Number Sense
Grade 6
Andrew Sundberg
Laporte School
[email protected]
Executive Summary
This unit is meant to be used as an introduction to using fractions,
decimals, and percents interchangeably. Students will also work with
ratios and understand how they are related to fractions, decimals,
and percents. Students will practice operations with fractions,
decimals, and percents. Concepts such as factors, multiples, LCM,
GCF, prime factorization should have been introduced prior to using
this unit. The goal of this unit is to make students comfortable in
flexibly working with fractions, decimals, and percents and to be able
to perform operations with all three representations.
Minnesota State Standards Covered in Grade 6
Standard-
Read, write, represent and compare positive rational numbers expressed as
fractions, decimals, percents and ratios; write positive integers as products of factors; use these
representations in real-world and mathematical situations.
No.- 6.1.1.2
Benchmark- Compare positive rational numbers represented in various
forms. Use the symbols < , = and >.
No.- 6.1.1.3
Benchmark - Understand that percent represents parts out of 100 and
ratios to 100.
No.- 6.1.1.4
Benchmark- Determine equivalences among fractions, decimals and
percents; select among these representations to solve problems.
No.- 6.1.1.7
Benchmark- Convert between equivalent representations of positive
rational numbers.
Standard -
Understand the concept of ratio and its relationship to fractions and to the
multiplication and division of whole numbers. Use ratios to solve real-world and mathematical
problems.
No.- 6.1.2.1
Benchmark- Identify and use ratios to compare quantities; understand
that comparing quantities using ratios is not the same ascomparing
quantities using subtraction.
No.- 6.1.2.2
Benchmark- Apply the relationship between ratios, equivalent fractions
and percents to solve problems in various contexts, including those involving
mixtures and concentrations.
No.- 6.1.2.3
Benchmark- Determine the rate for ratios of quantities with different units.
No.- 6.1.2.4
Benchmark - Use reasoning about multiplication and division to solve ratio and
rate problems.
Standard -
Multiply and divide decimals, fractions and mixed numbers; solve real-world and
mathematical problems using arithmetic with positive rational numbers.
No.- 6.1.3.1
Benchmark- Multiply and divide decimals and fractions, using efficient
and generalizable procedures, including standard algorithms.
No.- 6.1.3.3
Benchmark - Calculate the percent of a number and determine what
percent one number is of another number to solve problems in various
contexts.
No.- 6.1.3.4
Benchmark- Solve real-world and mathematical problems requiring
arithmetic with decimals, fractions and mixed numbers.
No.- 6.1.3.5
Benchmark- Estimate solutions to problems with whole numbers,
fractions and decimals and use the estimates to assess the
reasonableness of results in the context of the problem.
Sample MCA II Questions
Table of Contents
Day 1
Pretest
Day 2
Adding and Subtracting Decimals
Day 3
Multiplying Decimals
Day 4
Dividing Decimals
Day 5
Fraction Sense
Day 6
Adding and Subtracting Fractions and Mixed Numbers
Day 7
Multiplying Fractions
Day 8
Dividing Fractions
Day 9
Multiplication and Division with Mixed Numbers
Day 10
Fund Raiser
Day 11
Science Fair
Day 12
Handy Survey
Day 13
Summer Daze
Day 14
Order of Operations Bingo
Day 15
Post Test
Day 1 “Pretest”
Objective: Students will take the unit pretest so I can assess their prior
knowledge of the topics being covered.
Launch:
Tell the students they will be taking a pretest on fractions, decimals, and
percents. Tell them to do their best even though they may not have been taught
many of the topics on the pretest.
Explore:
Allow the students to work independently on their pretests. The test
shouldn’t take the whole math period.
Share:
When the whole class completes the pretest, have the students get in
groups of 2-4 and discuss what parts of the test they understood and what parts
were difficult for them. Have one group member record their results.
Summarize:
Have a class discussion about the pretest, and discuss difficulties. Let the
students talk about parts of the test they struggled with and see if their
classmates had any strategies to help with those problems. Tell them that we will
be covering these topics over the next few weeks.
