Unit 6

Operations with Decimals

Add and Subtract Through Thousandths-chapter 12

Multiply Decimals-chapter 13

Divide Decimals-chapter 14

Divide by Two-Digit Divisors-chapter 15

The standards covered in unit 6 are:

 Chapter 12

Number Sense: Add decimals and verify the reasonableness of the results.
Number Sense: Estimate, round and manipulate very large and very small numbers
Mathematical reasoning: Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy
Mathematical reasoning: Use estimation to verify the reasonableness of calculated results.

 Chapter 13

Number Sense: Multiply decimals and verify the reasonableness of the results.
Number Sense: Estimate, round and manipulate very large and very small numbers
Number Sense: Students compute with very large and very small numbers, positive integers, decimals and fractions and understand the relationship between decimals, fractions and percents. They understand the relative magnitude of numbers.
Mathematical reasoning: Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models to explain mathematical reasoning.
Mathematical reasoning: Use estimation to verify the reasonableness of calculated results.
Mathematical reasoning: Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.

Chapter 14

Number Sense: Divide with decimals and verify the reasonableness of the results.
Number Sense: Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.
Mathematical reasoning: Apply strategies and results from simpler problems to more complex problems.

Chapter 15

Number Sense: Demonstrate proficiency with division, including division with positive decimals and long division with multidigit divisors.
Number Sense: Add, subtract, multiply and divide with decimals and verify the reasonableness of the results.
Mathematical reasoning: Apply strategies and results from simpler problems to more complex problems.
Mathematical reasoning: Make precise calculations and check the validity of the results from the context of the problem.

 

Time for Some Practice

 

Estimate and then use a calculator to find the actual answer and check it with your estimate.

 

$ 7.83

+ 2.25

  $ 4.35

+ 3.12

  $ 12.15

+ 14.88

  $ 3.47

+ 2.25

  $ 7.76

+ 9.68

  $ 17.25

+ 23.49

 

 

Place the numbers 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 in the following grid so that the sum is 1.5 along each row, column and diagonal.

     
     
     

Back to the top!

 

 

Estimation

Use your estimation skills to estimate the answers to the following problems.
Then, use a calculator and see how accurate you are. Is there a difference between front-end and rounding?

 

 3.829 + 1.246 =  6.745 + 0.982 =
 0.487 + 0.512 =  7.13 + 5.931 =

 

For a bit more challenge:

 

 

Write the numbers 2-10 so that the sum of each row and diagonal is 18.

     
     
     

 

Miguel has one dollar in change. He has twice as many nickels as dimes. He has 14 more pennies than quarters. What coins does he have?

 

Find the missing addends in this addition table:

 +      16  
     14    
   11    17  
     27    41
   87      100

 

 

In a word game, a = 2 points, b= 4 points, c = 6 points, and so on. How many points is each of the following words worth?

quiz

math

addend

 

 

 

The Highview scout troop is planing a summer camping trip. The scouts buy their equipment on sale at Kauffman's Kamper World. Use a calculator to help them find the cost.

Item   Regular Price  Sale Price

Tent

Stove

Backpack

Boots

Sleeping Bag

Pad

 $249.95

$36.99

$79.50

$67.85

$162.50

$37.95

 $224.95

$30.55

$65.25

$52.80

$143.95

2 for $65.00


What two items can be purchased for about $100.00 at the sale price?

What is the cost of 10 pairs of boots on sale?

Estimate the cost of 1 stove, 6 sleeping bags, and 6 pads at the sale price.

A parka regularly sells for $59.99. Estimate its sale price if marked down similar to the stove.

About how much will the scouts save on 8 backpacks and 12 pairs of boots?

The scouts paid for a stove and backpack on sale with five $20 bills. How much was the change?

What is the sale price per pad?

What three items have an average sale price of about $50.00?

If the sales tax is $0.06 on each dollar, what is the total cost of one sleeping bag?

What is the total cost of 3 pairs of boots and 2 tents, including a $0.06 sales tax on each dollar?

 

Take your pick!

Use mental math, pencil and paper or a calculator to solve each of the following in the most efficient way.

 $32, 498 + $17, 120 = n
 10 x $28.32 = x
 $48.50 divided by 2 = a
 $50 - ( $18.25 = $1.75) = s
 $195.62 - $147.69 = p
 $25 = ($37 - $12) = b

 

 

Complete the chart and find the pattern:

X  2  0.2   0.02 0.002 
 6        
 2        
 4        
5        
 12        

 

 

Estimation Practice~

Estimate the following products by rounding each factor to the nearest whole number:

 15.3 x 2.8 ~ n
 24.8 x 3.2 ~ p
 7.2 x 19.7 ~ m
 3.6 x 25.4 ~ b
 39.6 x 5.9 ~ z
 12.2 x 4.1 ~ x

 

 

Estimate and then decide which is the correct product:

 2.68 x 42.7 = n  Is n = 114.36 or 1,114.36 ?
 0.5 x 14.8 = n  Is n = 0.740 or 7.4 ?
  0.92 x 4.5 = n  Is n = 4.140 or 41.4 ?
  5.3 x 12.07 = n  Is n = 63.971 or 639.71 ?
  4.87 x 72.1 = n  Is n = 35.1127 or 351.127 ?
  76.2 x 41.4 = n  Is n = 315.468 or 3, 154.68 ?
  176.5 x 4.1 = n  Is n = 72.365 or 723.65 ?

