Name:__________________________________                                       Date of Exam: _____
Math 5B/6B                                                                                                  Quarter 1 Cumulative Exam: Study Guide

 

 

Quarter 1 Cumulative Exam

Study Guide

 

Exam covers the following Massachusetts Department of Education Frameworks:

 

Number Sense and Operations Strand:      N   6.N.1          Demonstrate an understanding of place value to billions and thousandths. :   6.N.2          Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents   6.N.3     Demonstrate an understanding of positive integer exponents … when  used in               powers of ten      e.g., 102, 105. :   6.N.5      Identify and determine common equivalent fractions, … decimals,  and percents.         6.N.6         Find and position integers…and decimals …on the number line.   6.N.7        Compare and order integers …and…decimals…     6.N.8        Apply number theory concepts–including…divisibility rules for 2, 3, 4, 5, 6, 9, and 10   6.N.13     Accurately …add and subtract …whole numbers and positive decimals.   6.N.15      Add and subtract integers, with the exception of subtracting negative integers.   6.N.16     Estimate results of computations with whole numbers…

 

GEOMETRY Strand: G   6.G.3                 Identify relationships among points, lines, and planes, e.g., intersecting, parallel, perpendicular. 6.G.7                 Identify types of symmetry, including line and rotational.

 

 

measurement Strand: m        6.M.5     Identify, measure, and describe circles and the relationships of the radius, diameter, circumference, and area…

 

6.N.3       Demonstrate an understanding of positive integer exponents, in particular,

              when used in powers of ten      e.g., 10², 10⁵. :

 

 

HINT:                     Count the zeroes.

 

 

Examples:  10²=100      10⁶⁼1,000,000       10,000=10⁴       1,000,000,000=10⁹    

 

Practice:     10⁵=____________      10^{3 =}____________                 10^{4 =}____________

 

Practice:     100,000,000=10^____        10,000,000=10^____                    10 =10^___

 

 

 

6.N.7      Compare and order integers …and…decimals…

 

Be able to tell if the number is equal to, greater than, or less than the other number.

 

HINT:    Pay attention to the decimal point.

 

 

Examples:    9.59  > .959                0.5 = 0.50                  .9999 < 1.35

 

Practice:       798.9 ___ 2,560          0.08 ___ 0.0800 1.408 ___ .1408

 

 

6.N.4                Demonstrate an understanding of place value to billions and thousandths. :

 

Examples:   Underline the number in the hundreds place.   345,978.47

                                Underline the number in the hundredths place.   345,978.47

 

Practice:     Underline the number in the ten-thousands place.            345,978.47

 

              Underline the number in the tenths place.                                  345,978.47

 

6. N.16   Estimate results of computations with whole numbers…

 

Learning Strategy for Rounding Numbers:     ·        Underline the digit in that place value.                    “Underline the digit.” ·        Circle the number to the right.                       “Look next door.” ·        Is the circled number 5 or bigger?                 “Five or bigger?” o       If so, add 1 to the underlined number.        “Add one more.” o       If not, leave the underlined number alone.             ·        Make the circled digit and all the ones after it zeroes. ·        Leave all the digits to the left the same.                       Example:    Round to the thousands place.         3, 457, 682                                                                              3, 457, 682 3, 45_, 000 3, 458, 000

 

 

Examples:   Round the number to the hundreds place.   345,368.47 = 345,400.00

                               

Estimate  (by rounding the numbers to the hundreds place) the answer.

644 + 272 

                             600 + 300 = 900

 

Practice:     Round the number to the hundreds place.   123,456.32 = ___________

                               

Estimate  (by rounding the numbers to the hundreds place) the answer.

 

573    -  139

                             _____- ______ = __________

 

 

 

1.39   + 57.3 

                             _____+ ______ = __________

 

 

6. N.13     Accurately and efficiently add, subtract …whole numbers and positive

                decimals.

 

Be able to add and subtract numbers to the millions place and the hundredths place. 

 

HINT:  Be sure to line up the decimal.

 

 

Examples:       53.52 + 5.48                    18.5 – 6.75           

 

                       53.52                              18.50                                    

                     +  5.48                           -    6.75                          

59.0                                                                               11.75                   

 

 

 

Practice:         7.4 + 12.85                            20.00 – 5.75

 

                                                             

                        +       ___                                 -    ______

                                                    

 

 

Estimate then Solve: 

Examples:                         3, 976 => 4,000                    397.6 + 2.58 =  

– 2, 158 => 2,000              =>  400    + 3      =   403

   1, 818 => 2,000                    397.6 + 2.58 =   400.18

 

 

 

Practice:                        8, 775  => _,000                          72.6 + 5.25 =  

– 1, 126 =>  _,000                    => ___  + ___  =   _____

              =>    ,000                          

         Line up the decimals and add.

 

 

 

 

6.N.6  NUMBER LINES               Put the following numbers on each number line.

 

 

1.00                    0.71                    0.59                    0.23                     0.86

 

 

                                                                                                                                                                     

                                                           

6.N.5  Represent and compare very large (billions) and very small(thousandths) positive numbers in various forms such as expanded notation …

 

HINT: Line up the commas and the decimal point

           

***USE LINED PAPER or GRAPH PAPER to line up the numbers. ***

 

Examples:       Put 345,978.47 into expanded form.  

                             300,000

 40,000

   5,000

      900

        70

          8

          0.40

       + 0.07

 

                                300,000 + 40,000 + 5,000 + 900 + 70 + 8 + 0.40 + 0.07  

 

Practice:     Put 125,346.78 into expanded form.

