write its factors. Write the 3, 7, 7, and 6 in the corresponding cells.

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5. Remember when we noticed that both 4 and 6 were factors of both 36 and 24? Finding that 6 in the factor column for the previous step means that 6 cannot also be the factor of the clue pair 36 & 24. Therefore, you have found where the 4 should be written in the factor column. Write 4, 9, & 6 in their corresponding factor cells.

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6. You know that a 2 must appear somewhere in the factor column so let's consider everyplace 2 might go:

2 × 20 = 40, but you can't write 20 in the factor row.

2 × 8 = 16, but there's already an 8 in the factor row.

The only place in the factor column that the 2 can be written is in the cell next to the row with no clues.

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7. The factors of 16 are 4 × 4 and 2 × 8. Since 4 already appears in either the factor row or the factor column, 4 × 4 cannot be the factors of 16 needed here. Write 2 in the factor row and 8 in the factor column.

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8. The only number 1 - 10 missing in the factor column is 10. Since 10 × 4 = 40, write 10 & 4 in the cells. Now count from 1 to 10 while you determine what number is missing in the factor row. In this case the missing number is 10.

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9. Now all the factors have been found! At this point I don't always fill in the rest of the table, but when I do, I can complete a 10 x 10 table in less than 3 minutes and a 12 x 12 table in less than 5. It would benefit any child to see an adult filling in a table just for the fun of it. What a powerful example of lifelong learning would be set!

All of the steps listed above can be summarized in a single chart.

Video explanations of how to solve:

Here I've made videos of each level of the Find the Factors 1 - 10 puzzles getting solved. My goal was to make the videos short, so each video is no more than 2 minutes 20 seconds long. Enjoy!

An extra complicated level 6:

Even though every row and every column of this puzzle has at least one clue, the logic is very complicated. I've written several notes on the puzzle, but it will still take a couple of minutes just to use logic to figure out where to start.

Challenge Puzzle:

I explain how to use logic to get started on this Find the Factors 1-12 Challenge Puzzle:

Perfect Square (findthefactors.wordpress.com)

Just Like Sudoku? (findthefactors.wordpress.com)

Dimensions (findthefactors.wordpress.com)

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Written explanation of how to solve FIND THE FACTORS is a logic puzzle based on the multiplication table. In this table, the numbers 1 - 12 in the top row and first column are factors of the products listed on the inside of the table. Since several of the products are listed more than once,...

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Recognizing fractions greater than 1 (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Slice a pizza, and we get fractions:

The top number says how many slices we have.
The bottom number says how many equal slices the whole pizza was cut into.

Have a try yourself:

Equivalent Fractions

Some fractions may look different, but are really the same, for example:

=

=

(Four-Eighths)

(Two-Quarters)

(One-Half)

=

=

It is usually best to show an answer using the simplest fraction ( in this case ). That is called Simplifying, or Reducing the Fraction

Numerator / Denominator

We call the top number the Numerator, it is the number of parts we have.
We call the bottom number the Denominator, it is the number of parts the whole is divided into.

You just have to remember those names! (If you forget just think "Down"-ominator)

Adding Fractions

It is easy to add fractions with the same denominator (same bottom number):

Another example:

Five-eighths plus one-eighth equals six-eighths, equals three-quarters

Adding Fractions with Different Denominators

But what about when the denominators (the bottom numbers) are not the same?

Three-eighths plus one-quarter equals ... what?

We must somehow make the denominators the same.

Three-eighths plus two-eighths equals five-eighths

There are two popular methods to make the denominators the same:

(They both work nicely, use the one you prefer.)

Other Things We Can Do With Fractions

We can also:

Visit the Fractions Index to find out even more.

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The top number says how many slices we have. The bottom number says how many equal slices the whole pizza was cut into. Some fractions may look different, but are really the same, for example: = = (Four-Eighths) (Two-Quarters) (One-Half) = = It is usually best to show an answer using the simplest fraction ( in this case ).