 

 

Complete these practice problems:

 X  0.5  2.6
0.9     
3.8     
 14.2    
 76.5    
 34.7    
 15.23    
 10.06    
 13.48    
12.75     

 

 

 

Complete this chart:

Percent   Decimal  Fraction
 25%    
 50%    
 10%    
 5%    
 1%    
 20%    
 53%    

 

 

Time to be challenged!

The product of two numbers is 90. One number is 2.5 times as great as the other. What are the two numbers?

Ms. Sanchez fills the vending machines at Heights Motel. Every Monday she fills the soft drink machine. She fills the snack machine every third day. She fills the coffee machine every fifth day. She fills all three machines on Monday, August 3. What is the next date on which she will fill all three machines?

 

Have an old calendar around?

 

 These are zoinks:

242; 143; 132; 484; 561;

These are not zoinks:

450; 144; 133; 494; 566

What makes a zoink a zoink?

What two digit number are all zoinks a multiple of?

 

At Bev's birthday party, 10 of her friends wore party hats and 8 of her friends used noisemakers. There were 12 guests. How many of her friends wore a hat and used a noisemaker?

 

 

 

How about some ?

 

Decimal Links for
Adding and Subtracting

 How do you add decimals? How do you subtract decimals? 
Adding Decimals  Subtracting Decimals
Adding Decimals-Money  Subtracting Decimals-Money 
Adding & Subtracting Decimals Tutorial   Subtraction Basketball-Decimals
 Adding and Subtracting Workout-
tutorial and practice
 Interactive Quiz

 

Algebra Links
 Practice Addition with one-digit numbers  Working with Variables
 Practice Addition with two-digit numbers  Solving Equations 1
 Practice Addition with three-digit numbers  Solving Equations 2
 Practice Subtraction with one-digit numbers  Solving Equations 3
 Practice Subtraction with two-digit numbers  Solving Equations 4 
Practice Subtraction with three-digit numbers  Algebra is fun!

 

Rounding Sites~

  Basketball Rounding Match Game-
decimals/whole numbers
 Flashcards-tenths
Rounding Riddles #1  Flashcards-
decimals/whole numbers
  
Concentration-tenths
Rounding Riddles #2  Concentration-
decimals/whole numbers
Rounding to Tenths
Match Game-tenths   Estimating and Rounding Rounding to Hundredths

 

Tutorials, explanations and practice for multiplying and dividing decimals

 Samples, explanations and practice of decimal multiplication
 Samples, explanations and practice of decimal division
 Tutorial on how to multiply fractions with a workout at the end!
 Tutorial on how to divide fractions with a workout at the end!


Practice decimal problems online from aaamath.com

Multiplying Thousandths by Tenths
Multiplying Thousandths by Hundredths
Multiplying Thousandths by Thousandths
Dividing a Decimal by a Whole Number
Dividing a Decimal by a Decimal-I
Dividing a Decimal by a Decimal-II 
REVIEW: Decimal Place Values
REVIEW: Rounding Decimals to the Nearest Tenth
REVIEW: Rounding Decimals to the Nearest Hundredth

 

 

 Decimals, Percentage, and Fractions

The Meaning of Percent

The Relationship between Percents and Decimals

The Relationship between Decimals and Percents

Percentages, Decimals and Fractions-Nice Summary Chart

Writing Fractions as Percents

Practice How Quick You Are 

 

Time to Exercise the Brain~

 

Samples from Math League Climb Math Mountain Puzzler Archive Cyberchase
Puzzler The Train Race Online Mankala  Play Bathroom Tiles
Who Wants to Win $1,000,000.00? Grade Five Problems Family Math Challenges  Online Math Games
 What's the Best Way to get Paid?  Mystery Math Coin Flipping Math Hunt 

 

 

to the math sites that we love!

 

Great Help for Most for Place Value Need help? Ask Dr. Math
Practice rounding with online flashcards Math Dictionary for Kids
Online Flashcards-all operations Tons of chances for practice-worksheets
Totally Tessellated A+ Math Games
Runaway Math Practice Late Delivery-Great Algebra Practice
Mystery Math-How do they do that? Order of Operations
Puzzler Math Baseball
Multiplication tips by kids Exponent Basketball
The Fruit Game Math Playground