Day 2 “Adding and Subtracting Decimals”
Objective: Students will review the steps of adding and subtracting decimal
numbers. They will talk about reasonableness of solutions, and
extend the problems into a real life context.
Standard Covered:
No.- 6.1.3.4
Benchmark- Solve real-world and mathematical problems requiring
arithmetic with decimals, fractions and mixed numbers.
Launch:
Begin with a real life problem involving adding or subtracting of decimals,
such as going grocery shopping. Purposely line everything up on the right side
(decimals not lined up). See if the students are checking for the reasonableness
of the answer. Review the rule that the decimal points must be lined up or
stacked up when performing addition or subtraction of decimal numbers. Have
the class give some more examples of when adding or subtracting decimals is
used in real life.
Explore:
Next, have the students get in pairs and have them come up with 3 word
problems that would include addition or subtraction of decimals. Make sure the
problems are easy to understand and well-written, because they will be switching
their group’s problems with another group’s problems to work on. Let them
switch and figure out each other’s problems.
Share:
Let each group pick out their favorite problem they made and give it to the
rest of the class to work on together. Allow them to share strategies to find
correct solutions.
Summarize:
I will explain the two major points I want students to remember. First, the
decimal points must line up when doing addition or subtraction or else the place
values won’t line up. Secondly, the students should be checking for the
reasonableness of their answers. A good way of doing this is estimating before
you actually work the problem.
Extension/Homework:
Problem set with 5-10 word problems involving addition and subtractions
of decimal numbers.
Day 3 “Multiply Decimals”
Objective: Students will learn how to multiply decimal numbers by using a
variety of methods. They will also check the reasonableness of
their solutions by estimating prior to working out the problem.
Standard(s) Covered:
No.- 6.1.2.4
Benchmark - Use reasoning about multiplication and division to solve ratio and
rate problems.
No.- 6.1.3.1
Benchmark- Multiply and divide decimals and fractions, using efficient
and generalizable procedures, including standard algorithms.
Launch:
Begin the class period by reviewing what we learned yesterday about
addition and subtraction of decimal numbers. Next, talk about a type of problem
that requires multiplication of decimal numbers, buying gasoline. Tell them I
bought ____ gallons of gas at ____ per gallon. Have them estimate how much
money I spent on gas. Next, show them how to multiply decimals (forget the
decimals, put in the decimal when finished).
Explore:
Give the students a “car” and tell them we are going on a trip. They have to
choose their destination and find out how far it is away from Laporte. Then, help
them figure out how many gallons of gas they would need to buy to get to their
destination depending on the gas mileage of the car. Once they know the amount
of gas needed, they can figure out how much it will cost depending on the current
gas prices.
Share:
Let the students work in groups of three with their car and have them first
come up with a reasonable estimate of how much gas money they will need to
get where they’re going. Then have them work it out with the algorithm to see if
their estimates were close. They can share with a neighboring group to see the
differences with cars and trucks, etc.
Summarize:
Talk the students about the importance of getting a reasonable estimate
before doing the problem. It makes you think about what the answer should be
near so if you screw up on the work, you will know that. Review the steps of
multiplying decimal numbers before letting the kids out.
Day 4 “Dividing Decimals”
Objective: Students will learn how to divide decimals numbers with decimal
numbers in the dividend, divisor, or both. Then, students will relate
the problems to real life context and check the reasonableness of
their solutions.
Standard(s) Covered:
No.- 6.1.3.1
Benchmark- Multiply and divide decimals and fractions, using efficient
and generalizable procedures, including standard algorithms.
No.- 6.1.3.4
Benchmark- Solve real-world and mathematical problems requiring
arithmetic with decimals, fractions and mixed numbers.
Launch:
We will continue to work off of yesterday’s launch of gas prices. Briefly
review how we found the total amount of the cost of gas yesterday using
multiplication of decimal numbers. Today we will reverse the situation. I could
say it cost me ______ to fill my gas tank up, and gas costs ______ per gallon. How
many gallons of gas did I buy? Hopefully students will recognize this as a division
problem. Again, each group of students will be assigned a certain type of car, and
they will pick a destination to drive to.
