Mrs. Aitoro’s Bar Modeling Donut Challenge
The Challenge (Should You Choose to Accept It):
Earn a completed progress report for each of the four Thinking
Block Programs:
Addition & Subtraction Practice
Multiplication & Division Practice
Practice with Fractions
Ratio & Proportion Practice
Rules:
All four progress reports should be completed by the close of Q2.
(Date tentative due to potential snow days.)
Student should complete all of their Thinking Blocks practice in one format to
ensure their practice is saved (use a specific computer or a personal iPad).
Once a progress report has been completed, students should print the
certificate or save the iPad image. These should be kept safe by the student
until all four progress reports can be handed in.
Rewards:
At any point from today through the last day of Q2, Mrs. Aitoro will
buy a donut for every student the day after they can show proof of
completing all four program progress reports. Students get to request
the type of donut they would like.
Twins: Each twin should complete work on a particular program until completion. For example, Dave would
work on Addition & Subtraction Practice until he earned his progress report. At the same time, Dana could
work on Multiplication & Division. Once their progress reports are completed, they can be printed and the
twins can swap which programs they are working on.
Visit mrsaitoro.weebly.com to access the four Thinking Blocks websites. These same four websites are also
available as FREE apps for iPads.
Addition & Subtraction Practice
Part Whole Model – 2 Parts
1) If you add 9 to a mystery number, the sum will be 37. What is the mystery
number?
2) Doug won some money. He used $21 to buy a DVD player. He used the
remaining $26 to buy a radio. How much money had Doug won?
3) Matt had 33 blocks. His sister gave him 12 blocks. How many blocks did Matt
have then?
4) When Nova & Comet stand on a scale together, the scale reads 43 pounds.
Nova weighs 21 pounds. How many pounds does Comet weigh?
5) Blake won some money. He used $38 to buy a radio. He used the remaining
$10 to buy a CD. How much money had Blake won?
Addition & Subtraction Practice
Part Whole Model – 3 Parts
1) 43 students signed up for a writing class. There were 12 fifth grade students
and 20 sixth grade students. The rest of the students were in sixth grade. How
many sixth grade students signed up for the writing class?
2) Rachel has 31 balloons. 14 balloons are blue and 10 balloons are white. The
rest of the balloons are green. How many green balloons does Rachel have?
3) Claire bought a radio for $6. She also bought a science kit for $7. If Claire
had $26 at first, how much money did she have left?
4) Kiara counted her Halloween treats. She counted 21 mints and 9 gummies. She
also counted 8 chocolates. How many pieces of candy did Kiara have
altogether?
5) Kevin gave 11 gumballs to Lexi and 19 gumballs to Noah. If Kevin had 10
gumballs left, how many gumballs did he have at first?
Addition & Subtraction Practice
Change Model – 2 Parts
1) Kayla had 11 nickels. She found 24 nickels in her backpack. Kayla used 18
nickels to buy a cupcake. How many nickels did Kayla have then?
2) 45 children attended the school dance. 18 children left during the first hour.
20 children came during the second hour. How many children were at the
school dance then?
3) Blake saved $24. He then receive $6 for his birthday. Blake spent $14 at the
movies. How much money did Blake have then?
4) Danny had 27 hockey cards. He lost 14 cards at the park. Danny bought 28
cards at the store. How many cards did Danny have then?
5) Mrs. Johnson’s class borrowed 37 books from the library. They returned 30
books. Later, the class borrowed 23 new books. How many books did Mrs.
Johnson’s class have then?
Addition & Subtraction Practice
Comparision Model – 1 Step
1) The difference between two numbers is 20. If the bigger number is 46, what is
the smaller number?
2) Amy’s container weighs 34 ounces while Naomi’s container weighs 14 ounces.
How much less does Naomi’s container weigh than Amy’s container?
3) Sam’s rope is 9 centimeters longer than Maya’s rope. Maya’s rope is 33
centimeters long. What is the length of Sam’s rope?
4) Juan has 27 stickers and Drew has 38 stickers. How many more stickers does
Drew have than Juan?
5) Raven solved 22 math problems on Sunday. She solved 9 more problems than
that on Saturday. How many problems did Raven solve on Saturday?