 

________ + _______ + ________ + _________ +_______ + _____ + _______ + _______

 

Examples:       Put  300,000 + 40,000 + 5,000 + 900 + 70 + 8 + 0.40 + 0.07 into standard form.

                                                            300,000

 40,000

   5,000

      900

        70

          8

          0.40

       + 0.07

                                                345,978.47  

OR

Use the “short cut”

Learning Strategy for putting Expanded Numbers into Standard Form:   o 50, 000 + 4, 000 + 700 + 8   ·  Look at the largest (longest) number.  o  50, 000 + 4, 000 + 700 + 8   ·  Count the number of “spaces”.  o There are 5 spaces   ·  Use lines and commas to set up your answer. o   __ __ , __ __ __   ·  Put each digit in the correct place value. o   5_  4_, 7_ __ 8_   ·  Put zeroes in all empty spaces. o   5_  4_, 7_ 0_ 8_

 

 

Practice:     Put 500,000 + 40,000 + 3,000 + 200 + 10 + 9 + 0.80 + 0.07 into standard form.  

 

                        Short Cut: ______________________________________________________

 

                                                                                    OR

 

                  use next page

 

 

 

Practice:     Put 500,000 + 40,000 + 3,000 + 200 + 10 + 9 + 0.80 + 0.07 into standard form.  

                  ____________________

 

 

 
6.N.5      Identify and determine common equivalent fractions, … decimals,  and percents.

 

1.  Draw a straight line through the center of each circle.  (This is the diameter). 2.  Draw an intersecting line so that each circle is divided into four equal parts.

 

Color in one section.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

 

******************************************************************

 

Color in two sections.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

 

******************************************************************

 

Color in three sections.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

 

******************************************************************

 

Color in all the sections.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

Name:__________________________________      Date of Exam:__________________

Math 5B/6B                                                                 Quarter 1 Cumulative Exam

 

Quarter 1 Cumulative Exam

Practice Exam

 

 

6.N.1  Demonstrate an understanding of positive integer exponents, in particular, when used in powers of ten      e.g., 10², 10⁵. :  ***Hint:  Zeroes

 

Solve:                          10²=__________      10⁶⁼_____________     10⁴⁼_____________

 

1,000=10^___                  1,000,000,000=10^___               100,000=10^___  

 

 

6.N.2  Demonstrate an understanding of place value to billions and thousandths. :

 

            Underline the number in the ten-thousands place.               456,172.38

 

Underline the number in the tens place.                                              456,172.38     

           

      Underline the number in the tenths place.                                     456,172.38

 

      Underline the number in the hundredths place.                    456,172.38

 

 

 

6. N.16   Estimate results of computations with whole numbers…

 

Round the number to the hundred-thousand place.                                   456,172.38       ________________

 

Round the number to the tens place.                                                                               456,172.38      ________________

 

Round the number to the tenths place.                                                                     456,172.38       ________________

 

 

Round the number to the ones place.                                                                             456,172.38       ________________

 

6.N.7    Compare and order integers …and…decimals…

 

Tell if the number is equal to, greater than, or less than the other number.

 

7,759 ___ 7,597          33,783 ____33,873        506,044____560,044

 

 

9.59 ___ .959              0.5 ____0.50000             32.75____32.075

Put into expanded form.           582,941.36

 

 

 

 

 

 

Answer:

_______________ + ____________ + ____________ + __________ + ______ + ___ + ______ + ________

                                                           

 

6.N.3  Represent and compare very large (billions) and very small (thousandths) positive numbers in various forms such as expanded notation without exponents

 

 

Put into standard form:  Use the “short cut” or do it the long way.

 

________________________________________________________________________

 

100,000 + 80,000 + 2,000 + 400 + 0 + 6 + 0.30 + 0.07

     

                       

 

 

 

 

Answer: ________________________________________________________________________

 

 

 

 

6. N.16   Estimate results of computations with whole numbers…

 

Estimate the answer (by rounding the numbers).  Do NOT solve (just estimate)

 

644 + 272 =  ______    644-272 =  ______                109 + 807 =  ______                      

 

 

5.1 x 5.99 =  ______    1.92 x 2.77 =  ______            99.75 divided by 2.2 =  ______

 

 

                       

                       

6. N.13     Accurately and efficiently add and  subtract …whole numbers and positive decimals.

 

First, estimate the answer (by rounding the numbers) THEN SOLVE.

 

644 + 272 =  ______            644-272 =  ______

                                 

 

 

 

 

 

3.33 + 2.66 =  ______                   3.33 + 0.6 =  ______

 

 

 

 

 

 

 

64.4 + 27.2 =  ______                   64.4-27.2 =  ______

 

 

 

 

 

 

 

 

 

6.N.6  NUMBER LINES               Put the following numbers on each number line.

 

 

1.00                    0.10                    0.48                    0.22                     0.33

 

 

                                                                                                                                                                     

6.N.5      Identify and determine common equivalent fractions, … decimals,  and percents.

 

1.  Draw a straight line through the center of each circle.  (This is the diameter). 2.  Draw an intersecting line so that each circle is divided into four equal parts.

 

Color in two sections.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

 

******************************************************************

 

Color in one section.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

 

******************************************************************

 

Color in three sections.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________

 

******************************************************************

 

Color in all the sections.

 

Write the fraction:__________

 

Write the percent: __________

 

Write the decimal: __________