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Fraction walls are a great way to teach about fractions and in particular equivalent fractions. In a fraction wall each row or layer of the wall represents one whole number. The layers are divided into a number of bricks and hence each brick represents a fraction whose denominator is equal to the number of bricks in that layer. Each brick can be turned on or off by clicking it. This wall also allows the display of decimal and percentage values. To the right of the wall are boxes which can be hidden, the value of each box is fraction of the wall that has been turned on.

Selecting different walls

When you launch this interactive teaching program the initial wall is a mixed one showing 3 distinct fraction families. Change the wall by using the mode control. 'Large' displays a wall in which the layers are split 1,2,3 up to 12. The others split the wall along 2s, 3s or 5s. The 5s also includes a lower wall of 100 bricks, this naturally works quite well in explaining percentages since each brick represent ¹⁄ ₁₀₀ or 1%.

Fractions, decimals or percentages

Use the display type control to display decimals (rounded to 2dp), percentages (rounded to 1dp), fractions or none.

The equivalent fraction control

Normally when you click a brick to turn it on or off, only that brick is affected. However if you turn on the equivalent fraction function by clicking the 'Eq' toggle button. Now when a brick is clicked the other layers will turn on bricks if they can match an equivalent fraction. Note, this is not always possible, in fact if you select the primes wall it is never possible to show an equivalent fraction. In this case all the other layers have bricks turned off.

Least Common Multiple

Also known as 'the lowest common multiple' or 'smallest common multiple' is crucial when adding, subtracting or comparing fractions. This button will calculate the LCM based on the rows that have active bricks. Pressing the LCM button will create a new wall that contains the originally selected fraction but also a new layer with the number of divisions equalling the least common multiple of the denominators of the other rows. Sounds complicated, but it really just means that it is always possible to create an equivalent fraction in the LCM row from the other rows.

Other controls

The other controls are

'On' button when clicked will turn on all the bricks

'Off' button when clicked will turn off all the bricks

'Random' button creates a randomized wall in which roughly half the bricks are on. Usually you would hide the totals before pressing this and then the class can work out each fraction in the random wall.

' < ' button will align all the bricks to the left hand side of the wall. This is often pressed after using the randomize function. Fractions can then be compared by considering the length of each row of on bricks.

hide totals click to hide all the totals. The individuals total can then be clicked to show the value.

show totals reveal all the totals.

Advanced Section

To show or hide the advanced section click the advanced toggle button

When the advance controls are on, each layer of the wall has a dedicated slider, move this to change the number the number of bricks in that layer.

Automatic 1 button when clicked create a new wall by dividing the top layer by all its ascending prime factors. So for example if you move the top slider so the top layer has 42 bricks and then click the button. The primefactors of 42 are 2,3 and 7. So the second layer will have 42÷2=21 bricks, the third layer will have 21÷3=7 bricks and the final layer will have 7÷7= 1 brick.

Automatic 2 is similar but creates a layer for every factor of the top layer value.

Add Layer adds a new layer to the bottom of the wall.

total type select control will change the type of total to display. The default is to match what the wall shows, so in this case if the wall is showing fraction the total will be a fraction. But using this control it is now possible for fractions to be shown in the wall but the total to be given as a percentage.

Further fractions

Closely related to this activity is the percentage fraction and decimals grid, which can be used to display a square or circle fraction representation.

Other activities that can be used to teach fractions are the clock activity which uses the clock face to show the fraction of minutes passed in an hour. Launch the activity and select the fractions mode, this mode also show equivalent fractions for example ³⁰⁄ ₆₀ = ¹⁄ ₂. The number explorer activity can show the fraction resulting from division of a number.

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Interactive Fraction Wall | online fraction | percentage | decimal | visnos

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Online fraction wall, easily display fractions using interactive white board. Simple to explore fraction,decimals and percentages . Step by step view equivalent fractions. Beautiful display which children love.