Addition & Subtraction Practice
Comparison Model – 2 Steps
1) Nicole bought a CD and a game cube for $47. The game cube cost $33. How
much more did the game cube cost than the CD?
2) Will gave away 12 fewer marbles than Kyle. If Will gave away 15 marbles, what
was the total number of marbles given away?
3) Mason has 18 fewer magnets than Steve. If Mason has 7 magnets, how many
magnets do the two friends have altogether?
4) Tina bought a science kit and a CD player for $26. The CD player cost $17.
How much more did the CD player cost than the science kit?
5) Ella has 22 tunes on her iPod. She has 15 Justin Bieber tunes. The rest are
One Direction tunes. How many fewer One Direction tunes does Ella have?
Addition & Subtraction Practice
Comparison Model – 3 Quantities
1) John rode 16 miles in a bike-a-thon. Jesse rode 7 fewer miles than John but
4 more miles than Ashley. How many miles did they ride in all?
2) Robert, Mason, and Hunter have 60 toys altogether. Robert has 32 toys. Mason
has 13 fewer toys than Robert. How many more toys does Mason have than
Hunter?
3) Lily has 19 more marbles than Patrick. Patrick has 13 more marbles than Dana.
If Lily has 44 marbles, how many marbles do they have altogether?
4) Emily, Megan, and Greta spent $58 at the store. Emily spent $33. Megan spent
$16 less than Emily. How much more money did Megan spend than Greta?
5) Mrs. Chin counted 35 science fair supplies. There were 18 magnifiers and 6
more magnifiers than batteries. The rest of the supplies were prisms. How many
more batteries did Mrs. Chin have than prisms?
Multiplication & Division Practice
Find the Missing Product
1) Ricky donated his collection of adventure books to a local school. He packet 6
books into each of his 10 boxes. How many books did Ricky donate?
2) A Moon Rover can travel 10 feet in one second. How far can it travel in 9
seconds?
3) Maya cut a length of wood into 10 pieces. Each piece measured 6 centimeters.
What was the length of the wood before it was cut?
4) The Super Sleuths detective agency solves an average of 7 mysteries each
month. How many mysteries can the club solve in 9 months?
5) Mr. Nutmeg has 10 boxes of brownies. Each box contains 5 brownies. How
many brownies does Mr. Nutmeg have altogether?
Multiplication & Division Practice
Find the Missing Divisor or Quotient
1) 40 fourth graders are going on a field trip to the art museum. Each bux can
carry 8 students. How many buses will be needed?
2) Steve lives to read fantasy stories. His new book is 21 pages long. Steve wants
to finish the book in 3 days. How many pages should Steve read each day in
order to reach his goal?
3) 8 members of the soccer team shared the cost of lunch at the Food Factory.
The bill came to $96. How much money did each person pay?
4) When the Hog Wild Restaurant checked its food inventory at the end of the
month, it had 54 pounds of apples. How many days will the apples last if 6
pounds of apples are used each day?
5) Space cadets on Planet Algebra are required to travel in groups of 11 during
intergalactic space flights. The cadets use space mobiles to get around the
galaxy. How many space mobiles would be needed for a class of 66 cadets?
Multiplication & Division Practice
Compare Quantities – One Step Model
1) Zoey’s poster is 3 times longer than Morgan’s poster. If it takes 9 paperclips to
measure Zoey’s poster, how many paperclips would it take to measure
Morgan’s poster?
2) Lily has 28 lollipops. Lauren has half as many lollipops as Liliy. How many
lollipops does Lauren have?
3) Oliver has 4 times as many toys as Taylor. If Oliver has 32 toys, how many
toys does Taylor have?
4) Weak Willy can only do 8 push-ups. Nimble Nina can do 7 times as many
push-ups as Weak Willy. How many push-ups can Nimble Nina do?
5) A Whiz Car costs 6 times as much as a Sun Racer. If a Whiz Car costs $72,
how much does a Sun Racer cost?
Multiplication & Division Practice
Compare Quantities – Two Step Model
1) Clay and Will sold a total of 96 candy bars to help raise money for the
school band. Clay sold 7 times as many candy bars as Will. How many fewer
candy bars did Will sell than Clay?
2) Maddie has 5 times as many lollipops as Morgan. Together they have 66
lollipops. How many lollipops does Maddie have?
