6/11/2014
1.
RISING 6 TH GRADERS
MEA N I N G F U L MATH TASKS
June
Jo and Gina were arguing about the
magnitude of two numbers. Jo thought that
seven-hundredths was ten times bigger
than seven –tenths. Gina thought that
seven-tenths was ten times bigger than
seven-hundredths. Explain who was
correct. Use drawings/models to support
your answer.
2.
Emmett earns $12.58 each hour that he
babysits his brother. He works ten hours
each day. How much money dies Emmett
earn in one day? How much does he earn
after 100 days?
Justify your answer using drawings, equations, or words.
3.
The swimmers in
the chart competed
in the 2012
Summer Olympics.
Which swimmers
won the gold,
silver, and bronze
metals for the
fastest times?
Justify your
answers using
drawings, a
number line,
numbers or words.
Country
Swimmer
Time in
seconds
USA
Anthony Ervin
21.78
Brazil
Bruno Fratus
21.5
Italy
Florent Manaudou
21.34
Australia
Eamon Sullivan
21.98
Trinidad
George Bovell
South Africa Roland Schoeman
21.82
21.8
USA
Cullen Jones
21.54
Brazil
Cesar Cielo
21.59
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4.
Since gas is so expensive, Jen shops for the
best deal. Gas-N-Go charges $4.4469 per
gallon and Fast Fuel charges $4.2183. If Jen
needs 10 gallons of gas, how much would
Jen spend at each gas station? About how
much would she save by buying the less
expensive gas? Solutions should show exact amounts that
Jen would pay or save. Explain how you solved the problem using
drawings, number lines, or words.
5.
Micah was in a reading contest. He
read three days in a row. Each day he
read four times as long as the previous
day. If he read 3 minutes on day one,
how many minutes did he read in all?
Justify you answer.
6.
7.
Why is it important to use the order of
operations in the following expression?
[30 – (10+5)] ÷ 3
Create your own expression that
demonstrates that the order to perform
operations is often not the same way in
which they are written in the expression.
Without actually computing, determine if the
statements/expressions in each row are equivalent.
PEMDAS
3 times more than the sum of 18 and 37
Double 5 and then add 26. Divide the total by 4
3 x [(18+920)] ÷ 4]
2(10 x 5)
3(18+37)
2(5+26)÷ 4
3x18+920÷4
10 x 10
How did you decide if the statements/expressions were equivalent?
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8.
The average heart pumps about
693,500 gallons of blood through it
each year. How may gallons is that in
one month? One week? One day?
9.
Michael needs to sell 100 raffle tickets. On
Monday, he sold ¼ of his tickets. On
Tuesday, he sold ¼ of the remaining tickets.
How many tickets does Michael still need to
sell?
Justify your answer using drawings, models,
numbers or words.
Flip over for the rest of your June Problems.
10.
11.
Marty wants to determine how many square
feet of carpeting he needs to buy for his
living room, which measures 17 feet by 23
feet. However, when he tried to put his
measurements into his calculator, he noticed
the “7” key was broken! Is it possible for
Marty to still use his calculator to find the
amount of carpeting needed for his living
room? Explain your reasoning.
George is having a hard time solving
division problems, and he has asked you for
help. Teach George a useful strategy for
solving this division problem.
485 ÷ 4 =
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12.
The students at Gray’s Creek Middle School
were asked to bring treats to the fall festival.
Since Mary’s dad runs a donut shop, she
decided to bring enough donuts for each of
the 1,024 students in the school. One box
holds a dozen donuts, and Mary brought 84
boxes to school. Will she have enough
donuts to feed every student? Justify your
answer.
13.
Joni wants to make super fruity punch for a
party. If her punch bowl holds 3.21 liters of
liquid, will it be big enough to hold all of the
punch? Explain your answer.
Recipe
1.25 liters Lemon-lime soda
.6 liters Lemonade
.75 liters Lemon-lime sherbet
14.
15.
Lorraine was making pillows for her sofa.
She bought 1.2 pounds of stuffing to fill the
pillows. If she put .2 pounds of stuffing in
each pillow, how many pillows can she
make?
Jude built a wooden dog bed with
measurements of 1.5 meters by .9 meters
and found that the perimeter was too small
for his dog. He added .3 meters to each of
the .9 meter sides. What is the perimeter of
the old and new dog bed.