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Pattern Shapes by The Math Learning Center

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Students use Pattern Shapes to explore geometry and fractions, create their own designs, or fill in outlines. As they work with shapes, students think about angles, investigate symmetry, and compose and decompose larger shapes.

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Explore different representations for fractions including improper fractions, mixed numbers, decimals, and percentages. Additionally, there are length, area, region, and set models.

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This applet allows you to create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line.

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Improper Fractions Mixed Numbers Worksheets * EasyTeaching.net

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improper fractions mixed numbers worksheets: find positions on number lines, convert improper fractions to mixed numbers using pizza models and much more!

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Welcome to our Improper Fraction Worksheets page.

Here you will find a wide range of free printable Fraction Worksheets which will help your child understand and practice how to convert improper fractions to mixed numbers.

Improper Fraction Worksheets

Proper and Improper Fractions & Mixed Numbers

A fraction is a number with the form: \[ {n \over d} \]

If the numerator is smaller than the denominator (if n < d), then the fraction is called a proper fraction, and its value is less than 1.

If the numerator is greater than the denominator (if n > d), then the fraction is called an improper fraction, and its value is greater than 1.

If the numerator is equal to the denominator, then the fraction's value is equal to 1.

A mixed number (or mixed fraction) is a number that has a whole number part to it, and a fraction part to it.

Types of Fractions Examples

\[{3 \over 7} \; , \; {2 \over 10} \; and \; {17 \over 26} \] are all proper fractions.

\[ {31 \over 5} \; , \; {15 \over 10} \; and \; {37 \over 23} \] are all improper fractions.

\[ 3{1 \over 5} \; , \; 2 {5 \over 8} \; and \; 4 {1 \over 2} \] are all mixed numbers or mixed fractions.

Improper Fractions Support

Here you will find the support page on how to find equivalent fractions if you get stuck or want some support.

Improper Fraction Worksheets

Here you will find a selection of Fraction worksheets designed to help your child to understand and practice converting improper fractions.

The sheets are carefully graded so that the easiest sheets come first, and the most difficult sheet is the last one.

We have split the sheets into two sections with the first section looking at improper fractions visually.

The sheets in the second sections are more abstract and tricky!

Using these sheets will help your child to:

understand what improper fractions are;

convert improper fractions to mixed numbers;

convert mixed numbers to improper fractions.

These sheets are aimed at students at 4th and 5th grade, with the more abstract worksheets for 5th graders.

Improper Fraction Worksheets to Mixed Numbers
Visual Fractions

Mixed Numbers to Improper Fraction Worksheets
Visual Fractions

Convert Improper Fraction Worksheets
Visual Fractions

Convert Improper Fractions to Mixed Fractions Trickier Sheets

Convert Mixed Fractions to Improper Fractions Trickier sheets

Improper Fraction Calculator

If you just want a calculator to do the hard work for you, then try our Improper Fraction Calculator.

The calculator will convert any mixed number to an improper fraction, or an improper fraction into a mixed number.

The great thing is that it will also show you all the working out - job done!

Simplifying Fractions

Take a look at our Simplifying Fractions Practice Zone or try our worksheets for finding the simplest form for a range of fractions.

You can choose from proper fractions, improper fractions or both.

You can print out your results or benchmark your scores against future achievements.

Good for practising equivalent fractions as well as converting to simplest form.

Great for using with a group of children as well as individually.

Comparing Fractions

We have some carefully graded worksheets on comparing and ordering fractions.

You can choose from supported sheets with diagrams for students who need extra help to harder worksheets for those more confident.

Learning Fractions

Are you looking for free fraction help or fraction support?

Here you will find a range of fraction help on a variety of fraction topics, from simplest form to converting fractions.

There are fraction videos, worked examples and practice fraction worksheets.

Fraction Riddles

Riddles are a great way to get children to apply their knowledge of fractions.

These riddles are a good way to start off a maths lesson, or also to use as a way of checking your child's understanding about fractions.

