Gemma 2B on 3.OA.C.7
Common Core Standard 3.OA.C.7
This standard covers the following:
Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
Problem: On a slide, for each 1 meter of sliding, Isaac gains 3 times the speed. If Isaac slides down 1 meter, how much speed does he gain?
Gemma 2B:
Reasoning: If Isaac gains 3 times the speed on 1 meter, then on 1 meter, he gains 3 * 1 = <<3>> times the speed. Therefore, if Isaac slides down 1 meter, he gains 3 * 1 = <<3>> times the speed. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: In light of the original problem, suppose for each 1 meter of sliding, Isaac now gains 5 times the speed instead of 3 times the speed. In this case, how much speed does he gain after sliding 1 meter?
Gemma 2B:
Reasoning: If Isaac gains 5 times the speed on 1 meter, then on 1 meter, he gains 5 * 1 = <<5>> times the speed. Therefore, if Isaac slides down 1 meter, he gains 5 * 1 = <<5>> times the speed. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: In the forest, for every 9 brown bears there are 11 times as many black bears. If there are 9 brown bears, how many black bears are there in the forest?
Gemma 2B:
Reasoning: There are 9 x 11 = <<9x11=99>> black bears in the forest. ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: In a particular pond, there are 7 fish. If each fish has 2 sides, how many fish sides are there in total in the pond?
Gemma 2B:
Reasoning: Each fish has 2 sides, so there are 7 fish x 2 sides/fish = <<7 fish x 2 sides/fish=14 sides>>14 sides in the pond. ### Answer: 14
Expected answer: 14
Correct? Yes
Problem: In an experiment, it is determined that the fuel needed for a rocket is a product of the mass of that rocket and 12. If the mass of the rocket is 8, how much fuel is needed for the rocket?
Gemma 2B:
Reasoning: The fuel needed is 8 * 12 = <<8*12=96>>96. ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: In a further experiment, a third rocket with the same mass of 8 is tested, but this time it is equipped with an improved fuel system that requires less fuel. Now, this rocket requires only 5 units of fuel per mass. How much fuel is this third rocket going to need?
Gemma 2B:
### Answer: 80
Expected answer: 40
Correct? No
Problem: Theresa planted 80 flower seeds evenly among 10 plots. This means each plot received a certain amount of flower seeds. If she later planted an extra plot with the same amount of seeds as in each of the previous plots, how many seeds did she use for the extra plot?
Gemma 2B:
Reasoning: Each plot received 80/10 = <<80/10=8>>8 seeds. The extra plot received 8 seeds. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: In addition to planting seeds in the plots, Theresa wanted to give 7 gift bags each containing as many seeds as the number she planted in each plot. How many seeds should Theresa set aside for the gift bags?
Gemma 2B:
Reasoning: Each plot received 8 seeds, so each gift bag should contain 8 seeds. Therefore, Theresa should set aside 8 seeds for each gift bag. ### Answer: 8
Expected answer: 56
Correct? No
Problem: In a change of plans, Theresa divided the 80 seeds evenly between only 2 plots instead of 10. This meant each plot now received a different number of seeds than before. If she later planted an extra plot with the same amount of seeds as in each of the new plots, how many seeds did she use for the extra plot?
Gemma 2B:
Reasoning: Each plot received 80/2 = <<80/2=40>>40 seeds. The extra plot received 40 seeds. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: A dress needs 1 yard of fabric for 1 section. How many yards of fabric are needed to make that section of the dress?
Gemma 2B:
Reasoning: The dress needs 1 yard of fabric for 1 section. Therefore, the number of yards of fabric needed to make the entire dress is equal to the number of sections in the dress, which is 1. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Going back to the first part of the previous problem, suppose that each section of the dress actually requires 6 yards of fabric instead of 1. How many yards of fabric are needed for one section of the dress in this case?
