In this pdf, we will get to know about place values in numbers. Place value is the value of each digit in a number. For example, the 5 in 350 represents 5 tens, or 50; however, the 5 in 5,006 represents 5 thousands, or 5,000.
1. **Please use the resources on this page to review and practice math concepts learned throughout the year.** **I highly recommend that you create a username and password for Learn Zillion. It is free and there are video lessons to help with every math standard. I link to those videos throughout this webpage.** Place Value Place Value Vocabulary place value – the position of a value – what an individual digit digit – a symbol used to make a digit in a number (ex. In 4.345, is worth in a number (ex. in numeral (ex. 8 is a digit that the 5 is in the thousandths 4.345, the value of the 3 is makes up the number 568.) Just place.) Place value is a word. 0.3, or 3/10.) Value is a number. as letters make words, digits make numbers. standard form – the most expanded form – writing a word form – A number common way to write a number to show the value of written out in words (ex. 4.345 number (ex. 435,678) each digit (ex. 4.345 = (4 x 1) + = four and three hundred forty (3 x 0.1) + (4 x 0.01) + (5 x five thousandths) 0.001)) model – showing a number using decimal – a point between a compare – tell whether a base ten blocks, number lines, or whole number and a decimal number is greater than, less another method. fraction than, or equal to another number tenths – one part in ten equal hundredths – one part in one thousandths – one part in one parts (ex. 1/10, 0.1) hundred equal parts (ex. 1/100, thousand equal parts (ex. 0.01) 1/1000, 0.001) greater than - > (ex. 5.5 is less than - < (ex. 5.4 is less than equal to – = (ex. 5.50 is equal greater than 5.4; 5.5 > 5.4) 5.5; 5.4 < 5.5) to 5.5; 5.50 = 5.5) Decimal Place Value (position) and Value (worth) Ones Decimal (and) tenths hundredths thousandths 4 3 2 5
2. The 4 is in the ones place. The value of the 4 is 4 The 3 is in the tenths place. The value of the 3 is 0.3 The 2 is in the hundredths place. The value of the 2 is 0.02 The 5 is in the thousandths place. The value of the 5 is 0.005 Video Lesson for place value of decimals: http://studyjams.scholastic.com/studyjams/jams/math/decimals- percents/place-value-decimals.htm Game to practice decimal place value: Paper Boy Place Value: http://www.sheppardsoftware.com/mathgames/decimals/scooter QuestDecimal.htm Pirate Place Value: http://mrnussbaum.com/placevaluepirates1/ Video Lesson for reading decimals: https://learnzillion.com/lessons/428-name-decimals-through-the- thousandths-place Game for practice with reading decimals: Decimals of the Caribbean: http://mrnussbaum.com/docrb1/ Standard form, word form, and expanded form: Standard Expanded Form Word Form 0.034 (3 x 0.01) + (4 x 0.001) Thirty-four thousandths 5.67 (5 x 1) + (6 x 0.1) + (7 x 0.01) Five and sixty-seven hundredths
3. 8.9 (8 x 1) + (9 x 0.1) Eight and nine tenths Writing Decimals in standard form: Standard form is the common way we write numbers. For example, five and twenty-three hundredths is 5.23 in standard form. Writing Decimals in Expanded Form: In the past grades, expanded form has been simpler. For 456, you would write 400 + 50 + 6. In fifth grade, the complexity of expanded form changes. Each written value is broken down even further, adding in a multiplication component. Now, 456 would look like this: (4 x 100) + (5 x 10) + (6 x 1) Let’s look at a decimal number in 5th grade expanded form. For instance, 4.567 in expanded form could look like this: (4 x 1) + (5 x 0.1) + (6 x 0.01) + (7 x 0.001) or this: (4 x 1) + (5 x ) + (6 x ) + (7 x ) Video Lesson for expanded form: https://learnzillion.com/lessons/429-write-decimals-in-expanded- notation Writing Decimals in Word Form: When you write a decimal number in word form you simply read the decimal and write what you say. For example, if I see the decimal 5.673, I would read the decimal to myself, remembering that I say “and” when I come to the decimal point, and write what I say. 5.673 in word form would be five and six hundred seventy-three thousandths.