Explore:
Once the students have figured out how many miles it is to their
destination, they will find out how many gallons of gas it will take to get their
according to the gas mileage their car gets. First, the students will estimate a
reasonable amount without knowing the division algorithm of moving the decimal
points. Once every group has a reasonable estimate, I will show the group the
“trick” of moving the decimal point to the end in the divisor and moving it the
same amount of places in the dividend.
Share:
Have students share with other groups what they found for their amount of
gas needed. Let them explain any mistakes they made, and share any successes
they had as some may have another way of explaining the problem that makes
better sense to other students.
Summarize:
I will show again the process of first coming up with a reasonable estimate
for each problem to eliminate answers that don’t make sense. Then we’ll review
how to move the decimal points in different situations in division.
Extension:
For homework, give the students a small problem set of real world
problems involving addition, subtraction, multiplication, and division of decimal
numbers.
Day 5 “Developing Fraction Sense”
(lesson modified from NCTM Illuminations website)
Objective: Students will gain strategies to understand fractions in relation to
the benchmarks 0, ½, and 1. They will understand the relationship
between the numerator and the denominator so they understand
what fractions actually mean.
Standards Covered:
No.- 6.1.1.4
Benchmark- Determine equivalences among fractions, decimals and
percents; select among these representations to solve problems.
No.- 6.1.1.2
Benchmark- Compare positive rational numbers represented in various
forms. Use the symbols < , = and >.
Materials:
http://illuminations.nctm.org/Lessons/FractionalClothesline/FractionalClothesline-AS.pdf
Launch:
There will be a clothesline strung across the room with the whole numbers
0,1,2,3, and 4. We will talk about what numbers would go between each number,
and that each whole number should be an equal distance apart. We will review
fractions, mixed numbers, equivalent fractions, and improper fractions so
students will have a better chance of placing their given card in the correct area
on the clothesline.
Explore:
Give each student a card with either a fraction, mixed number, or improper
fraction on it with a clothesline fastener. Tell the students they need to go up to
the clothesline and clip their card where they think it belongs. They have to
justify why they chose to put it where they did. The other students aren’t allowed
to comment on their classmates’ decisions until everyone has had their turn.
Share:
After everyone has had their turn, students are allowed to comment on
cards that they think might need to be moved. They have to be able to explain
why they think the card must be moved when they move it. The whole class
needs to agree at the end that they have the number line looking the way they
want it to look. When they say they are finished, I will look it over and see if I
agree with their placement.
Summarize:
We will talk about the benchmarks 0, ½, and 1 and how we can use them to
put each of the cards in a reasonable place. We will also discuss improper
fractions and mixed numbers, and how to be flexible in moving between these
two ways of displaying numbers. We will talk about how on mixed numbers you
should first look at the whole number to see which two whole numbers it’s
between, then look at the fraction to find where you should put it between the
two numbers.
Day 6 “Adding and Subtracting Fractions and
Mixed Numbers”
Objective:
Students will be able to add and subtract fractions and mixed
numbers using common denominators. They will use the concepts
of “carrying” and “borrowing” to successfully complete these
problems.
Standards Covered:
No.- 6.1.3.5
Benchmark- Estimate solutions to problems with whole numbers,
fractions and decimals and use the estimates to assess the
reasonableness of results in the context of the problem.
No.- 6.1.3.4
Benchmark- Solve real-world and mathematical problems requiring
arithmetic with decimals, fractions and mixed numbers.
Launch:
I will give the class of a couple of real world sample problems where adding
and subtracting fractions and mixed numbers would be necessary. I will make the
mistake of adding the numerators and the denominators and ask the class if I
arrived at the correct solution. I will use virtual manipulatives from NLVM on the
SmartBoard to show the class about the importance of using common
denominators when adding or subtracting fractions.