All the fraction riddles consist of 3 or 4 clues and a selection of 6 or 8 possible answers. Children have to read the clues and work out which is the correct answer.

The riddles can also be used as a template for the children to write their own clues for a partner to guess.

How to Print or Save these sheets

Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!

How to Print or Save these sheets

Need help with printing or saving?
Follow these 3 easy steps to get your worksheets printed out perfectly!

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

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Welcome to our Improper Fraction Worksheets page. Here you will find a wide range of free printable Fraction Worksheets which will help your child understand and practice how to convert improper fractions to mixed numbers.

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Comparing fractions with the same numerator (video) | Khan Academy

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- [Voiceover] Let's compare 2/4 and 3/4. First let's think about what these fractions mean. 2/4 means we have some whole, and we've split it into four equal size pieces, and we get two of those pieces. Maybe we can think about pizza for an example. We split a pizza into four equal size pieces, and we ate two of them. 3/4 means that same whole, that same pizza was again split into four equal size pieces, but this time, what's different is we got three of the pieces. So maybe from that description, we can start to think about which one is larger, but let's draw them also just to be sure that we can decide which one is larger. So for 2/4, we're gonna have a fraction, maybe it's a pizza, and it's gonna be divided, split into four equal size pieces. These may not be perfect lines, but should represent four equal size pieces. And we get two of those pieces. So this represents 2/4, two out of four. 3/4, again, will be the same as the four equal size pieces, but this time, we get three of the four. So, one, two, three of the four pieces. And this will represent 3/4. Now we can look at it visually and see very clearly that 3/4 is greater, or takes up more space, or we can say that 2/4 is less than 3/4. Remember this is the less than symbol 'cause we always want this open, bigger side facing our larger number. In this case, it's facing the second number. So we'll say 2/4 is less than 3/4. Each of these fourths is the same size, so two of them is less than three of the fourths. Here we can try one more, but this time, let's don't draw the picture. Lets' just think about what they mean and see if we can figure it out. So for 5/8, we have a whole, and it's been divided into eight equal pieces. For 3/8, same thing, eight equal pieces. But here in 5/8, we get five of those pieces, and in 3/8, we get three of the pieces. So the pieces are the same size. They're eighths on both side. These are eighths, and these are eighths, but here we have five of the eights, and here we have three. So if the pieces are the same size, five pieces is greater than three pieces or 5/8 is greater than 3/8. And here our open end, our bigger side is still facing our bigger number, but our bigger number is first this time, so this is the greater than symbol. 5/8 is greater than 3/8.

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Comparing fractions with the same denominator (video) | Khan Academy

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Voiceover] Let's compare 2/4 and 3/4. First let's think about what these fractions mean. 2/4 means we have some whole, and we've split it into four equal size pieces, and we get two of those pieces. Maybe we can think about pizza for an example.

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Comparing fractions with the same numerator