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16.
For a summer picnic, Ms. Moore baked a
pan of brownies that she cut into 8 equalsized pieces. Before she got to the picnic,
she noticed that ¼ of the pan was missing.
She figured out that her two boys each ate a
brownie. She then decided to taste test the
brownies and ate another 1/8 of the pan.
What fraction of the brownies has been
eaten and what fraction is left for the picnic?
17.
A tangram puzzle is made of
a square cut into seven shapes.
Cut out the pieces of your
tangram puzzle and determine
the fractional part of each piece.
Remember, the sum of the
fractional parts must equal one
whole tangram puzzle.
18.
RI SI N G 6 T H G RA D ERS
MEA N I N G F U L M A T H TA SK S
July
Mr. Mack threw a pizza party for his class.
He gave each table pizzas to share. Five
large pizzas were to be shared equally
among a table of eight students. Three large
pizzas were to be shared equally among a
table of six students. One student
complained that some students got a greater
share than those at other tables. Is the
student correct? Justify your answer.
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19.
20.
Six friends decide to chip in for the Crazy
Cookie Special. If each friend gets an equal
share of cookies, how many boxes will each
friend receive?
Seymour and Marta were having a
hamburger eating contest. Marta ate
four hamburgers. Seymour ate 7/8 the
amount that Marta did. Who won the
contest? Justify your answers.
Crazy Cookie Special
19 boxes for $10
21.
22.
Mike, Robbie, and Chip took turns jumping
on a pogo stick to see who could jump the
longest. Robbie jumped 3 ¼ times longer
than Mike. Chip jumped ¼ as long as Mike.
Who jumped for the longest amount of time?
Prove that your answer is correct.
Melvin planted a garden in his
backyard. Half of the garden was
vegetable. One third of the vegetables
were green beans. What fraction of the
whole garden was green beans?
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23.
Jenny made a giant piñata for her birthday
party. It took 8 bags of candy to fill the
piñata! If each bag weighed 1/3 of a pound,
how many pounds of candy were in Jenny’s
piñata?
25.
Brandi has six cups of lemonade to sell at her
lemonade stand. She needs to decide how much
lemonade to give each customer. If Brandi gives
each person a 2 cup serving, how many people
could she serve? How many people could she
serve if she gave half of that serving. Justify your
reasoning.
24.
Maggie wants to make scrambled eggs for
breakfast, but the only recipe she could find
serves 4 people. Help Maggie Adjust the
measurements so that it would be for one
serving.
Recipe
8 eggs
½ cup milk
1 cup of cheese
26.
A Middle School Class went on a field trip. At
lunch, they ordered a giant sub to share.
The students sat at four different tables, and
there were five students at each table. If
each table gets ¼ of the giant sub, how
much of the sub will each student get?
Explain your answer.
Flip over for the rest of your July Problems.
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27.
28.
Rebecca was celebrating her 11th birthday.
She invited 5 friends and together they ate
half of her birthday cake. If each person had
an equal share, how much cake did each
person eat?
Jo and Ty were asked to solve the
following question. How many 1/3 ft.
segments are in a 6 ft. piece of ribbon?
Explain your answer.
29.
30.
Carrie’s Candy Company is going to start
making and selling licorice. The company
must decide how to package their licorice.
Their packaging machine can cut and wrap
the licorice in meter, decimeter or centimeter
sized pieces. If a batch makes a 5.65 meter
long rope which packaging option will leave
the least amount of leftover licorice?
A teacher asked her students to bring in
containers that would hold liquid. Students
worked in groups to determine the capacity
of each container. These are their results.
4 cups
1 quart 4 pints
3 pints
3 quarts ¾ gallon 12 cups 2 pints
6 cups
½ quart What observations
can you make about the data?
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31.
32.
A teacher asked her students to bring in clay
for a project. The information below displays
the amount of clay (in pounds) each student
brought to class. If all the clay was lumped
together and then redistributed evenly, how
much clay would each child receive in
pounds? Pounds of clay: ¼, ¼, ½, ¾, ¾, 1,
1½,1½,2¾
Jay wants to fence in his garden. The
dimensions of the garden is 10 ft. by 20
ft. Lowes has fencing for sale at $3 a
foot. What would be the cost to fence in
Jay’s garden?