4. Modeling Decimals with Base-ten Blocks: You can model decimals using base-ten blocks. Here is how: If we are modeling a decimal that only goes to the tenths or hundredths place (ex. 4.5 or 4.56), we can use the hundreds block (“flat”), the tens rod (“long”), and the ones cubes. Flat: Long: Small Cubes: 1 whole 1 tenth 1 hundredth 1 0.1 or 1/10 0.01 0r 1/100 1.24 3.6 0.75 If we are modeling a decimal that goes to the thousandths place, the base ten blocks would represent different values. To represent one whole, we would use the large cube as one whole, the “flat” as one tenth, the “long” as one hundredth, and the small cube as one
5. Large Cube: Flat: Long: Small Cube: 1 whole 1 tenth 1 hundredth 1 0.1 or 1/10 0.01 or 1/100 1 thousandth 0.001 or 1/1000 2.456 0.870 1.003 Video Lesson for Decimal Models: https://learnzillion.com/lessons/3776-read-and-write-decimals- using-base-ten-blocks Games/Practice for practicing decimal models: o Decimals to Tenths Place: http://www.sheppardsoftware.com/mathgames/decimals/D ecimalModels10.htm o Decimals to Hundredths Place: http://www.sheppardsoftware.com/mathgames/decimals/D ecimalModels.htm o Decimals to Thousandths Place:
6. Model the following decimals using base ten blocks on paper: 6.678 1.340 2.522 Showing Decimals on a Number Line: Decimals can be placed on a number line just like whole numbers. For example, 1.5 would fall here on the number line: 1 1.5 2 1.55 would fall here: Video lesson for placing decimals on a number line: http://studyjams.scholastic.com/studyjams/jams/math/decimals- percents/place-decimal-number-line.htm Game for placing decimals on number line: http://www.sheppardsoftware.com/mathgames/decimals/mathm an_decimal_numberline.htm Comparing Decimals: You can compare two decimals using the symbols > (greater than), < (less than), and = (equal to). There are several ways to compare
7. 1. Compare decimals using fractions: When we read decimals, what we say sounds like a fraction. For example, 0.3 is three tenths, or 3/10. If we convert both decimals we are comparing to fractions, we can easily compare them. For example: Compare: 0.9 > 0.8 Video Lesson for Comparing Decimals using Fractions: https://learnzillion.com/lessons/562-compare-decimals-using- fractions Practice for Comparing Decimals using fractions: o Compare the following: 1.19 1.11 0.344 0.034 2. Comparing Decimals Using a Number Line: We can also compare decimals by placing them on a number line and visually comparing their positions. Watch the following video lesson to see how. Comparing Decimals Using a Number Line Video Lesson: https://learnzillion.com/lessons/563-compare-decimals-using-a- number-line 3. Comparing Decimals Using Base ten Blocks: We can also compare decimals by looking at the models we create with base ten blocks. For example, let’s compare 0.04 and 0.045 using models. 0.04 < 0.045
8. < Video Lesson for Comparing Decimals with Models: https://learnzillion.com/lessons/564-compare-decimals-using-base- ten-blocks 4. Tricks for quickly comparing decimals: Now that you have an understanding of the strategies you can use to compare decimals, here are some quick ways: “Balancing out” the numbers – It can look difficult when having to compare decimals that go to different place values. For example, you might be asked to compare 1.45 and 1.451. To easily compare these decimals, you can make them look similar by adding a zero to the end of the decimal with fewer places. 1.450 < 1.451 Adding a zero will not change the value of the decimal because 45/100 is the same amount as 450/1000. Now both decimals look similar, and you can easily tell that four hundred fifty thousandths is less than four hundred fifty-one thousandths. “Cross-out Method” – this method can be useful when comparing decimals or whole numbers. In this method, you examine each place value carefully and cross out the place values that match from left to right. For example, let’s compare 0.009 and 0.09. 0.009 < 0.09
9. If we cross out the matching place values first, we would cross out the ones place on both numbers because they are both zero, and the tens place on both numbers because they are both zero. Now we are looking at a zero in the hundredths place of the first number, and a nine in the hundredths place of the second number. Since zero hundredths is less than nine hundredths, 0.009 is less than 0.09. Game for Comparing Decimals: http://www.sheppardsoftware.com/mathgames/decimals/Compa reDecimals.htm Ordering Decimals: Once you have learned how to compare decimals, you can put them in order from least to greatest or from greatest to least as well. Watch the following videos to see how to order decimals: https://learnzillion.com/lessons/34-compare-and-order-simple- decimals https://learnzillion.com/lessons/35-compare-and-order-decimals- to-the-thousandths-place Rounding Decimals to Any Place: You may be asked to round a decimal number to the nearest whole number, to the nearest tenth, to the nearest hundredth, or to the nearest thousandth. You can round decimal numbers by using a number line. Click on the following links to see how to round decimals using a number
10. Round decimals to the nearest whole number: https://learnzillion.com/lessons/3430-round-decimals-to-the- nearest-whole-number Round decimals to the nearest tenth: https://learnzillion.com/lessons/3432-round-decimals-to-the- nearest-tenth Round decimals to the nearest hundredth: https://learnzillion.com/lessons/3322-round-decimals-to-the- nearest-hundredth Round decimals to the nearest thousandth, or any other place: https://learnzillion.com/lessons/3522-round-decimals-to-any-place You may also use another strategy to round decimals. For example, let’s round 3.456 to the nearest tenth. Step one: Underline the place you are rounding to 3.456 Step two: Circle the place to the right of the underlined place 3.456 Step three: If the circled number is 4 or less, then the underlined number stays the same. If the circled number is 5 or more, then the underlined number increases by one. 3.456 Step four: The numbers to the right of the underlined number change to zeros, and the numbers to the left of the underlined number stay the same. Answer: 3.500 or 3.5 Games for Rounding Decimals: http://www.sheppardsoftware.com/mathgames/decimals/scooter QuestDecRound.htm
