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Grade 05 Mathematics - EC: M05.A-T.1.1.4

Grade 05 Mathematics - EC: M05.A-T.1.1.4

Continuum of Activities

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

  • Instructional activities designed to be integrated into planned lessons
  • Questions/activities that grow in complexity
  • Opportunities for differentiation for each student’s level of performance

Grade Levels

5th Grade

Course, Subject

Mathematics

Activities

  1. Which is larger, .25 or .75?

  2. If Karen had .55 of the cake and Dimitri had .45, who had the smallest piece?

  3. True or False?   .61 = .610

  4. Which is greater .078 or .27?

  5. What is the name of the sign <?
  1. Identify the value of the 2 in the decimal .462?

  2. In which number does the 7 represent a larger value?
    1. 42.794
    2. 49.07      

  3. Compare the numbers by inserting <, >, or = in the blank.   .096   ______  .09

  4. Is the following true?  .204   <  .24  Why or why not?

  5. In the number sentence below, change one digit that will make the statement false.
                .523    <   .532

  6. Which value of 4 is greater, the one in the first decimal or the second?
                .74            .984

  7. Identify which one of the following is incorrect.
    1. .064 = .0640
    2. .719 > .971
    3. .87 < .871
    4. .99 > .989

  8. Identify what digit makes the number sentence false?       .36   >  .371

  9. Compare the following decimals and place them in order from smallest to largest using the appropriate symbol between them (< or >).
                .43         .04       .407

  10. Insert >, <, or = into the number sentence to make it true:     .9   ______  .089
  1. In which decimal is the value of the 4 larger?  By how much?   Explain your thinking.                   .947                               .42

  2. What value of x will make the number sentence true?  Explain your thinking.
                .x64 <  .36x

  3. Which of the following is NOT true for any value of x?
    1. .04x < .9x2
    2. .x56 > .x507
    3. .06x > .x69

  4. Is the following statement true for any value of x:   x.1x5 < x.21x   Why or why not? 

  5. If 0< a.axb > .a7b

  6. If the decimals are ordered from least to greatest, what value must x have?  Why?
                .01x                 .02x                 .13x                 .1xx                  .15x    

  7. If the decimal 3x.x4 is less than the decimal 34.xx but greater than 3x.15, list two statements that must be true about x regarding its value.  Explain your reasoning for each statement.

  8. For what values of x is 2.xx4 > 2.6xx? Explain your reasoning.

  9. Explain how a decimal with a 6 in the hundredths place can be greater than a decimal with a 9 in the hundredths place?  How many examples are possible?

Answer Key/Rubric

  1. .75

  2. Dimitri

  3. True

  4. .27

  5. Less than
  1. 2 thousandths or 0.002

  2. a

  3. > 

  4. Yes, if you make them both to the thousandths place you will have 204 thousandths is less than 240 thousandths.  204 is less than 240.

  5. Ex:  .553 < .532.  Answers will vary - must change the 2 in .523 to anything equal to or greater than 3

  6. First decimal

  7. b

  8. The 6 or the 7

  9. .04  <  .407  <  .43

  10. > 
  1. .42; It is 10 times larger.   Answers will vary but should contain a reference to place value.

  2. x can equal 0, 1 or 2.  Answers will vary but should contain a reference to place value.

  3. c

  4. Yes because the 2 in the tens place will always be greater than the 1 in the tenths place of the first decimal.

  5. The smallest value of x is 8.  The value of a is irrelevant because it is the digit in the tenths place of both numbers therefore it is equivalent in value.  The hundredths place for the smaller decimal is a 7, which means that if the first decimal is always to be greater it must be greater than 7.  Answers for the explanation will vary.

  6. X must be 4.   The place value of x in the first two decimals does not matter because .01 is already less than .02.  Similar argument for the second and third decimal.  It will began to matter between the third and fourth decimal where x must be greater than 4 because of the 3 in the tenths place of the third decimal.  The five in the hundredths place of the last decimal force x = 4 because the digit in the hundredths place must be less than 5.
    .014                 .024                 .134                 .144                 .154

  7.  X can equal 3.  X can equal 2.  If 3x.x4  is less than the decimal 34.xx that means that x must be less than 4 and greater than 0 because of the 4 in the tens place in the second number.  If 3x.x4 is greater than 3x.15 then x can be a 2 or a 3 because these digits work ( 33.34 > 33.15, 32.24 > 32.15).

  8. x = 7 , 8, 9    Since the ones place is identical in both numbers, the tenths place is the next value that needs to be compared.  The tenths place in the second number is 6 and since 2.xx4 is greater than 2.6xx, x must be greater than 6

  9. Explanations will vary.  However, the explanations must contain a reference to the value of the digits in the places to the left of the hundredths place.   There are infinite examples.
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