3) 24 students voted for their favorite afternoon snack – pretzels or muffins.
There were 7 times as many votes for pretzels as for muffins. How many fewer
students voted for muffins?
4) Riley the Robot completed 5 times as many space missions as Astronaut Ben.
Riley completed a total of 15 space missions. How many more space missions
has Riley completed than Ben?
5) Joe’s Clothes sold 12 green jackets on Friday. The store sold twice as many
black jackets as green ones. How many jackets were sold altogether?
Multiplication & Division Practice
More than One Operation
1) Danny had some money when he entered Great Buy. After buying 7 identical
robots costing $4 each, Danny had $13 left. How much money did Danny have
at first?
2) 97 students are attending Physical Fitness Day. Each of the 7 scavenger hunt
teams have 10 students. The rest of the students are watching the teams play.
How many students are watching?
3) Emma had 28 sport cards in her collection. She decided to keep 8 sport cards
and share the rest evenly among her 4 siblings. How many sports cards did
each sibling get?
4) Sean read 8 pages of his detective book every day. After reading for 7 days,
Sean still had 26 pages left. How many pages are in Sean’s detective book?
5) Chef Tracy had 40 cups of flour. She used 12 cups of flour to make cupcakes
and still had enough to make 4 batches of muffins. How many cups of flour
are needed for each batch?
Multiplication & Division Practice
Compare Three Quantities
1) Corey, Jake, and Kayla shared 48 nickels. Corey received 4 times as many
nickels as Jake. Kayla received 3 times as many nickels as Jake. How many
more nickels did Corey receive than Jake?
2) Evan purchased prizes for the school carnival. There were 5 times as many
pinwheels as super balls and 4 times as many keychains as super balls. Evan
counted 25 pinwheels. How many prizes did Evan purchase in all?
3) Terry has 4 times as much money as Haley. Karen has twice as much money
as Haley. Altogether, they have $21. How much money does Terry have?
4) Mary has 4 times as many stickers as Haley. Monica has 5 times as many
stickers as Haley. If Monica has 50 stickers, how many stickers do they have
altogether?
5) Oliver sold 9 times as many candy bars as Nicole. Griffin sold twice as many
candy bars as Nicole. Altogether, they sold 96 candy bars. How many candy bars
did Oliver sell?
Practice with Fractions
Find a Fraction of a Number
1) Car Care had 30 customers today. ⅖ of the customers came in for a tire
rotation. The rest came in for a tune-up. How many customers came to the
shop for a tune-up?
2) The sixth grade class decorated the school gym with 12 purple and white
balloons. 2/3 of the balloons were purple. How many balloons were white?
3) 49 sixth graders were invited to test two new computer games. 2/7 of the
students preferred Astro-Bots. The others preferred Space Pals. How many
students preferred Astro-Bots?
4) Jay is riding his bicycle 12 miles from Digitopolis to Vertex Valley. He has
completed ⅓ of his trip. How many miles must Jay ride until he reaches his
destination?
5) My puppy, Milkshake, dug 20 holes in the yard. ⅘ of the holes were in the
front yard. The rest were out back. How many holes had Astro dug in the back
yard?
Practice with Fractions
Find the Total or Part
1) ⅚ of the children at the track meet were girls. There were 9 boys. How many
girls attended the track meet?
2) Jada is played a game of Cosmic Blobs. She located 5/7 of the widgets she
needs to find in order to win the game. There were 20 widgets remaining. How
many widgets had she found?
3) ⅗ of my marbles are white. I have 33 white marbles. How many marbles do I
have altogether?
4) Mrs. Martin, the science coach, poured 84 ounces of water into a container.
The container was then 7/9 full. What was the capacity of the container?
5) Morgan has a collection of marbles. After giving ¾ of her marbles to her
friend, she had 4 marbles left. How many marbles did Morgan give to her
friend?
Practice with Fractions
Add Fractions with Like Denominators
1) Lily spent 3/6 of her allowance on a t-shirt and 1/6 of her allowance on a
board game. What fraction of her allowance did Lily spend altogether?
2) Samantha rode in a bike-a-thon. She completed 7/1 of the distance before
lunch. She continued riding and by the end of the day Samantha had
completed 8/11 of the distance. What fraction of the distance did Samantha
complete after lunch?
