Activities

1. .5 + .5 =
   
   
2. .26 ÷  2 =
   
   
3. Is the solution 66?

4. Which division problem has a larger quotient?   .62 ÷ 2   or   6.2 ÷ 2
   
   
5. .12 - .04 = ?

6. Identify the correct solution to .23 x .4

1. 92
2. .92
3. .092
4. 9.2

7. Compare the two problems and solutions.  Which one has the correct work and solution?

8. .59 - .4
   
   
9. What is the sum of 23.17 and .43?
   
   
10. 2.45 is doubled and added to 10.9, what is the result?
    
    
11. 4.52 x .2 = 9.04     True or false
    
    
12. Carmon purchased three packages of candy for $3.42 each and then gave the cashier a coupon for $1.25 off the purchase.  How much did he owe?
    
    
13. What digit must replace x in the equation?   97.23 – 30.x8 = 67.15

14. Is 11.52 the solution to 9.6 x 1.2?

15. Identify the problem for which 3.16 is NOT the solution?

1. 3.96 - .8
2. 2.85 + .31
3. 12.63 ÷ 3
4. 79 x .04

16. Derek and John solved the addition problem using different methods.  One of them is correct.  Which one is correct?    Explain the error in the incorrect work.
    
    Derek                7.92
                            + 1.3
                7+ 1        8                  
                .3 + .9   1.2                
                               .02                       
                             9.22               answer 9.22
    
    John                  7.92           2 + 3 = 5    9 + 1 = 10
                            + 1.3                9 + 1 = 10  write the 0 and carry the 1
                             8. 0 5           7 + carried 1 equals 8                       

                                                            answer   8.05

17. When dividing a decimal number by a whole number, is the solution larger or smaller than the whole number?  Use models or examples to explain your thinking.

18. Havanna has saved $102.75 and is going to Target to purchase prizes for the games at her party. She needs to buy the maximum number of prizes possible while still getting at least 5 of each item.  She wants to spend as close to all of her money as possible.  Tax is $0.06 for each dollar spent.  Indicate how many of each item she should purchase.  Explain your reasoning.
    
    $0.79 candy bars       $0.75 bubbles   $5.00 iTunes cards      $1.09 packs of gum

19. Without actually calculating the solutions, order the expressions from least to greatest.  Explain your thinking in ordering the expressions without doing any calculations. Then, strategically choose two problems and do the multiplication. 
    
      40.25 x .75                100.1 x 2.5                  40.5 x 7.5                    100.25 x .25               

20. 113.04 ÷ 12 = 9.42.   Is 9.42 the solution to this equation? Justify your answer by showing the work for two different methods and explaining your thinking.
    
    
21. Write a word problem that will model the expression below.  Explain what the solution means in terms of the problem.   12.4 + 8.41
    
    
22. Use the digits below to create an addition problem with two 3-digit decimal numbers with the largest possible solution.  One decimal must have a digit in the hundredths place and the other decimal with a digit in the tenths place.   Digits can only be used once in each number.  Explain your reasoning.

5   3   7   1

23. Which of the following is true for any division problem with a decimal dividend and whole number divisor?
    
    
    1. The solution is always greater than the dividend
    2. The solution is always less than the dividend
    3. The solution is always less than or equal to the dividend
    4. The solution is always greater than or equal to the dividend
       
       
24. Describe the process for subtracting two decimals. Explain why the place value of one number can only be subtracted from the same place value in another number.  For example, in the expression below h must be subtracted from b.

                         ne.a b c d
                        -  g.f h j k

25. Klarin is placing her monthly order for supplies for the bakery she runs.  She began the month of May with four 22.68 kilogram bags of flour. She used 24.3 kilograms in week one, 22.9 kilograms in week two, and 25.4 kilograms in week three.  She accidentally dumped .75 of one bag on the floor in week three so she purchased a 20 lbs bag of flour at the local grocery store.  During week four she used 21.25 kilograms of flour.  For the month of July she typically uses 2.25 times that used in May.  How much should she purchase for July?  Explain your thinking.

Answer Key/Rubric

1. 1.0
   
   
2. .13
   
   
3. No
   
   
4. 6.2 ÷ 2
   
   
5. .08

6. c
   
   
7. A
   
   
8. .19
   
   
9. 23.6
   
   
10. 15.8
    
    
11. False
    
    
12. $9.01
    
    
13. 0
    
    
14. Yes
    
    
15. c

16. Derek is correct.    John did not align the decimals places correctly and added the ones place to the tenths place. He also added the hundredths place in the first number to the tenths place in the second number.
    
    
17. The solution can be smaller or larger depending on the numbers in the dividend and the divisor.  Student may use models and examples to illustrate this point.  Explanations will vary.
    
    
18.  12 candy bars, 76 bubbles, 5 iTunes cards and 5 packs of gum for a total of $102.7458 – rounded up to $102.75.   Students must explain how they figured out the numbers.
    
    
19. 100.25 x .25     40.1 x .75     100.1 x 2.5      40.5 x 7.5     Explanations will vary but must contain a reference to approximating the solution for each expression.  Students have the choice as long as they can explain a logical reason for their choice that helps them check their order.  However, the most logical would be 100.1 x 2.5 and 40.5 x 7.5 or    100.25 x .25     40.1 x .75     because these sets of numbers are close. 
    
    
20. Yes.  Methods and explanations will vary. Students may use repeated addition and equal grouping.  Another possibility is to use guess and check.
    
    
21. Problems and explanations will vary.  Students must calculate the solution correctly (20.81) and connect it to the word problem.
    
    
22. 75.3 + 7.53    The largest possible solution can be gained by using the digits with the highest value so 7, 5, and 3 were utilized.  Meeting the condition of 3 digits and the tenths place is 75.3.  Meeting the condition of 3 digits and the hundredths place is 7.53.  The digit with the largest value, which is 7, must be placed as far left of the decimal as possible because the value of the number increases as digits reside in places to the left of the decimal. 
    
    
23. c
    
    
24. Student must accurately describe the subtraction process using whatever method they choose (and is of course correct).  It is only possible to subtract the same place values for instance f from a because of the meaning of the numbers. Students must correctly reference place value in their reasoning.
    
    
25. Ten bags of flour.  24.3 + 22.9 + 25.4 + 21.25 = 93.85 kilograms. 93.85 x 2.25 = 211.1625 kilograms needed for July.  22.68 x 9 = 204.12 which is not enough.