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introduction to data handling

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pictographs

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- [Voiceover] Let's do some examples creating picture and bar graphs. So it says Mr. Smith assigned a special project about the ocean to the students in his Earth Science class. To find out if students who spend more time on their projects got better grades, he asked the students how much time they spent completing their projects. Create a bar graph to show how much time each student spent completing the ocean project. So James spent 36 minutes. So I'm gonna click here and I'm gonna move this up to 36. Eji spent 54 minutes. So I'm gonna move this up to 54 minutes. Then Minli spent 36 minutes. So I'm gonna move Minli up to 36 minutes. Then Simone spent 30 minutes. So I'm gonna move Simone up to 30. Then Kiran spent 12 minutes. So I'll move Kiran up to 12. And there you go, I have constructed the bar graph. Let's do a couple more of these. All right. So on Thursday, Ming went to see a loud and exciting performance by the Dinosaur Orchestra. Create a bar graph to show how many of each type of dinosaur were in the Dinosaur Orchestra. So I guess there were 42 Stegosaurus's. I don't know if that's a plural for Stegosaurus. So there are 42 Stegosaurus's, 63 Raptors. So we move the Raptor up to 63. 35 Triceratops. Then you had 49 Tyrannosaurus. 49 of these. So fairly straightforward. So let's do a couple more of these. All right, so now it tells us Rose's flower shop makes bouquets for special occasions. Each bouquet comes with a different number of flowers. Create a picture graph to show the number of flowers in each bouquet. So this is kind of like a bar graph, but instead we're gonna use pictures. Each picture shows a certain number. So in this case, a picture of a flower represents three flowers. So the Mother's day bouquet has 21 flowers. So 21 flowers. Now you might be tempted to put 21 pictures of flowers here, but you have to remember each of these flowers represent three flowers. So one way to think about it, you could count by threes. Three, six, nine, 12, 15, 18, 21. So that over here, this right over here, would represent 21 flowers. And you notice I just made seven of this picture, and that makes sense because seven of these pictures, and each of these pictures represent three flowers, seven times three is 21. The Mother's Day bouquet has 21 flowers in it. All right, the Anniversary bouquet has 27 flowers. So three, six, nine, 12, 15, 18, 21, 24, 27. I have nine flowers here. Nine times three is 27. The Birthday bouquet has 18. So three, six, nine, 12, 15, 18. And I just made six pictures here because each of them represent three flowers. Six times three is 18. Then finally, the Congratulations bouquet has 12 flowers in it. Three, six, nine, and 12. There you go. I think we're done. I think we're done. Let's do one more of these. All right. Barry Bee and his bee friends love to pollinate flowers. They created a chart and a picture graph to show how many flowers each of them pollinated today. Use the information in the chart to answer the question about the picture graph. So it says, On the picture graph, each flower equals blank flowers, or each picture of a flower, I should say, equals a blank number of flowers. So it says Barry pollinated 27. These are impressive bees that they sit there making charts. Barry pollinated 27 flowers, and they only drew three pictures here. So these three flower pictures must represent 27. So the way that they would represent 27 is if each of these represent nine because we'd have nine, 18, 27. So each of these must be nine flowers. But let's see if that works. So for Bumbly, 63. So let's see, nine, 18, 27, 36, 45, 54, 63. Yep, it looks like it works out. Betty is one, two, three, four, five, six. Six, six times nine is 54. That is the number of flowers she pollinated. Bertie, one, two, three, four, five. If each of those pictures represent nine, then this would be five times nine is 45. That is the number of flowers Bertie had actually pollinated.

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Voiceover] Let's do some examples creating picture and bar graphs. So it says Mr. Smith assigned a special project about the ocean to the students in his Earth Science class. To find out if students who spend more time on their projects got better grades, he asked the students how much time they spent completing their projects.

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Bar graphs

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- [Voiceover] How many more bikes does Bike World have than Bikes R Us? So let's compare Bike World to Bikes R Us. So Bike World is right over here and we see that Bike World, if we just look at this right over here, Bike World has 19 bikes, has 19 bikes. And they wanted us to compare Bike World to Bikes R Us and say how many more bikes does Bike World have than Bikes R Us? So Bike World has 19, how many does Bikes R Us have? This is Bikes R Us right over here, Bikes R Us has, Bikes R Us has 12 bicycles. So how many more does Bike World have than Bikes R Us? Well we can just subtract Bikes R Us's number of bikes from Bike World's, 19 minus 12. What is that going to be? Well if we look at the ones place, nine ones minus two ones is seven ones, and then one ten minus one ten is no tens. I could write no tens there but I don't have to write that. So there's seven more bikes at Bike World than Bikes R Us. And you can also see it here. If you start at Bikes R Us, If you were to start at Bikes R Us and you wanted to go and you wanted to see how many more bikes would I have to get to the same number of bikes as Bike World, you would see that you would have to go from 12 to 19, or you would have to add seven bikes, or that Bike World has seven more bicycles than Bikes R Us, one, two, three, four, five, six, seven. So how many more bikes does Bike World have than Bikes R Us? It has seven more bikes.