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Video transcript

we've already seen that if we take a whole and in this example the whole is this entire green circle and if we were to split it into five equal sections one two three four five so we've split it into five equal sections and if we were to select one of those five equal sections so let's say we select this section right over here that we have selected one-fifth of the whole one out of the 5 equal sections we could do the exact same thing on a number line everything we've been doing so far has to deal with shapes but we could do the exact same idea on a number line so let me draw a number line here so let me draw it pretty big so we get a sense of things so go all the way to there and let's say let's say that this is 0 this is 1 and this is 2 and of course we could keep going if we had more space 2 3 4 and and on and on and on and what I want to do instead of taking a circle and dividing it into five equal sections I want to take the section of our number line between 0 and 1 and divide it into five equal sections so let me see if I can do this so so 1 2 3 4 5 that looks pretty good I'm drawing it as as exact as I can with my hand but let's just assume these are five equal sections so what would happen what would you think would be a good label for this number right over here well it's the exact same idea between 0 & 1 I've traveled 1 out of the 5 equal sections towards 1 and actually let me make it a little bit neater than that make it make the equal sections look a little bit better 1 2 3 4 5 and what we're thinking about is this what what should be called this number here this number is clearly between 0 & 1 it's clearly closer to 0 and we've gone 1 out of the 5 equal sections towards 1 well it makes complete sense that look we had five equal sections here five equal sections here and we've traveled one of them towards one so we should call this number right over here 1 so when we're talking about the fraction 1/5 it's not just talking about hey what part of a pizza pie have I eaten or something like that it's actually this is actually a number this is a number and we can actually plot it on the number line now you might say okay well that's fair about one-fifth but what about all these other slashes what numbers would we call that well we have we can make the same it's the exact same idea if up here instead of shading in 1 out of the 5 equal sections if I shaded in two of the five equal sections then I wouldn't say this is 1/5 anymore I would say that this is 2/5 and so if I go to of the equal sections towards 1 then I should call this number right over here I should call this 2/5 and I can keep going this right over here should be 3 3 over 5 this right over here I've gone one two three four out of the five sections towards one so I could call this 4/5 4/5 and that could keep going I could call this right over here I've traveled five out of the equal out of the 5 equal sections towards five so I could call this right over here five let me do that in a red color I could call this right over here five over five anyone's any weight but five over five we've gotten to one and that's exactly right if I were to shade in five things over here let me do that a little bit cleaner if I were to shade in five that's not the color I want to use if I were to shade in five things over here we've already seen that shading in five things so if this is let me make this a little bit neater if this is now five over five or five fifths we've already seen that this is a whole and over here if we've traveled five fifths of the way towards one we've gotten to the whole one five fifths is the exact same thing five fifths is the exact same thing as one it is equal to a whole

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Fractions on a number line (video) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

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Number Line helps students visualize number sequences and demonstrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing.

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Fractions - Fractions on a Number Line - Online

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This activity will help students identify fractions on a number line. It gives immediate feedback.

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Woot Math

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Students understand a fraction as a number on the number line, label a number line using fraction notation, and place fractions on a number line in a variety of real-world contexts. Fractions are less than 1, between 1 and 2, and whole numbers written in fraction form.

Real World Number Line Applications

Placing Fractions Between 1 and 2 on a Number Line

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Free online math practice problems for use with interactive whiteboard. Students understand a fraction as a number on the number line, label a number line using fraction notation, and place fractions on a number line in a variety of real-world contexts. Fractions are less than 1, between 1 and 2, and whole numbers written in fraction form.

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Woot Math.

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Free online math practice problems for use with interactive whiteboard. Students use visual models to name fractions as a⁄b where a is how many parts are represented and b is how many equal-sized parts are in the whole. The whole is equal to whole fraction circles, other fractions, and sets of objects.

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Woot Math

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Free online math practice problems for use with interactive whiteboard. Students use bars, number line, and real-world contexts to determine if two fractions are equivalent and to build equivalent fractions. Students determine how many objects in a set are equal to 1⁄2, 1⁄3, or 1⁄4 of the set.

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Intro to equivalent fractions | Fractions | 4th grade | Khan Academy

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Equivalent fractions | Fractions | Pre-Algebra | Khan Academy

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Students often struggle with the concept of fractions. This interactive fraction strips tool helps students visualize fractions. With these online fraction strips, students can model fractions, solve fraction problems, explore equivalent fractions, and observe the differences between denominators.

To use the interactive fraction strips tool, click and drag the strips onto the canvas. You can drag as many of each fraction as you'd like. To remove the strips, drag them off the canvas. Change the chart to accommodate two whole units by pressing the "Unit Double" button. Add annotations using the pencil tool and erase using the eraser. To clear the canvas, press the trash can button.

A few activities you can do with students while using the online fraction strip tool include:

Have students model a given fraction, mixed or not. For example 1 1/4 or 3/6.