3) Ben and Ella played their favorite game, Lotsa Money. Ben won 8/11 of the
games. Ella won 1/11 of the games. The rest of the games ended in a tie.
What fraction of the games that were played had a winner?
4) Justin ate 1/6 of the pizza and Max ate 3/6 of the pizza. What fraction of the
pizza did the boys eat together?
5) Evan bought 7/10 pound of fruit. He ate 6/10 pound after dinner. How much
fruit does he have left?
Practice with Fractions
Add Fractions with Unlike Denominators
1) Mark bought ½ pound of chocolate and 1/7 pound of lollipops. How much
candy did he buy altogether?
2) The distance from Oliver’s house to the tennis court is 9/10 mile. He rode ½
mile, then he stopped to help a neighbor. How far does Oliver have left to
travel?
3) Cool Desserts has ¾ gallon of chocolate ice cream. ½ gallon was used to
make sundaes. How much chocolate ice cream was left?
4) Tyler traveled from his house to the candy shop. He walked ½ mile and then
ran 1/6 of a mile. Har far did Tyler travel from his house to the candy shop.
5) Tori purchased some string at the store. She used ½ meter in her Girl Scout
project and 3/8 meter in her art project. How many meters did Tori use in
both projects?
Practice with Fractions
Multiply & Divide Fractions
1) Miguel purchased ¾ pound of chocolate. He ate 1/3 of his stash after lunch.
How much chocolate did Miguel eat?
2) Peter bought 3/7 gallon of paint. He used ½ of it to paint the boat. How
much did Peter use?
3) 2 packages of lollipops weigh 5/6 pound. What is the weight of 1 package?
4) Marissa has a piece of elastic that measures 1/3 meter. She used 1/3 of it to
sew herself a skirt. What is the length of elastic that Marissa used?
5) Diana purchased 4/5 pound of licorice. She placed an equal amount of licorice
into 2 snack bags. What was the weight of the licorice in each snack bag?
Practice with Fractions
Work with a Fraction of a Remainder
1) John saved 1/3 of his paycheck and spent 1/3 of the remaining money. He
was left with $8. What was the original value of John’s paycheck?
2) Mrs. Molasses prepared a variety of cookies. 3/5 of the cookies were peanut
butter and 1/3 of the remaining cookies were gingerbread. There were 8
chocolate chip cookies. How many cookies did Mrs. Molasses prepare
altogether?
3) I traveled from Fairfield to Hartford last week. I completed 1/3 of the journey
in the morning and 1/5 of the remaining distance in the afternoon. I still had
16 miles to travel. What is the distance from Fairfield to Hartford?
4) I had $15 in my wallet. I spent 1/3 of the money on Wednesday and 1/5 of
the remainder on Saturday. How much money did I have left?
5) Claudio is played Alien II on his computer. He finished ½ of the levels last
week and ½ of the remaining levels this week. He had 4 more levels to
complete. How many levels does Alien II have?
Ratio & Proportion Practice
Find the Missing Quantity
1) Amy made some trail mix by combining pretzels and granola in a 4:5 ratio.
Amy used 16 ounces of pretzels. How many ounces of granola were used?
2) The ratio of the number of Clay’s postcards to the number of Hope’s
postcards is 3:4. If Hope has 44 postcards, how many postcards does Clay
have?
3) Sam created a new energy drink by mixing 2 parts papaya juice with 3 parts
kiwi juice. Sam used 8 ounces of papaya juice. How many ounces of kiwi juice
would be needed?
4) Ben and Angela shared some markers in the ratio 8:3. If Angela had 21
markers, how many markers did Ben have?
5) The ratio of boys to girls in Mrs. Santiago’s class is 4:3. If there are 36 girls,
how many boys are in the class?
Ratio & Proportion Practice
Find the Total or Difference
1) The ratio of Jacob’s pennies to Diego’s pennies is 3:4. If Diego has 24 pennies,
how many pennies do they have altogether?
2) For every 3 push-ups Hope does, Morgan does 2. If Hope did 24 push-ups,
how many more push-ups did Hope do than Morgan?
