Number and Operations - Fractions Operations and Algebraic Thinking MATH UNIT 3 Number and Operations - Fractions Operations and Algebraic Thinking

DECIMAL FRACTIONS

A fraction where the denominator (the bottom number) is a power of ten A fraction where the denominator (the bottom number) is a power of ten. You can write decimal fractions with a decimal point and no denominator.

7/10 is a decimal fraction and it can be shown as 0 7/10 is a decimal fraction and it can be shown as 0.7 43/100 is a decimal fraction and it can be shown as 0.43

EQUIVALENT FRACTIONS

DENOMINATOR

NUMERATOR

TENTHS

HUNDREDTHS

ONE WHOLE

EXPANDED FORM

Students will read decimal fractions with denominators of 10 and 100. Students will write decimal fractions with denominators of 10 and 100. Students will identify decimal fractions with denominators of 10 and 100. MAFS.4.NF.3.5

Each of these fractions is special Each of these fractions is special. What is special about each of these fractions?

When you read fractions with a denominator of 10 or 100 you say: TENTHS or HUNDREDTHS. This fraction is read as : three tenths This fractions is read as : eight hundredths

READ EACH FRACTION 3/10 60/100 8/10 45/100 12/100 7/10 29/100 2/10 5/10 99/100 9/10 78/100

fifty-eight hundredths seven tenths thirty-four hundredths four tenths WRITE EACH FRACTION fifty-eight hundredths seven tenths thirty-four hundredths four tenths three tenths five hundredths sixty-seven hundredths twenty-one hundredths eight hundredths one tenth forty-two hundredths nine tenths

Students will represent fractions with a denominator of 10 and fractions with a denominator of 100 using models. grids - base ten blocks - number lines

One unit is 1/100 or 0. 01 One rod or long is 1/10 or 10/100 or 0 One unit is 1/100 or 0.01 One rod or long is 1/10 or 10/100 or 0.1 or 0.10 One flat is one whole or 10/10 or 100/100 or 1

WRITE THE FRACTION

Write as a fraction and a decimal. Remember: equals 1/100

Write as a fraction and a decimal. Remember: equals 1/100

Write as a fraction and a decimal. Remember: equals 1/100

Write as a fraction and a decimal. Remember: equals 1/100

Write as a fraction and a decimal. Remember: equals 1/100

Write as a fraction and a decimal. Remember: equals 1/100

You can use a number line to show decimal fractions You can use a number line to show decimal fractions. The top number line has a denominator of 10. The lower number line has a denominator of 100.

Use the number line to locate the decimal fraction. 0.7 or 7/10

Use the number line to locate the decimal fraction. 0.1 or 1/10

Use the number line to locate the decimal fraction. 0.4 or 4/10

Use the number line to locate the decimal fraction. 0.9 or 9/10

Use the number line to locate the decimal fraction. 0.3 or 3/10

Use the number line to locate these decimal fractions. 30/100 or 0.30

Use the number line to locate these decimal fractions. 62/100 or 0.62

Use the number line to locate these decimal fractions. 9/100 or 0.09

Use the number line to locate these decimal fractions. 75/100 or 0.75

Use the number line to locate these decimal fractions. 26/100 or 0.26

Use the number line to locate these decimal fractions. 100/100 or 1.00

Look at the base ten blocks. The ONE is cut into 10 pieces which are Rewrite a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100. Look at the base ten blocks. The ONE is cut into 10 pieces which are each cut into 10 pieces. That means there are 100 cubes in the WHOLE ONE flat. 10 X 10 = 100 ONE FLAT TEN RODS 100 CUBES WHOLE TENTHS HUNDREDTHS

X 10 = 100 X 10 HINT: There are 10 rods in a flat. There are 10 unit cubes in each rod. 10 X 10 = 100

Write the equivalent fractions. 3/10 = 7/10 = 1/10 = 5/10 = 9/10 = 2/10 = 8/10 = 4/10 = 6/10 = 80/100 = 40/100 = 10/100 = 70/100 = 50/100 = 30/100 = 90/100 =