Ask students to model addition, subtraction, multiplication, or division problems using the fraction strips.

Ask students to find equivalent fractions for a certain fraction. For example, how many sixths are equivalent to 1/3?

Ask students to use the pencil tool to divide one of the wholes on the chart into fourths. Then, students can check their work by dragging fourths onto the chart afterward.

Looking for more fraction manipulatives? Try our interactive fraction circles.

Visit classplayground.com for more resources and printables about fraction strips.

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Fraction Strips | Free Virtual Manipulatives | Toy Theater

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Use the interactive fraction strips tool to help students visualize, model, and explore fractions. Students can also solve problems using fraction strips.

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Use this interactive online fraction bars tool to help students visualize and understand fractions. This free fraction bars tool is great for exploring fractions through operations, equivalent fractions, and modeling.

To use the tool, press the arrows to change the numerator and denominator. As you do so, the fraction bar below will adjust to represent the fraction visually. Once you've chosen your fraction, you can click, drag, and drop it onto the chart above. To remove fraction bars from the chart, click and drag them off. Or, you can simply put another fraction bar on top of the others. Conveniently, the colors of the bars change to make comparing the fractions easy.

Wondering how to use the online fraction bars too? Here are some ideas:

Ask students to display a fraction and put it on the chart as a fraction bar (ie. 1/2). Then, ask students to display an equivalent fraction bar (ie. 2/4).

Ask students to model operations involving fractions.

Invite students to compare fractions by displaying various different ones on the chart. Which fractions show more than half? Which show less than half? Which show more than a quarter?

Visit classplayground.com to access more resources on fractions.

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Fraction Bars | Teaching Tools | Toy Theater Educational Games

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Modeling fractions is easy with this interactive fraction bar tool. Use it to study equivalent fractions, operations with fractions, and more!

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Equivalent Fractions | Math for 3rd Grade | Kids Academy

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Compare fractions to a benchmark of one half using number lines

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In this lesson, you will learn how to compare fractions with different numerators and denominators to the benchmark fraction of one half by using number lines.

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Let's think about how or what 1/2 times 5 represents. So one way to think about it is that this could be five 1/2's added together. So you could view this as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is the same thing as 1 plus 1 plus 1 plus 1 plus 1, over 2, which is equal to 5/2. The other way to think about this is that you start with 5 things. So let's say, that's 1 thing. Let me copy and paste that so they all look the same. So then let me paste it. So that's 2 things. That's 3 things. That's 4 things. And that's 5 things. So the other way to think about it is you start with 5 things, and you take 1/2 of them. So what would be 1/2 of this? Well, let's see. You have 5 things, so you would get-- 5 divided by 2 would be 2 and 1/2. So you would get this far. Let me make it like this. So you would get this one. You would get this one. And you would get this one. Now, is this the same thing as 5/2? Well, what happens if we divide each of these wholes into halves? So let's do that. So if we just multiplied-- so we just divide each of these into 2. So instead of having 5 wholes, we now have 10 halves. How many of those halves have we filled in? Well, we have filled in 1, 2, 3, 4, 5. So this is also equal to 5/2. So far we just did it thinking about what multiplication actually means. But if you said, well, how did I compute this? Well, the way you could think about it, and multiplying fractions is actually straightforward from that point of view, is as long as you can express both of them as fractions, and 5 we already know is the same thing as 5 ones, so this we can just multiply times 5/1. So now that I've expressed both of them as fractions, I can just multiply the numerator. So 1 times 5 over 2 times 1. And what's that going to be equal to? Well, 1 times 5 is 5. 2 times 1 is 2. So once again, we get 5/2.

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Multiplying unit fractions and whole numbers (video) | Khan Academy

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Let's think about how or what 1/2 times 5 represents. So one way to think about it is that this could be five 1/2's added together. So you could view this as 1/2 plus 1/2 plus 1/2 plus 1/2 plus 1/2, which is the same thing as 1 plus 1 plus 1 plus 1 plus 1, over 2, which is equal to 5/2.

