December 10, Unit Two - Operations with decimals
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1 Unit Two - Operations with decimals
2 Unit Two - Operations with Decimals Introduction (or re-introduction) to place value Read the following numbers (properly!) Place Value
3 1,000, ,000 Place Value millions hundred thousands ten-thousands 10,000 thousands hundreds tens ones tenths hundredths thousandths ten-thousandths
4 Place Value Teacher's Notes The value of a digit is based on its place in a number. This is known as its place value. Place Value Chart thousandths ten thousandths hundred thousandths millions tenths hundredths thousandths ten thousandths 1,356, decimal point Example ones tenths hundredths
5 To write a number in expanded notation, take each digit times its place-value, then add the pieces together. For zeros in the number, just skip over those place values, you don t need to write them ,085.06
6 Write the number in expanded notation x x x x 0.001
7 Write the number in standard form. (3 x 1) + (2 x 0.1) + (2 x 0.01) (4 x 100) + (1 x 1) + (6 x 0.001) + (3 x ) (6 x 10) + (7 x 1) + (3 x 0.1) + (9 x 0.001)
8 Standard Form Words To write a number in words: say the whole number part say AND in place of the decimal say the decimal part, finishing with the place value where the number ends Click to hear number said in words
9 Going from words to standard (number) form: Ex: Three hundred sixteen and fifteen thousandths Tells you where the decimal part ends thirty-four and sixteen hundredths one hundred twenty-two thousandths eleven and three hundredths
10 Match the number in standard form and in words Click on a number to hear it said in words.
11 Drag the numbers to the right to reveal the number in words forty-four and four hundredths 0.46 forty-six hundredths four and four hundred four thousandths 4.6 four and six tenths four hundred forty and four tenths forty-six thousandths
12
13
14 Round off to Number of Digits Round off the number to three decimal places. Teacher's Notes
15 Activity Write the correct round off values of pi ( ) to the specified number of digits. Teacher's Notes 0 decimal digits 1 decimal digit 2 decimal digits 3 decimal digits 4 decimal digits 5 decimal digits 6 decimal digits Correct Answer
16 Check Your Understanding 1 Round off the number to two decimal points. A B C D Select the correct answer.
17 Round off to Place Values Teacher's Notes In the year 2009, the population of the state of New York stood at 19,541,453. Round off the population to its nearest thousands. 1 9, 5 4 1, 4 5 3
18 Activity Round off the number to: Teacher's Notes Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Correct Answer
19 Estimating with Decimals Why would we need to estimate?
20 Place the decimals on the number line
21 Which of the decimals round to 0.02?
22 Place the decimals on the number line
23 Which of the decimals round to 0.01?
24 Round to the highest place value ?? ? ? ? 0.003
25 Use rounding to estimate these sums = = =
26 Use rounding to estimate differences = = =
27 Homework Complete the Estimating side of the worksheet
28 Adding and Subtracting Decimals December 10, 2015
29 How to Add and Subtract Decimals: Adding Decimals Subtracting Decimals
30 Adding Decimals
31 What was Courtney's total score? How much more did she score on the beam than the floor? 9.53
32
33 Homework Worksheet - adding and subtracting decimals p Complete any 10 questions (1 a.b.c counts as one question)
34 Working with powers of ten Multiplying Decimals
35 Review: Multiplying Whole Numbers by 1, 10, 100, and 1,000. Click on each black dot to reveal answers to the problems in the second column. 2 x 1 = 2 36 x 1 = 36 2 x 10 = 20 2 x 100 = x 10 = x 100 = 3,600 2 x 1,000 = 2, x 1,000 = 36,000
36 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Click on each problem's answer to see the pattern x 1 = x 101 = x = x 1, = The decimal point stays in the same place. The decimal point moves 1 place to the right. The decimal point moves 2 places to the right. The decimal point moves 3 places to the right.
37 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Click on each black dot to reveal the answer for the problems x 1 = The decimal point stays in the same place x 10 = x 100 = x 1,000 = The decimal point moves right 1 place. The decimal point moves right 2 places. The decimal point moves right 3 places.
38 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Help Deci the Frog jump the correct number of lily pads and reveal the answer! x 10 Answer 0.002
39 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Help Deci the Frog jump the correct number of lily pads and reveal the answer! x Answer
40 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Help Deci the Frog jump the correct number of lily pads and reveal the answer! x ,016.8 Answer
41 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Click on each black dot to reveal the answer for the problems. 3.5 x 1 = 3.5 x 10 = 3.50 x 100 = 3.500x 1,000 = ,500 The decimal point stays in the same place. The decimal point moves right 1 place. 1 zero must be added as a place holder. 2 zeroes must be added as place holders. Sometimes you must add zeroes to the end as place holders!