Gemma 2B:
Reasoning: Each section of the dress would then require 6 yards of fabric instead of 1. Therefore, the number of yards of fabric needed to make the entire dress would be equal to the number of sections in the dress, which is 1. ### Answer: 1
Expected answer: 6
Correct? No
Problem: Captain Blackbeard buries 11 treasure chests in a secret underground cave. To keep the treasure safe, he creates a magical spell that triples the amount of treasure chests inside the cave. How many treasure chests will be in the cave after the spell is cast?
Gemma 2B:
Reasoning: After the spell is cast, there are 11 * 3 = <<11*3=33>>33 treasure chests in the cave. ### Answer: 33
Expected answer: 33
Correct? Yes
Problem: Remembering his magical spell, Captain Blackbeard starts to second guess himself. What if his magical spell had only doubled the amount of treasure chests instead of tripling? How many treasure chests would be in the cave in that case, after the spell is cast?
Gemma 2B:
Reasoning: If the spell had only doubled the amount of treasure chests, there would be 11 * 2 = <<11*2=22>>22 treasure chests in the cave after the spell is cast. ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: If a baby giraffe grows by 4 feet every year, how tall would the giraffe be after 11 years?
Gemma 2B:
Reasoning: The baby giraffe will be 4 feet + 11 * 4 = <<4+44=48>>48 inches tall after 11 years. ### Answer: 48
Expected answer: 44
Correct? No
Problem: Pete has 4 pieces of rope. If each piece of rope is 8 feet long, how many feet of rope does Pete have in total?
Gemma 2B:
Reasoning: Pete has 4 pieces of rope each of which is 8 feet long. So, Pete has 4 * 8 = <<4 * 8=32>>32 feet of rope in total. ### Answer: 32
Expected answer: 32
Correct? Yes
Problem: After examining his ropes, Pete figures out that he needs to use all of his rope for a project. If he combines all 4 pieces of his 8 foot long ropes, how many feet of rope will he have for his project?
Gemma 2B:
### Answer: 32
Expected answer: 32
Correct? Yes
Problem: Upon rechecking his inventory, Pete realizes he actually has 12 pieces of rope not 4. If each of these 12 ropes are 8 feet each, how much total length of rope does Pete have now?
Gemma 2B:
### Answer: 12 * 8 = <<12 * 8=96>>96 feet
Expected answer: 96
Correct? Yes
Problem: In the Marine Institute, there are 81 starfish. If these starfish are equally distributed in 9 tanks, how many starfish will be placed in each tank?
Gemma 2B:
Reasoning: Each tank will have 81/9 = <<81/9=9>>9 starfish. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: Earlier, we learned the Marine Institute distributed 81 starfish equally across 9 tanks. But what if they had only 12 starfish instead? How many starfish would equal distribution across the 9 tanks result in then?
Gemma 2B:
Reasoning: If there were only 12 starfish, each tank would have 12/9 = <<12/9=1.33>>1.33 starfish. ### Answer: 1.33
Expected answer: 4/3
Correct? No
Problem: In a sandbox, Lisa found a toy. If she finds twice as many toys every next day, how many toys will she find on the second day?
Gemma 2B:
Reasoning: If Lisa finds twice as many toys every next day, then on the second day, she will find 2 * 4 = <<2*4=8>>8 toys. Lisa will find 8 toys on the second day.
Expected answer: 2
Correct? Yes
Problem: After finding toys in the sandbox for two days, Lisa decides to bury and later dig up the exact square of the number of toys she found on the second day. How many toys will Lisa bury and dig up if she follows this plan?
Gemma 2B:
### Answer: 16
Expected answer: 4
Correct? No
Problem: Instead of finding twice as many toys as the previous day, Lisa now finds ten times as many toys as the previous day. How many toys will she find on the second day following this new rule?
Gemma 2B:
### Answer: 80
Expected answer: 10
Correct? No
Problem: A robot can process information in 11 microseconds, but it has to be divided by 11 to match the system's speed. How quickly can the robot process information to match the system's speed?