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Multiplying fractions is about combining parts of a whole. When you multiply two fractions together, you're taking a part of a part. When you multiply a fraction by a whole number, you're taking multiple copies of that fraction. In both cases, the result is a new fraction that represents a different part of a whole. Created by Sal Khan.

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Video transcript

Let's think a little bit about what it means to multiply 2/3 times 6. One way to think about it is to literally take six 2/3 and add them together. This is six 2/3 right over here. And if we wanted to actually compute this, this would be equal to-- well, we're going to take these six 2's and add them together. So we could view it as 2 times 6 over 3. 2 times 6 over 3, which is the same thing, of course, as 2, 4, 6, 8, 10, 12, 12/3. And what is 12/3 equal to? Well, we could rewrite 12 as-- so this is equal to-- we could rewrite 12 as 3 plus 3 plus 3 plus 3 over the yellow 3. Let me do it like this so I don't have to keep switching colors. This is going to be the same thing as 3/3 plus 3/3 plus 3/3 plus 3/3. And each of these are obviously a whole. Each of these equal 1. That's 1 and that's 1, so this is going to be equal to 4. So that's one way to conceptualize 2/3 times 6. Another way to think of it is as 2/3 of 6. So let's think about that. Let me draw a number line here. And I'm going to draw the number line up to 6. So what I care about is the section of the number line that goes to 6. So that looks pretty good. So this is 1, 2, 3, 4, 5, and 6. So if we want to take 2/3 of 6, we can think of this whole section of the number line between 0 and 6 as the whole. And then we want to take 2/3 of that. So how do we do that? Well, we divide it into thirds, to three equals sections. So that's one equal section, two equal sections, and three equal sections. And we want two of those thirds. So we want 1/3 and 2/3. Now where does that get us? That gets us to 4. So we get, obviously, to the same answer. We would be in a tough situation if somehow we got two different answers. Either way, 2/3 times 6 or 6 times 2/3, either way, that is going to be equal to 4. But there are two different ways of viewing this. This first way is literally viewing it as 2/3 six times. And this way is we're taking a fraction of the number 6. We're going 2/3 of the way to 6, which would get us to 4.

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Multiplying fractions and whole numbers (video) | Khan Academy

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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teaches Common Core State Standards 4.NF.B.4.a http://corestandards.org/Math/Content/4/NF/B/4/a

teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1

teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6

teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8

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2. Playing Fill Three: Multiplying unit fractions by whole numbers (FP)

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Lesson objective: Multiply a unit fraction by a whole number. This lesson helps to build fluency with multiplying a unit fraction by a whole number. Number lines are used here because they support the understanding that fractions are numbers and can be operated on in the same ways as whole numbers can be operated on.

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Fractions on a Number Line - 3rd Grade Math Videos for Kids

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In this lesson, you will learn how to solve word problems involving adding fractions with the same denominator by using a number line. (Targeted, concept-based 3-5 minute instructional video to help you plan your lesson.)

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Lesson video for 'Add fractions with like denominators using a number line'

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In this lesson, you will learn how to solve word problems involving adding fractions with the same denominator by using a number line. (Targeted, concept-based 3-5 minute instructional video to help you plan your lesson.)

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Add and subtract fractions with like denominators using number lines. Grade 4