Explore:
The class will be put in groups of three to explore the problem. They will
each be responsible for coming up with four real world problems; one for adding
fractions, one for subtracting fractions, one for adding mixed numbers, and one
for subtracting mixed numbers. They will not solve the problems yet, we will do
that together as a class.
Share:
When each group has made their four problems, we will come back
together as a class. I will pick a variety of problems from the groups, and students
will have to choose which operation would be appropriate to use for the
problems. We will use the NLVM applets to show common denominators while
the students write the problem using common denominators on their paper.
Summarize:
To finish the period, I will talk about how the background we gained from
visually seeing the common denominators can be used to find the solution
without using manipulatives, if the students are comfortable with that. We’ll
practice a couple of problems together where the students can choose to use or
not use manipulatives.
Extension/Homework:
Problem Set with adding and subtracting mixed numbers and fractions in
real world scenarios.
Day 7 “Multiplying Fractions”
Objective:
Students will gain an understanding of what is actually happening
when multiplication of fractions occurs. They will first see a
pictorial model and then be able to transfer that knowledge to be
able to use an algorithm.
Standard Covered:
No.- 6.1.3.1
Benchmark- Multiply and divide decimals and fractions, using efficient
and generalizable procedures, including standard algorithms.
Launch:
I will give a situation where multiplication of fractions would exist in a real
life situation, such as “There is a half of pizza and your brother eats half of what’s
left. How much is left of the entire pizza?” After letting the students struggle for
the answer for a bit, I will show them the array model for multiplying fractions.
Make sure they understand the vertical and horizontal division of the array.
Explore:
Give the students a couple of problems to work on in pairs, using the array
model. Make sure they understand that when you multiply fractions, the product
is actually smaller than the factors themselves. (This will seem strange to them
because they’re used to multiplication making larger products than their factors)
Once they seem to have a good understanding of the array model, show them the
algorithm of multiplying the numerators and the denominators.
Share:
Students can share a couple of problems they solved, and show it in both
the array model and with the algorithm so they are making the connection
between the two of them. Allow students to share any “shortcuts” they may
have noticed, such as the reducing the numerator and denominator for separate
fractions.
Summarize:
Show students the reducing trick in the algorithm, but keep going back to
the array so the students don’t lose the understanding of multiplying fractions.
Explain it by saying we are taking part of another fraction, so the answer will get
smaller than the original amount.
Extension:
Who Wants to Be a Millionaire Multiplying Fractions game link
http://www.math-play.com/Multiplying-Fractions-Millionaire/MultiplyingFractions-Millionaire.html
Day 8 “Dividing Fractions”
Objective: Students will learn the final operation with fractions in this unit,
division. Using prior knowledge that division is the opposite or
inverse of multiplication, we will approach this type of problem as
doing the opposite of multiplying.
Standard:
No.- 6.1.3.1
Benchmark- Multiply and divide decimals and fractions, using efficient
and generalizable procedures, including standard algorithms.
Launch:
We will review what we learned about multiplication of fractions from
yesterday. Since it is very rare to come up with real world situations where
division of fractions is used, we will talk about division of a whole number with a
fraction. A good example would be if there was a whole cake made and you
wanted to eat ¼ of the cake, how many times would be able to eat cake? I will
then show the students the invert and multiply trick.
Explore:
Have the students work on a set of problems in groups of 2-3. Make sure
they are following the algorithm correctly, as it is easy to switch which fraction is
flipped. Allow the students to share any strategies that are useful to them.
Challenge the students to come up with any real life context to the division
problems they are doing. This can be very difficult.
Share:
Have the groups share their answers with other groups. When any
disagreements come up, allow the students to discuss and justify the answers
they chose to see if they want to stick with their answer or switch to another
answer.
Summarize:
Make sure the students understand that the second fraction is the one that
gets flipped or is the reciprocal in the division problem. Tell the students that it is
difficult to find context for dividing fractions, so challenge them to find situations
where they are applicable.