3) Eric and Troy won first and second place in the spelling bee. They had to split
the cash prize in the ratio 5:4. Eric received $30. How much more money did
Eric receive than Troy?
4) Molly downloaded Glee songs and American Idol songs to her computer in the
ratio 3:7. She had 18 Glee songs. How many more American Idol songs does
Molly have?
5) For every 4 hats that Oliver sold, Will sold 3. Oliver sold 32 hats last month.
How many hats did they sell in all?
Ratio & Proportion Practice
Use the Total or Difference to Find a Quantity
1) The sum of two numbers is 28. The ratio of the bigger number to the smaller
number is 4:3. What is the smaller number?
2) Kiara has a total of 110 songs on her new iPod. The ratio of Selena Gomez to
Justin Bieber is 9:2. How many Selena Gomez songs does she have?
3) The ratio of the number of Diego’s markers to the number of Ashley’s markers
is 2:3. Together, they have 45 markers. How many markers does Diego have?
4) During the holiday sale, Save at Gabe’s sold DVDs and books in the ratio 2:5.
The store sold 18 more books than DVDs. How many books were sold?
5) The ratio of the weight of Justin’s backpack to the weight of Rachel’s backpack
is 2:5. Rachel’s backpack weighs 12 more ounces than Justin’s backpack. How
much does Rachel’s backpack weigh?
Ratio & Proportion Practice
With with Part:Total Ratios
1) Justin built a gaming website. The website had 42 visitors on Saturday. 3 out
of every 7 visitors played Space Pats. The other visitors played Galactic Gamer.
How many visitors played Galactic Gamer?
2) Mrs. AItoro’s class conducted a survey about pets. According to the survey, 2
out of 5 students do not have a pet. There are 12 students who have at least
one pet at home. How many students participated in the survey?
3) For every 11 games the Red Sox played, the team won 6 of them. If they won
9 more games than they lost, how many games did they win?
4) Adam and Scott took turns driving to New York City. Adam drove 4 out of
every 7 miles traveled. By the time they reached New York City, Scott had
driver 3 fewer miles than Adam. How many miles did Adam drive?
5) 8 out of 15 students selected Mr. Clapp for the teacher of the year award. The
other students selected Miss. Steeves. If Mr. Clapp won by 9 votes, how many
votes did Mr. Clapp receive?
Ratio & Proportion Practice
Work with Ratios that Compare Three Quantities
1) Griffin, Oliver, and Jason ran a web design business during school vacation.
They had $110 in one day and decided it would be fair to share the money in
the ratio 2:4:5. How much more money did Jason get than Oliver?
2) Three numbers A, B, and C are in the ratio 8:3:1. The sum of the numbers is
96. What is the value of Number A?
3) Comet, Astro, and Pepper are puppies. The ratio of Comet’s weight to Astro’s
weight is 5:4. The ratio of Astro’s weight to Pepper’s weight is 4:3. Comet
weighs 50 pounds. How much do they weight altogether?
4) Emma found a bag filled with coins. It contained nickels, pennies, and half
dollars in the ratio 1:2:4. There were 28 coins in the bag. How many half
dollars did she find?
5) A board is painted yellow, black, and gray in the ratio 5:3:2. The section of the
board that is painted yellow is 40 inches long. What is the length of the
board?
Ratio & Proportion Practice
Apply Ratios to More Challenging Problems
1) Riley had 1/6 as many sports cards as Justin. When Justin gave half of his
sports cards to Riley, he had 3 fewer sports cards than his friend. How many
sports cards did Justin have at first?
2) Nina had 1/7 as many cakes to sell as Belle. The two friends decided to
share the work evenly. To do that, Belle had to give 15 cakes to Nina. What
was the total number of cakes the two friends had to sell?
3) The ratio of Chloe’s magnets to Jada’s magnets was 7:3. When Chloe gave 12
magnets to Jada, they each had the same amount. How many magnets did
they have altogether?
4) The computer club had ¾ as many members as the drama club. After half the
drama club members left to join the computer club, the computer club had 27
more members than the drama club. How many members did the drama club
have at first?
5) Paul and Jada have been playing a game called Planet Zak. Paul earned 1/9
as many points as Jada. When Jada donated 32 points to Paul, they each had
the same amount. How many points did the two friends have altogether?