11. http://www.math-play.com/rounding-decimals-game-1/rounding- decimals-game.html Place Value Relationships Place value relationships refers to the relationship between each place value in a number. In the number 8,888 the 8 in the tens place is worth 10 times the 8 in the ones place. The 8 in the hundreds place is worth 100 times the ones place. The 8 in the thousands place is worth 1,000 times the ones
12. Going the other way, the 8 in the ones place is worth of the tens place of the hundreds place of the thousands place Students need to be able to write statements comparing numbers in different place values. For example, they might be asked to compare the value of the 8 in 3.89 to the value of the 8 in 8.39. To compare the values of the numbers, you must first determine the value. The value of the 8 in 3.89 is 0.8. The value of the 8 in 8.39 is 8. Therefore, the value of the 8 in 3.89 is the value or 10 times smaller than) of the 8 in 8.39. Videos for Comparing Place Values: https://learnzillion.com/lessons/2676-recognize-place-value- relationships-by-multiplying-and-dividing-by-ten https://learnzillion.com/lessons/3363-compare-the-value-of-the- digits-in-a-decimal-number Games for Comparing Place Values: http://www.ixl.com/math/grade-5/convert-between-place- values http://www.sheppardsoftware.com/mathgames/placevalue/Place ValuesShapesShoot.htm
13. Exponents Note: Any number with an exponent of zero is equal to one (ex. =1) In fifth grade, we discover the meaning of exponents, then set our focus on powers of ten Powers of Ten Here are several videos to explain powers of ten. Explain Patterns in Zeros When Multiplying by Powers of Ten Represent Powers of Ten Using Exponents Explain Patterns in the Placement of the Decimal Point When Multiplying by Powers of Ten Explain Patterns in the Placement of the Decimal Point When Dividing by Powers of Ten In the past, students have learned that when multiplying by powers of ten (10, 100, 1,000, etc.) The amount of zeros in the power of ten
14. are added to the original number. For example, when multiplying 23 x 10, you would just add a zero to 23, making the product 230. When multiplying 23 x 100, you would add two zeros, making the product What is actually happening is that the decimal is moving. When you multiply 23 x 10, the decimal is moving one place to the right. When you multiply by 100, the decimal is moving two places to the right. 23 x 10 = 23.0. = 230 23 x 100 = 23.00. = 2,300 Here is how these problems look with the 10 and 1,000 in exponential 23 x = 230 23 x = 2,300 When dividing by powers of ten, the decimal shifts to the left rather than to the right, because when you divide, the number gets smaller 23 ÷ 10 = 2.3. = 2.3 23 ÷ 100 = .23. = .23 23 ÷ = 2.3. = 2.3 23 ÷ = .23. = .23 Another important concept to understand is that multiplying by a decimal is similar to dividing. Here are a few handy charts to sum up how the decimal moves with different operations.
15. To multiply a number by a power of ten, you can use the exponent to determine how the position of the decimal point changes in the product. Problem Exponent Move decimal point: 0 0 places to the right 1 1 place to the right 2 2 places to the right 3 3 place to the right You can use place-value patterns to find the product of a number and the decimals 0.1, 0.01, and so on. Problem Multiply by: Move decimal point: 1 x 2,457 = 2,457 1 0 places to the left 0.1 x 2,457 = 245.7 0.1 1 place to the left 0.01 x 2,457 = 24.57 0.01 2 places to the left To divide an number by 10, 100, or 1,000, use the number of zeros in the divisor to determine how the position of the decimal point changes in the quotient. Problem Number of zeros: Move decimal point: 147 ÷1 = 147 0 0 places to the left 147 ÷10 = 147 1 1 place to the left 147 ÷100 = 147 2 2 places to the left 147 ÷1,000 = 147 3 3 places to the left
16. To divide a number by a power of ten, you can use the exponent to determine how the position of the decimal point changes in the Problem Exponent Move decimal point: 0 0 places to the left 1 1 place to the left 2 2 places to the left Adding Decimals Volume Volume Vocabulary volume – the amount of 3- measurement – finding a attribute – a characteristic of demensional space an object number that shows the size or an object occupies amount of something solid figure – a 3-demensional right rectangular prism - a unit – a quantity used as a object (ex. cube, pyramid, prism in which the angles standard measurement rectangular prism, sphere, between the base and sides are cylinder, etc.) right angles. unit cube – a cube whose sides gap – a space or opening overlap – to cover part of the are one unit long edge of something cubic units – a unit to measure edge length – the length of an height – a measure of how tall volume edge of a solid figure something is area of base – the area of a multiplication – repeatedly adding addition – combining numbers to solid figure’s base (L x W) numbers to find a product find the total By the end of this unit, students should be able to recognize volume as an attribute of solid figures and measure the volume of right rectangular prisms using unit cubes and the formula for volume. Videos to help explain concepts of volume:
17. Identifying the parts of 3D figures Difference between a square unit and a cubic unit Understanding volume Finding volume by counting cubes Finding volume by multiplying the area of the base by the height Finding volume using the formula length x width x height (L x W x H) Finding edge lengths that aren’t labeled Decomposing irregular 3D figures to find the volume Games/Activities to practice concepts of volume: Measuring volume by counting cubic units Finding the volume of rectangular prisms (practice sheets)
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