Day 9 “Multiplication and Division with Mixed
Numbers”
Objective: Students will take the knowledge they’ve acquired the past two
days about multiplying and dividing fractions and apply it to mixed
numbers.
Standards Covered:
No.- 6.1.3.1
Benchmark- Multiply and divide decimals and fractions, using efficient
and generalizable procedures, including standard algorithms.
No.- 6.1.3.4
Benchmark- Solve real-world and mathematical problems requiring
arithmetic with decimals, fractions and mixed numbers.
Launch:
We will review what we have learned the last couple of days in
multiplication and division of fractions. Then we will talk about changing of mixed
numbers to improper fractions, which is something we covered in Day 5 of this
unit. We will combine these two concepts to be able to successfully complete
these types of problems.
Explore:
Let the students work on the given problems in pairs. Allow some students
to do the problems without first changing the mixed numbers to improper
fractions and compare them to someone who has done the proper changing. Talk
about how the problems do not have the same solutions, and that the correct
solution has the mixed numbers changed to improper fractions.
Share:
Allow students to share their solutions within their groups and share
successful strategies. Have them talk about any common mistakes made so they
are aware of these and can hopefully avoid them in the future.
Summarize:
Reinforce the importance of changing the mixed numbers to improper
fractions. Also, pound home the rule of using the reciprocal on the second
fraction or mixed number in division problems.
Day 10 “Fund Raiser”
(Activity found in NCTM Navigating through Number and Operations Grade 6-8)
Objective: Students will take what they’ve learned about fractions and
decimals from earlier in the unit and extend that knowledge into
percents. They will use a visual representation to show a part to
whole relationship.
Standards Covered:
No.- 6.1.1.3
Benchmark - Understand that percent represents parts out of 100 and
ratios to 100.
No.- 6.1.3.3
Benchmark - Calculate the percent of a number and determine what
percent one number is of another number to solve problems in various
contexts.
Launch:
Begin the activity by asking the students what they know about fund
raisers. Make sure they understand the concept of setting a goal for fund raising,
and then tracking progress towards that goal. Discuss how the visual
representation of a thermometer could track progress toward a fund raiser’s goal.
Distribute the activity sheet to the students.
Explore:
Have the students work individually on the activity sheet. Have the
students describe everything they can about the fund raiser in question 1. They
should be able to come up with quite a list. Then, have the students turn over
their activity sheet and come up with an announcement for the daily
announcements about the progress of the fund raiser. Observe the students to
see how they approach the paragraph.
Share:
Have student volunteers come up and share what they’ve determined
about the fund raiser. Have them explain their strategies for how they
determined what fraction has been completed, what percent has been
completed, and other observations the students came up with. See what the
students came up with for how many days they think it will take the class to
achieve their goal.
Summarize:
Make sure that the students agree that it appears the class is ¼ or 25% of
the way to their goal. Once they have agreed upon that, we can assess how long
the class will take to achieve their goal. We can talk about there are different
ways of coming up with the solution, but we should agree that it’ll take the class 8
days to achieve their goal if their current pace continues.
Day 11 “Science Fair”
(Activity found in NCTM Navigating through Number and Operations Grade 6-8)
Objective:
Students will interchangeably work with fractions, decimals, and
percents. They will also recognize the need to look at these
numbers in a common form for a given problem.
Standards Covered:
No.- 6.1.1.4
Benchmark- Determine equivalences among fractions, decimals and
percents; select among these representations to solve problems.
No.- 6.1.1.7
Benchmark- Convert between equivalent representations of positive
rational numbers.
Launch:
Distribute a copy of the activity sheet “Science Fair” to the students.
Explain that three middle schools are going to hold a joint Science Fair at a
gymnasium. The gym will allocate space based upon how many students each of
the three schools have. Tell them the amount of students each of the three
schools have.
Explore:
Have the students work in pairs to divide the gym space into three areas
based upon how many students each of their schools have. Make sure the
students show the fractional part and the percent of the gym each school will
receive.