Equivalent fractions please… 6 / 10 = 60 / 100 or 6 / 10 = 60 / 100

Equivalent fraction please… ___ / 100 = ___ / ___

Equivalent fraction please… ___ / 100 = ___ / ___

Equivalent fraction please… ___ / 100 = ___ / ___ = _____

Write both the fraction and the words

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ _____ hundredths = 0.___ = ____ tenths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. _____ / _____ = ____ / ____ _____ tenths = 0.___ = _____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ ____ tenths = 0.___ = ____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ _____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ ____ tenths = 0.___ = ____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ = ____ / ____ ____ tenths = 0.___ = ____ hundredths = 0.___

Write in word form and fractions and decimals Write in word form and fractions and decimals. ____ / ____ ____ hundredths = 0._____

Show 0.2 or 2/10 and 20/100 in the models below.

Show 0.5 or 5/10 and 50/100 in the models below.

Show 0.46 and 46/100 in the model below.

Show 0.11 and 11/100 in the model below.

___/___ = 0.___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = 0.___ ___/___ = 0.___

___/___ = 0.___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = 0.___ ___/___ = 0.___

___/___ = 0.___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = 0.___ ___/___ = 0.___

___/___ = 0.___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = 0.___ ___/___ = 0.___

___/___ = 0.___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = 0.___ ___/___ = 0.___

___/___ = 0.___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = 0.___ ___/___ = 0.___

___/___ = ___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = ___ ___/___ = 0.___

___/___ = ___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = ___ ___/___ = 0.___

___/___ = ___ ___/___ = 0.___ Compare the base ten blocks to compare fractions and decimals. < = > ___/___ = ___ ___/___ = 0.___

Compare the base ten blocks to compare fractions and decimals. < = > ___ / ___ = 0.___ ___ / ___ = 0.___ Write the fraction and the decimal.

Compare the base ten blocks to compare fractions and decimals. < = > ___ / ___ = 0.___ ___ / ___ = 0.___ Write the fraction and the decimal.

Compare the base ten blocks to compare fractions and decimals. < = > ___ / ___ = __.___ ___ / ___ = __.___ Write the fraction and the decimal.

Compare the base ten blocks to compare fractions and decimals. < = > ___ / ___ = __.___ ___ / ___ = __.___ Write the fraction and the decimal.

Students will identify the place value of digits to the right of the decimal point. Students will demonstrate place value of decimals through the hundredths using concrete materials. Students will use different-sized grids to represent equivalency of decimals to fractions with denominators of 10 or 100. Students will explain the relationship between fractions and decimals in graphic models. MAFS.4.NF.3.6

This is a PLACE VALUE chart. Learn to draw a place value chart.

Identify and label each part of the PLACE VALUE chart.

Write the number 589 and 4/10 in the PLACE VALUE chart.

Write 703 and 54/100 in the Place Value chart.

Write an eight in the tens place. Write a three in the ones place Write an eight in the tens place. Write a three in the ones place. Write a five in the hundreds place. Write a one in the tenths place. READ YOUR NUMBER

Write an nine in the tenths place. Write a four in the hundredths place. Write a seven in the ones place. Write a two in the tens place. READ YOUR NUMBER

Write an six in the hundredths place. Write a five in the tens place Write an six in the hundredths place. Write a five in the tens place. Write a zero in the ones place. Write a two in the tenths place. READ YOUR NUMBER

Write an zero in the tenths place. Write a five in the tens place Write an zero in the tenths place. Write a five in the tens place. Write an eight in the hundredths place. Write a nine in the ones place. READ YOUR NUMBER

Write a seven in the tens place. Write a nine in the hundredths place Write a seven in the tens place. Write a nine in the hundredths place. Write a four in the ones place. Write a three in the hundreds place. Write a five in the tenths place. READ YOUR NUMBER!

Write a zero in the hundredths place. Write an eight in the tens place Write a zero in the hundredths place. Write an eight in the tens place. Write a six in the ones place. Write a two in the hundreds place. Write a one in the tenths place. READ YOUR NUMBER.

Write a four in the tenths place. Write a three in the ones place Write a four in the tenths place. Write a three in the ones place. Write a two in the hundredths place. Write a nine in the hundreds place. Write a six in the tens place. READ YOUR NUMBER.