42 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Draw Deci's path and then move Deci to the lily pad to check your answer x ,160 Answer
43 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Draw Deci's path and then move Deci to the lily pad to check your answer. 0 4 x Answer
44 Decimal Pattern in Products: Multiplying by 1, 10, 100, and 1,000. Move the decimal point to the correct postion and then click on Deci to check your answer! X 10 = $6.75 x 100 = $6 7 5 $ x 0.5 = You may need to add zeroes as placeholders.
45 Decimals Continue the pattern with decimal powers of ten.
46 Multiplying Decimals Use estimation to help determine if your answers are correct.
47 Modeling Decimal Multiplication example x = 0.8 X 0.2 = n What decimal represents the part of the whole that is orange? Click here for the 0.16 answer
48 Modeling Decimal Multiplication pull for problem
49 Guided Practice 9 x 0.2 = 1.8 Solution 4 x 0.5 = 2.0 Solution 6 x 0.23 = 1.38 Solution
50 Multiply Decimals by Whole Numbers example = 3 x 0.4 = n n Solution = 1.20
51 x 5 x 5 x 27 x Estimate Decimal Products To estimate decimal products, round each factor to the first significant (non-zero) digit or nearest whole number. (Pull for examples) Pull Pull Estimating the product can help you correctly position the decimal point in the product.. Pull
52 Multiply Decimals. 3 the numb places in Multiplying when one or more of the factors is a decimal number is like multiplying with whole numbers x Hit the bull's eye Remember! You can use your estimate to check your decimal placement in the product.
53 Using Decimal Multiplication The average lab rat weighs kilogram. If there are 15 rats in the lab, how much do they weigh altogether? work space Solution The Boston Marathon is about 26 miles. A mile is equal to kilometers. How many kilometers does a runner who completes the race run? work space Solution
54 How to Multiply Decimals: 3.77 x (2 decimal places) (1 decimal place) (3 decimal places) Click beside Click me 3.77 to to check place the product. decimal point.
55 Use rounding to estimate products 9.56 x x = x x = x 0.67 x 0.97 x x =
56 Use rounding to choose the most reasonable answer x x , , , x
57 Practice Multiplying x 6 6 x.6 x 7.9 x.06.8 x.07
58 Content/writing space December 10, 2015
59 Content/writing space December 10, 2015
60 Content/writing space December 10, 2015
61 Content/writing space December 10, 2015
62 Homework p 58 # 9-12, 17, - 20
63 Dividing Decimals December 10, 2015
64 Dividing with powers of ten December 10, 2015
65
66 1. Dividing a Decimal Number by a Whole Number To divide a decimal number by a whole number: Use Long Division (ignoring the decimal point) Then put the decimal point in the same spot as the dividend (the number being divided)
67 Example: Divide 9.1 by 7 Ignore the decimal point and use Long Division: 13 7 )
68 Practice December 10, 2015
69 Put the decimal point in the answer directly above the decimal point in the dividend: )9.1 The answer is 1.3
70 2. Dividing by a Decimal Number But what if you want to divide by a Decimal Number? The trick is to convert the number you are dividing by to a whole number first, by shifting the decimal point of both numbers to the right: Now you are dividing by a whole number, and can continue as normal. It is safe to do this if you remember to shift the decimal point of both numbers the same number of places.
71 Example 2: Divide 5.39 by 1.1 You are not dividing by a whole number, so you need to move the decimal point so that you are dividing by a whole number: move move 1
72 Since you have to move the decimal 1 time to the right so that 1.1 no longer has a decimal, you must also move the decimal in 5.39 once to the right. You are now dividing by a whole number, so you can proceed: Ignore the decimal point and use Long Division: ) December 10, 2015
73 Put the decimal point in the answer directly above the decimal point in the dividend: )53.9 The answer is 4.9
74 Pull How to Divide Decimals: Study this example:
75 Practice Dividing
76 Use rounding to estimate quotients = = x x =
77
78 2 Answer the following
79 3 Now try this one 6 2(1 + 2)
80 Order of Operations B - brackets E- exponents D - divide M - multiply A - addition S - subtraction
81 4 + 5 x 6 = 34 (5 + 5) 2 = (3 x 8) - 14 x 2 = 96
82 3 x (4 + 7) = x 5 = x 3 2 = 19 MAGIC TUNNEL Solve the equations. Drag through the tunnel to reveal the solution. (8 + 42) 5 = x 5 = 30
83 (18-11) x = x 4 = 55 MAGIC TUNNEL Solve the equations. Drag through the tunnel to reveal the solution x 3 = = x = 47
84
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