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- [Instructor] So let's see how we could approach four and 1/4 minus two and 2/4. Pause this video and have a go at that before we work on this together. All right, so the first thing that you might try to do is re-write this as four and 1/4 minus two and 2/4. And the reason why it's useful to write it this way is we could say look, each of these mixed number have a whole number part and then they have a fractional part. And so I could try to subtract the fractional part from the fractional part and then the whole number part from the whole number part. And that will often work. But when we go to just the fractional parts and we say hey, how do I subtract 2/4 from 1/4, 2/4 is larger than 1/4. You immediately might find yourself in something of a conundrum. So what do you do? Well, what comes to the rescue is a notion called regrouping and that's that we're not just subtracting 2/4 from 1/4. We're subtracting two and 2/4 from four and 1/4. So what we could do is we could take some of the value that's in this four and regroup it into the fraction. What do I mean by that? Well instead of four, if I view four as three and 4/4, 4/4. And so 4/4 plus 1/4 is 5/4, 5/4. So I could re-write this as three and 5/4 minus two and 2/4. Once again, why is that useful? Because 5/4 is greater than 2/4. What is 5/4 minus 2/4? Well that's going to be 3/4. And then what is three minus two? Well that's going to be one. And we get one and 3/4. Another way we could of thought about it is this is the same thing as four minus two plus 1/4, plus 1/4, minus 2/4, minus 2/4. And we have trouble with the 1/4 minus 2/4. That's what we saw right over here. So what we do is we take some of that value from the four. Instead of four we could re-write that as three plus 4/4. That's the same thing as four. And of course you have minus two plus 1/4 minus 2/4. And then if you add the 4/4 to the 1/4 that's going to give us 5/4. So you're going to have three minus two. That's that part and that part. And then you're going to have if you add the 4/4 and the 1/4, so plus 5/4 minus 2/4. And that exactly what we have here. Three and 5/4, three and 5/4 minus two, minus two, and minus 2/4. And so three minus two is one. 5/4 minus 2/4 is 3/4.

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Subtracting mixed numbers with regrouping (video) | Khan Academy

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Instructor] So let's see how we could approach four and 1/4 minus two and 2/4. Pause this video and have a go at that before we work on this together. All right, so the first thing that you might try to do is re-write this as four and 1/4 minus two and 2/4.

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We're asked to subtract and simplify the answer, and we have 8/18 minus 5/18. So subtracting fractions is very similar to adding fractions. If we have the same denominator, the denominator in the difference is going to be the same as the denominators in the two numbers that we're subtracting, so it's going to be 18. And our numerator is going to be the difference between the numerators. So in this case, it is 8 minus 5, and this will be equal to 3 over 18, which is the answer, but it's not completely simplified, because both 3 and 18 are divisible by 3. So let's divide them both by 3. So you divide 3 by 3, you divide 18 by 3, and you get 3 divided by 3 is 1. 18 divided by 3 is 6, so you get 1/6. And just to see this visually, let me draw 18 parts. Let me draw 18 parts here. So it might be a little bit of a messy drawing. I'll try the best I can. So let me draw six in this direction. So that is three right there. We have another three, so that's six parts. And then let me split this into three columns. So there we go. We have 18 parts. Now 8/18 is equal to one, two, three, four, five, six, seven, eight. That's 8/18. And now we want to subtract five of the eighteenths, so we subtract one, two, three, four, five. Now, what do we have left over? Well, we have three of the eighteenths left over, so you have that right there. You have three of the eighteenths left over. Now, if you turn three of the eighteenths into one piece, how many of those bigger pieces do you have? This is one of those big pieces. Now, where are the other ones? Well, this is another big piece right here. This is another big piece right here, another one, another one, and another one. If you had 18 pieces and you merged three of the pieces into one, then you actually end up with only six pieces. You end up with six pieces. Hopefully, you see that each row is one of the pieces now, and the blue is exactly one of the six, so 3/18 is the same as 1/6.

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Subtracting fractions with like denominators (video) | Khan Academy

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We're asked to subtract and simplify the answer, and we have 8/18 minus 5/18. So subtracting fractions is very similar to adding fractions. If we have the same denominator, the denominator in the difference is going to be the same as the denominators in the two numbers that we're subtracting, so it's going to be 18.

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In this lesson you will learn how to subtract mixed fractions by regrouping their fractional parts.

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Equivalent fractions with fraction models (denominators 10 & 100) (practice) | Khan Academy

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If you're seeing this message, it means we're having trouble loading external resources on our website. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.