Circle the value of this number in base ten blocks. 4.91

Circle the value of this number in base ten blocks. 3.02

Circle the value of this number in base ten blocks. 5.38

Circle the value of this number in base ten blocks. 8.26

Circle the value of this number in base ten blocks. 2.75

thirty-nine hundredths and can be written as 39/100 Students will translate the word form of a decimal into its equivalent fraction. 0.39 reads thirty-nine hundredths and can be written as 39/100 0.71 reads 0.28 reads 0.46 reads 0.05 reads 0.99 reads

0.17 reads 0.68 reads 0.06 reads 0.24 reads 0.03 reads 0.77 reads

0.94 reads 0.26 reads 0.82 reads 1.05 reads 0.60 reads 0.45 reads

you have an IMPROPER FRACTION Students will translate fractions greater than ONE with denominators of 10 and 100 into equivalent decimal form. When the NUMERATOR is larger than the DENOMINATOR you have an IMPROPER FRACTION resulting in a whole number on the LEFT and a decimal fraction on the RIGHT.

Let’s translate some improper fractions into decimals. 13/10 = 1.3 13/10 = 1.3 Because the numerator: 13 is larger than the denominator: 10, we have an improper fraction - meaning that we have a WHOLE number and a part. 11/10 26/10 32/10 18/10

29/10 45/10 10/10 100/10 82/10 55/10 90/10 64/10 71/10 33/10 15/10 84/10

429/100 945/100 101/100 728/100 186/100 505/100 790/100 645/100 281/100 397/100 564/100 840/100

Students will represent a decimal value on a number line. What decimal does each dot represent? 0.2

What decimal and fraction does each dot represent?

Complete each fraction on the number line. Several are done for you.

P = _____ Q = _____ R = _____ Label the value of each dot on the number line. P = _____ Q = _____ R = _____

Label each decimal value on the number line. 0.32 0.59 0.11 0.75

Label each decimal value on the number line. 0.02 0.93 0.67 0.24

Label each decimal value on the number line. 0.46 0.88 0.23 0.67

Label each fractional value on the number line

Label each fractional value on the number line

Label each fractional value on the number line

Students will explain their thinking when labeling a decimal fraction on a number line. “I think that 32/100 is more than 30/100 (3/10) and that it is less than 40/100 (4/10). So I think it will be closer to 30/100. I would place it on the number line near that value.”

19/100 Explain your thinking . . . _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

63/100 Explain your thinking . . . _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

41/100 Explain your thinking . . . _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________

Students will explain that decimals can only be compared when they refer to the same whole. Students will compare decimals with and without models and record the comparison numerically using symbols < = > Students will justify the comparison by reasoning about the size of the decimal or by using a visual model. MAFS.4.NF.3.7

This is a candy bar. It is divided into 10 equal pieces This is a candy bar. It is divided into 10 equal pieces. This is a candy bar. It is divided into 10 equal pieces, too. We CAN NOT compare them because they are NOT THE SAME! Each model shows 10/10 but the whole Hershey’s is much bigger than the other candy bar so these decimals can not be compared.

Can these decimal fractions be compared? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.1 1/10 0.1 1/10

Can these decimal fractions be compared? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.1 1/10 0.1 1/10

Can these decimal fractions be compared? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.1 1/10 0.1 1/10

Can these decimal fractions be compared? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.1 1/10 0.1 1/10

Can these decimal fractions be compared? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.1 1/10 0.1 1/10

Can these decimal fractions be compared? Why not? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.45 45/100 0.01 1/100

Can these decimal fractions be compared? Remember that comparisons are only valid when the two decimals refer to the same whole. 0.01 1/100 0.01 1/100

Compare these decimal fractions. < = > 0.86 ____ 0.87

Compare these decimal fractions. < = > 0.32 ____ 0.50

Compare these decimal fractions. < = > 0.4 ____ 0.41

Compare these decimal fractions. < = > 0.2 ____ 0.28

Compare these decimal fractions. < = > 0.9 ____ 0.10

Compare these decimal fractions. < = > 0. 64 ____ 0.46

Compare these decimal fractions. < = > 2.1 ____ 2.09

Compare these decimal fractions. < = > 1.08 ____ 1.80

Students will identify and demonstrate numeric and growing shape patterns. Students will generate a number or shape pattern that follows a given one-step rule. follows a given two-step rule. Students will identify features in patterns following a given rule. MAFS.4.OA.3.5

This is a numeric pattern. Numeric means number This is a numeric pattern. Numeric means number. You have been doing numeric patterns since Kindergarten.