33.
34.
Mr. and Mrs. Smith are building a wall out of
bricks. They will need 450 bricks to finish the
wall. The bricks come on a pallet. Each layer
of the pallet holds 20 bricks. If the pallet is
15 layers tall, how many pallets will they
need? Draw a model and explain your
reasoning.
If this is an equilateral triangle with a
side measuring 6 inches in length, what
is the perimeter of this figure?
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35.
Rising 6th Graders
Meaningful Math Tasks
How many names can you think of for the
figure below? Explain why each of your
names fit.
AUGUST
36.
37.
Draw as many geometry figures as you can
and then create a Venn diagram to show
what they have in common and where they
differ.
Maxwell made a chart to help him
remember attributes of polygons.
Create your own chart and describe
why this could be a helpful tool.
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38.
39.
Plot three more points on the grid to
create a parallelogram and explain why
you chose those points.
Katie and Sammy were told to locate the
point (4,3) on a coordinate grid. Katie said, “
You must first move right on the x axis to 4,
and then move up on the y axis to 3.”
Sammy said, “No, you go up the y axis to 3,
and then go to the right on the x axis to 4.”
Who is right? Justify your thinking
40.
41.
Create a bar graph to represent the
following data, then explain how the graph
can help you understand the patterns.
Number of Animals Bird Legs Cat Legs
2
4
8
3
6
12
4
8
16
5
10
20
Jordan built a car in science class. He
measured the car’s speed. He found that the
car traveled 4 feet every two seconds.
Graph the car’s speed. What is the
relationship between the distance and
speed?
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42.
Mark was saving for a new mp3 player,
which costs $150. Mark makes $20 a
week for his allowance. If he saves half
his allowance each week, how long will
it take for Mark to save enough to buy
the mp3 player?
43.
Create a table graph to find the number of
squares needed to determine how many
squares will be in the 5th and 6th step of this
pattern.
Flip over for the rest of your August Problems.
44.
Ginny has incorrectly solved the following
problem.
364
X29
3276
+728
4004
What did she do wrong?
Why did this result in an incorrect answer?
What should Ginny have done differently?
45.
Examine the number 543,679.102. What is
the value of each digit in this number?
Round the number to the nearest hundredth.
Round the original number to the nearest
hundred thousand. Continue to round the
original number to each of the following
places: tenth, thousand, one, hundred, ten
thousand, and ten.
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46.
Examine the number 739.
What would happen to this number if you
multiplied it by 10?
What if you multiplied it by 100? 1,000?
What would happen to the number if you
divided it by 10? By 100? By 1000? What
patterns do you see? What happens to any
number when you multiply it or divide it by a
multiple of 10?
47.
The Sunny School Quiz Bowl team was having a
bake sale to raise money. They had 25 dozen
cookies to sell. After 3 hours, half of the cookies
had been sold. Then, a big client came and
bought 50 cookies. Write an expression to show
the sale of the cookies throughout the day. Your
expression should use brackets, parentheses, or
braces to show each step in the sale of the
cookies. How would the expression change if the
team had started with twice as many cookies at
the beginning of the day?
48.
49.
How are adding and subtracting decimals
like adding and subtracting whole numbers?
How are they different? Explain. Then
solve this…
Jenny has noticed that when you add and
subtract decimals, it is important to line up
the places. (The tenths places need to be
above each other, the ones places need to
be above each other, etc.) Why is this the
case?
Jonathan receives $12.50 in allowance from
his parents for doing his chores every week.
Each week, he saves half of it. How much
money does Jonathan have after 3.5
weeks?
At the end of 4 weeks, Jonathan wants to
buy some baseball cards that cost $6.75 a
pack. How many packs will he be able to
purchase?
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50.
51.
Suri was trying to decide if she should
have her birthday party at Bounce
Palace or Chuck E. Joe’s. Bounce
Palace will provide 3 pizzas for every 8
kids. Chuck E. Joe’s offers 2 pizzas for
every 5 kids. Which is the better deal?
Determine whether the following statements
are true or false.
Explain your response using words and
drawings.
All squares are rectangles.
All rectangles are squares.
A scalene triangle can be isosceles. An
isosceles triangle can be equilateral.
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