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Voiceover] How many more bikes does Bike World have than Bikes R Us? So let's compare Bike World to Bikes R Us. So Bike World is right over here and we see that Bike World, if we just look at this right over here, Bike World has 19 bikes, has 19 bikes.

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Reading Line Graphs

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A line graph is way to visually represent data, especially data that changes over time. Let's take a look at an example.

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Interpreting Line Charts- a very useful website

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Practicing Fifth grade math: 'Interpret line graphs'

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Fun math practice! Improve your skills with free problems in 'Interpret line graphs' and thousands of other practice lessons.

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Line Graphs

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Place value- base 10 number system- Whole Numbers

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Place value- base 10 number system- Whole Numbers

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Try this website and play a game to practice identifying the place value of a digit. The game is many levels: easy, medium, hard, and super brain. Choose your level, and when you get the hang of it, level up!

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Solve the puzzle by identifying place values.

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This website offers you the chance to practice family facts on many levels. Try to start at any level, and decide whether you need to level up or down.

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Practice your math facts with these flashcards. Find addition, subtraction, multiplication and division flashcards, from basic math facts to 3-digit problems.

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Use this link to play games in order to REVIEW place value objective covered in fourth grade. Then level up to fifth grade.

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In early childhood education, kids deal with only smaller numbers that they use in their everyday life. In 4th grade curriculum, they get introduced to multi-digit whole numbers, which they just imagine to exist. So, the introduction should be done using a lot of educational resources like math manipulatives, place value charts, fun math activities, and learning games for kids. Many math games for 4th graders are available online.

Place Value Progression

In grade 4, children learn about multi-digit place values and the connection between the place values of the digits of a number.

Consider the number 35269.

The number at the right most, 9 is at one's place, the number 6 at ten's place, 2 is the hundred's place, 5 is at thousand's place, and 3 is at ten thousand's place.

That is, there are 3 ten thousands, 5 thousands, 2 hundreds, 6 tens, and 9 ones in the number 35269.

The number can be expanded as or

In whole numbers, as you go from right to left, the place value gets multiplied by 10.

In other words, as you go from left to right, the place value gets divided by 10.

SplashLearn has a variety of place value activities for kids on understanding the multi-digit whole numbers place value definition. Practice place value up to hundred thousands to solve math problems involving place values.

Understanding Multi-digit Whole Numbers

In this level, children associate the place value strategies with reading and writing multi-digit whole numbers. Whole numbers are written in the groups of 3 separated by commas. Each set separated by commas should read as ones, tens, and hundreds respectively from right to left followed by base thousand unit.

A place value chart would make things clearer.

The place value worksheets for reading and writing multi-digit whole numbers available at SplashLearn covers the topic well.

Rounding Multi-digit Whole Numbers using Place Values

Once the kids have a deeper understanding of what is place value system, they can explain and reason about rounding a number to a specific place value.

For example, to round the number 77 to the nearest ten, first, the child needs to understand the number of tens in 77, that is 7. Now, the tens before and after 77 are 70 and 80 respectively. But 77 is closer to 80 than 70. Thus, rounding off the number 77 to the nearest ten results in 80.

The same logic applies for multi-digit whole numbers. To round 3578 to the nearest hundred, first, consider the hundreds before and after the number. The digit at the hundred's place is 5 and there are 35 hundreds in 3578. Thus, the hundred before and after the number are 3500 and 3600 respectively. Plot the number on a number line.

Since 3578 is closer to 3600 than 3500, the rounded to the nearest hundred is 3600.

The child basically follows the place value strategies than the standard algorithm for rounding here.

The child also applies the similar logic in rounding numbers before and after operations like addition, multiplication etc in math word problems. Many math worksheets for rounding numbers are available at round numbers.

Addition of Multi-digit Whole Numbers using Standard Algorithm

In lower grades, kids add numbers using a number line or by decomposing it to smaller place values etc. By grade 5, they learn to use the standard algorithm of addition by lining-up the same place value numbers together.

For example, to find the sum . The first step is to line up the digits that have the same place value. That is, here 4 and 1 have the same place value, hence they need to be lined up.

So, the correct alignment would be:

Now, the corresponding place values can be added to find the sum. There are 4 ones in the first number and 1 one in the second, adding them together there are 5 ones. Similarly, there are 2 tens and 7 tens that add up to 9 tens. There are 3 hundreds in the first number and no hundreds in the second number, making 3 hundreds in total.

Thus, .

The procedure is smoother when there are no compositions of place values.

Children already know that a bundle of ten ones make-up one "ten", a bundle of ten tens, make a "hundred" etc.

Consider the sum .

First, line up at the right-hand side with the one's places.

Start with adding the ones together, . But, 10 ones will add up to one ten and would be moved to the next place value on the left, tens leaving no more ones at the one's place. Thus, the one's place in the sum has a zero and one ten need to be added with the tens of the addends.

Continuing the process by adding the tens, there are tens in the sum. Again, 10 tens make a hundred and it gets carried to the next place value, hundreds.