These are also numeric patterns. Can you find the rule These are also numeric patterns. Can you find the rule? ____ ____ ____ Rule: ___________ ____ ____ ____

These are also numeric patterns. Can you find the rule?

Let’s play a game. Follow the Rules and see the pattern you create. Start at the number 7 Multiply by 2

Let’s play a game. Follow the Rules and see the pattern you create. Start at the number 100 Divide by 2

Let’s play a game. Follow the Rules and see the pattern you create. Start at the number 15 Add 7

Let’s play a game. Follow the Rules and see the pattern you create. Start at the number 19 Subtract 3

Let’s play a game. Follow the Rules and see the pattern you create. Start at the number 4 Multiply by 5

As you create numeric patterns look for features of that pattern. RULE PATTERN FEATURES START WITH 4 ADD 5 4, 9, 14, 19, 24, 29, … The numbers all end with a 4 or a 9 START WITH 1 MULTIPLY BY 5 1, 5, 25, 125, 625, … After the starting number all numbers end in a 5 All numbers are ODD Start with 100 and subtract 3 100, 97, 94, 91, 88, 85 … The numbers alternate from EVEN to ODD

Look for features of each pattern. RULE PATTERN FEATURES START WITH 12 ADD 3 START WITH 2 MULTIPLY BY 10 START WITH 100 DIVIDE BY 4

Look for features of each pattern. RULE PATTERN FEATURES START WITH 45 ADD 6 START WITH 88 SUBRACT 4 START WITH 8 MULTIPLY BY 3

Look for features of each pattern. RULE PATTERN FEATURES ADD 4 AND THEN MULTIPLY BY 2 START AT THE NUMBER 10 SUBTRACT 6 AND THEN MULTIPLY BY 3 START AT THE NUMBER 18 ADD 5 AND THEN DIVIDE BY 2

Look for features of each pattern. RULE PATTERN FEATURES MULTIPLY BY 3 AND THEN SUBTRACT 2 START AT THE NUMBER 11 MULTIPLY BY 6 AND THEN ADD 2 START AT THE NUMBER 1 MULTIPLY BY 5 AND THEN ADD 7 START AT THE NUMBER 10

Look for features of each pattern. RULE PATTERN FEATURES MULTIPLY BY 2 AND THEN SUBTRACT 4 START AT THE NUMBER 6 MULTIPLY BY 5 AND THEN ADD 3 START AT THE NUMBER 9 MULTIPLY BY 4 AND THEN DIVIDE BY 2 START AT THE NUMBER 15

Given the pattern – what is the RULE? 8, 15, 22, 29, ____ 3, 9, 27, 81, ____ 320, 160, 80, 40, ____

Given the pattern – what is the RULE? CHALLENGE 1, 3, 5, 7, 11, ___ 1, 1, 4, 4, 7, 7, 10, 10, ___ 1. emirp 2. 3+etanretla

This is a growing pattern This is a growing pattern. What does the figure look like that comes next? 5 6 7 8 What does the 8th figure look like?

WHAT COMES NEXT? These are growing patterns. See how the shape grows? WHAT IS THE RULE?

This is a growing pattern This is a growing pattern. What does the figure look like that comes next? What does the 7th figure look like?

This is a growing pattern This is a growing pattern. What does the figure look like that comes 10th?

This is a growing pattern This is a growing pattern. What does the figure look like that comes next?

This is a growing pattern This is a growing pattern. What does the figure look like that comes 6th?

This is a growing pattern This is a growing pattern. What does the figure look like that comes next?

This is a growing pattern This is a growing pattern. What does the figure look like that comes next?

What is the RULE for this growing pattern What is the RULE for this growing pattern? Can you predict what will be the 5th figure?