Share:
Let the students share their solutions with their classmates. Make sure
they justify their responses, and see if they first thought of their partitions as
fractions or as percents. See if any of the students notice that while their
diagram might not look like another groups, they actually may have the same
solution.
Summarize:
Talk about how dividing the gym in half at first might be a good strategy
because one school has half of the population of the three schools combined.
Talk about how some divisions of the gym might not be a good idea because they
aren’t compatible with all three schools. Finally, make sure students are
comfortable switching between all three forms of the rational numbers: percents,
decimals, and fractions.
Day 12 “Handy Survey”
(Activity found in NCTM Navigating through Number and Operations Grade 6-8)
Objective: Students will use different forms of rational numbers
interchangeably in an applied context. Students will also be able to
communicate their ideas to their classmates.
Standards Covered:
No.- 6.1.1.7
Benchmark- Convert between equivalent representations of positive
rational numbers.
No.- 6.1.3.4
Benchmark- Solve real-world and mathematical problems requiring
arithmetic with decimals, fractions and mixed numbers.
Launch:
Distribute a copy of “A Handy Survey” to each student. Explain that I read
somewhere that about 10% of the population is left handed. This statistic
surprised a group of students in a school, who went around and collected their
own data. Ask the students if the data collected is similar to the claim in the book
I read, or is it greater or less than the data collected?
Explore:
Allow the students to work in pairs to complete the activity sheet. Let the
students use whatever strategies they are comfortable with to compute what the
average of left handed people was in this particular school. Have the partners
discuss with each other the reasonableness of their answers so they are prepared
to back up their answers.
Share:
Let student volunteers come up and share their mathematical reasoning to
their solutions. Some students might combine all the data to find that the
school’s sample was 11%, slightly higher than the 10% in the book I read. Other
students might have realized that 10% of 80 is equal to 8, and that the sample has
nine which is also slightly higher.
Summarize:
Go through all the possible methods of solving this problem, and say that
any one of them is a good way to solve the problem. Using fractions, percents, or
decimals and the scope the students look at the problem may be different, but as
long as we can justify our answer and it’s reasonable, it’s a good strategy.
Day 13 “Summer Daze”
(Activity modified from NCTM Illuminations website)
Objective: Students will take a summer day and represent parts of their day in
fractional, decimal, and percent form. They will interchangeably
work between these representations of rational numbers.
Standard Covered:
No.- 6.1.1.4
Benchmark- Determine equivalences among fractions, decimals and
percents; select among these representations to solve problems.
No.- 6.1.1.7
Benchmark- Convert between equivalent representations of positive
rational numbers.
Launch:
Have a discussion about how a student may spend a typical summer day.
Let them suggest some things they like to do during the summer. Create a list of
activities students like to do during the summer, but get them thinking about the
things they spend the most time doing (sleeping, eating, swimming, watching TV,
etc.). Distribute the activity sheet to the students.
Explore:
Have the students individually create a table which shows how much time
they spend per day doing their summer activities. Make sure they are properly
making their hours into fractions, decimals, and percents on the worksheet.
Allow the stronger students to take it one more step to make a pie chart from
their data.
Share:
Let students share their typical summer day with their classmates. Look for
abnormalities in the data, and discuss whether these occurred because of a
calculation error or if they are correct and an unusual occurrence.
Summarize:
Make sure students are comfortable changing between fractions, decimals,
and percents. Look at the students’ pie charts and see if they’re properly labeled
so they’re easy to understand. Tell students that the sum of the percents or
fractions should be close to 100% or 1 because these are the activities they do the
most in the summer.
Day 14 “Order of Operations Bingo”
Objective: Students will review a concept covered earlier in the year, Order of
Operations, through a bingo game.
Standards Covered:
No.- 6.1.2.4
Benchmark - Use reasoning about multiplication and division to solve ratio and
rate problems.
Launch:
We will quickly review Order of Operations and PEMDAS, something we will
have covered earlier in the year. We will then do a couple of sample order of
operations problems so the students get accustomed to what they will be seeing
in the game. Finally, review how to play the game of bingo.