In a similar way, hundreds, thousands, and ten thousands can also be added.

Thus, the sum is 60,100.

Using place value chart, this can be shown as:

Addition of multi-digit numbers is explained in two different sections in SplashMath.

Subtraction of Multi-digit Whole Numbers using Standard Algorithm

Subtraction by taking away the base ten blocks from the minuend is something that kids are familiar with. In this level, kids get introduced to standard algorithm for subtraction.

Consider .

Like addition, the standard algorithm for subtraction starts with aligning the numbers on the right-hand side with one's places. The digits at the corresponding place values need to be subtracted from the other.

Here, 6 ones need to be subtracted from 3 ones which are not possible. Children have experience of decomposing one of the nearby tens into 10 ones while subtracting two digit numbers in grade 2. A similar procedure is followed here. But, instead of showing the base ten block numerals are used here. So, one of the 5 tens from the minuend is decomposed into 10 ones, thus, having 13 ones to subtract 6 ones from.

Now, the 2 tens have to be subtracted from 4 tens resulting in 2 tens.

At the hundred's place, 8 hundreds have to be taken away from 1. This requires a decomposition of one thousand from the left.

Now, the 5 ten thousands have to be taken away from 5 ten thousands resulting in 0 ten thousands. Also, taking away zero hundred thousands from 8 hundred thousands resulting in 8 hundred thousands.

Thus, 856153 - 52826 = 803327 .

Multiplication using Place Value Strategies

Two-digit by One-digit: The place value strategy to multiply a two-digit number by a one-digit number is to decompose the two-digit number into tens and ones. That is, write the two-digit number in expanded form.

Consider the product . The number 34 can be written in expanded form as 30 + 4.

A rectangle of dimensions 34 and 5 would have the area equal to the product. If the rectangle is divided lengthwise into two, each of length 30 and 4 respectively, the total area is the sum of the areas of the smaller rectangles.

This can be represented using array area model as:

That is, the total area is .

Three-digit or Four-digit by One-digit: When the two-digit number is replaced by three-digit or four-digit numbers, the mathematics behind the process remains the same. The number is written in the expanded form and added them after multiplying each part separately.

For example, consider the product .

The number 2843 can be written in expanded form as .

This can be represented using array area model as:

Again, the area of the rectangle of sides 4 and 2843 is the sum of the areas of the smaller rectangles.

That is,

Simplifying:

Two-digit by Two-digit:

The mathematical techniques used for multiplying a two-digit number by another one is the same. Since both the numbers have ones' and tens' places, both have to be written in the expanded form before multiplying.

Consider . The two numbers can be expanded as and respectively. So, the array area model rectangle of the product would have dimensions and . The product would be equivalent to the area of the rectangle which is divided into 4 smaller rectangles.

Find each product.

Add them.

Thus, .

A formative assessment of the concept learned can be done using free printable worksheets for kids available on the internet.

Division by One-digit Numbers

At this level, kids are not expected to follow the standard algorithm for dividing numbers. Instead, they use the connections between division and multiplication. And the logical question of how many divisors are "contained" in the dividend.

Consider the example .

The child knows that and . So, the quotient would be in between 10 and 20. Write the number 55 as . The number 30 contains 10 number of 3s. Now, consider 25. The child already knows that . So, the number 25 contains 8 number of 3s with a remainder 1.

Thus, the number 55 can be written as and .

Since 30 has ten 3s and 24 has eight 3s, has 10 + 8 or eighteen 3s. Thus, 55 can be written as . That is, when 55 is divided by 3, the quotient is 18 and the divisor is 1.

When the dividend is 3- or 4-digit numbers the calculations and estimation of the contained divisors become more tricky.

Consider .

The dividend 2786 can be written in expanded form as .

Consider a few multiples of 6 to estimate the number of 6s contained in 2786.

and are way too bigger than the dividend and is less than the dividend. So, the quotient would be between 400 and 500. Decompose 2786 with one part equal to 2400. That is, .

In the next level, the child needs to estimate the number of 6s in 386.

The number 300 is less than 386 and there are fifty 6s in 300.

Thus, .

Now, the next estimation would be the number of 6s in 86.

So, the number of 6s in 86 is between 10 and 15. But since 6 times 15 is just 4 greater than 86, try

Thus, the expanded form can be .

Now, the last digit in the expanded form is 2 and 2 < 6. So, the procedure can be stopped.

The total number of 6s in 2786 would be the number of 6s in each of these addends in the expanded form.

So, the total number is or .

Thus, the quotient is 464 and the remainder is 2.

SplashLearn provides well-organized 4th grade worksheets from easy to difficult math problems for both multiplication and division.

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Place Value Games for 4th Graders Online - SplashLearn

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In early childhood education, kids deal with only smaller numbers that they use in their everyday life. In 4th grade curriculum, they get introduced to multi-digit whole numbers, which they just imagine to exist. So, the introduction should be done using a lot of educational resources like math manipulatives, place value charts, fun math activities, and learning games for kids.