Explore:
Hand out bingo cards to the each student and let them pick which numbers
they want to use to fill in the empty spots. Next, put the problems on a projector
and have the students calculate the problem and fill in the numbers with markers.
Whoever gets a bingo first gets to yell bingo, but must tell how they got each
number on their card.
Share:
Ask the students if there were any strategies that helped them to win the
game, or if it just a game of luck. Let them explain why they feel the way they do,
but make them justify their answers.
Summarize:
Review PEMDAS with the students as well as any other concepts from the
unit students want to go over before tomorrow’s post-test.
Day 15 “Post Test”
Objective: Assess the students’ progress made during the unit on decimals,
fractions, and percents.
Launch:
Tell the students they will be taking a test similar to the pretest taken a few
weeks ago. It will measure how much they have learned about the topics we’ve
been covering.
Explore:
Allow the students to work independently on the post test. The post test
should take the majority of the hour.
Share:
When everyone has completed the test, let the students share with a
partner any problems that may have arisen on the test and let them discuss
solutions.
Summarize:
If any problems were troublesome for a majority of the class, discuss the
problem and find out any common errors.
Name ________________
Number Sense Pretest
1. Perform the following operations with decimal numbers.
a. 6.2 + 3.45=
b. 10.7 – 8.88=
c. 6.4 * 3.45=
d. 5.5 / 1.2=
2. Perform the following operations with fractions and mixed
numbers.
a. ½ + ¾=
b. 1 1/3 – 3/5=
c. 4/5 * 1/10=
d. 3 ¼ / 1 1/5=
3. Tell whether the following fractions are closest to the
benchmarks 0, ½, or 1.
a. 1/10 ________
b. 99/100 ________ c. 11/20 ________
d. 2/3 ________
e. 2/5 _________
f. 7/100 ________
4. Give the solution to each problem, using the order of
operations.
a. 5 + 3(4) / 6 =
b. 10 * 9 + (2 + 8) – 50=
5. Fill in the missing boxes in the table. Reduce fractions if you are
able to.
Fraction
Decimal
Percent
¼
40%
0.65
73%
7/20
6. Joe read in an article that approximately 10% of people in the
USA are left-handed. He decided to collect some data in his
class. He found that 4 out of 26 students in his class were lefthanded. Would you say that Joe’s class has more or less lefthanded people than average? Justify your answer.
7. The Senior Class is saving for their class trip. They have a candy
bar sale as a fund raiser. They are hoping to raise $800 in the
sale. After two days, they had raised $150. If they keep the
same pace of selling, about how long will it take them to reach
their goal? Justify your answer.
Name ________________
Number Sense Post-Test
1. Perform the following operations with decimal numbers.
a. 7.14 + 12.6=
b. 191.7 – 84.83=
c. 0.98 * 23.4=
d. 15.6 / 1.2=
2. Perform the following operations with fractions and mixed
numbers.
a. 2 ½ + 1 ¾ =
b. 5/12 – 1/3=
c. 4/9 * 2 3/10=
d. ¾ / 1/3 =
3. Tell whether the following fractions are closest to the
benchmarks 0, ½, or 1.
a. 5/12 ________
b. 95/100 ________ c. 112/200 ________
d. 1/5 ________
e. 3/8 _________
f. 2/100 ________
4. Give the solution to each problem, using the order of
operations.
a. 5 + 3*8 - 12 =
b. 12 * 3 + (10 – 5) * 15 / 3=
b. Fill in the missing boxes in the table. Reduce fractions if you are
able to.
Fraction
Decimal
Percent
2/5
48%
0.36
82%
9/20
c. Kevin Love made 78% of his free throws last season. During the
month of January, he made 67 out of his 83 free throws. Was he
a better or worse free throw shooter in January compared to last
season? Justify your answer.
d. The 8th grade Class is saving for their class trip. They have a
cookie sale as a fund raiser. They are hoping to raise $600 in the
sale. After two days, they had raised $75. If they keep the same
pace of selling, about how long will it take them to reach their
goal? Justify your answer.