Gemma 2B:
Reasoning: The robot can process information in 11 microseconds. The system's speed is not specified in the context, so we cannot calculate the robot's processing speed. ### Answer: The context does not specify the robot's processing speed.
Expected answer: 1
Correct? No
Problem: Each tomato seed will produce 3 tomatoes. If Nina plants 6 tomato seeds, how many tomatoes will she produce in total?
Gemma 2B:
Reasoning: Each seed will produce 3 tomatoes, so 6 seeds will produce 3*6 = <<3*6=18>>18 tomatoes in total. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Each of these tomatoes will produce 3 new seeds of its own. Using all the seeds from the tomatoes that Nina grows, how many new tomato plants could she potentially grow?
Gemma 2B:
### Answer: 36
Expected answer: 54
Correct? No
Problem: An alien is learning the human language. For every human word, they can transmit it to their spaceship 11 times per minute. How many words will the alien be able to transmit after 1 minute if they learn a new word?
Gemma 2B:
Reasoning: The alien can transmit 11 words per minute, so after 1 minute, they can transmit 11 words. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: In the above problem, the alien learned another new word. If they transmit each word 11 times per minute and the alien can now transmit two words, how many transmissions will the alien be able to make after 1 minute?
Gemma 2B:
### Answer: 22
Expected answer: 22
Correct? Yes
Problem: In the previous problem, instead of transmitting each word 11 times per minute, suppose the alien can only transmit each word 3 times per minute. How many transmissions will the alien be able to make after 1 minute if they learn a new word?
Gemma 2B:
Reasoning: The alien can transmit 3 words per minute, so after 1 minute, they can transmit 3 words. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: A unicorn travels 35 miles over 7 hours. How many miles does the unicorn travel in one hour?
Gemma 2B:
Reasoning: The unicorn travels 35 ÷ 7 = <<35 ÷ 7=5>>5 miles in one hour. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: If the unicorn maintains the same speed, how many miles would it travel in 3 hours?
Gemma 2B:
### Answer: 150
Expected answer: 15
Correct? No
Problem: If instead the unicorn traveled 35 miles in 2 hours, how many miles would the unicorn travel in one hour?
Gemma 2B:
Reasoning: If the unicorn traveled 35 ÷ 2 = <<35 ÷ 2=17.5>>17.5 miles in 2 hours, then in one hour it would travel 17.5 ÷ 2 = <<17.5 ÷ 2=8.75>>8.75 miles. ### Answer: 8.75
Expected answer: 35/2
Correct? No
Problem: Superhero Green Gauntlet has the ability to multiply his strength by a factor of 3. If Jetstream, another superhero, has 5 times the strength of Green Gauntlet, what is the strength of Jetstream?
Gemma 2B:
Reasoning: Jetstream's strength = 5 * Green Gauntlet's strength = 5 * <<Green Gauntlet's strength>> = 5 * <<48>> = 240. ### Answer: 240
Expected answer: 15
Correct? No
Problem: Jason is stringing beads onto a necklace. If each necklace requires 6 beads, how many beads will be needed to make 1 necklace?
Gemma 2B:
Reasoning: Each necklace requires 6 beads, so 1 necklace requires 6 beads. Therefore, 1 necklace will need 6 beads. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: Jason had made one necklace requiring 6 beads, but now he wants to make a total of 3 necklaces. How many beads will he need in total to make these 3 necklaces?
Gemma 2B:
Reasoning: To make 3 necklaces, Jason will need 3 * 6 = <<3 * 6=18>>18 beads. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: In the original problem, Jason made one necklace using 6 beads. But what if he wanted to use a new design that requires 8 times as many beads as his original design? How many beads would Jason need to create this new necklace?
Gemma 2B:
Reasoning: If Jason's original design required 6 beads, then his new design requires 8 * 6 = <<8*6=48>>48 beads. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: A puzzle box indicates that you need to multiply 2 by 3 to unlock it. What is the unlock code for the puzzle box?
Gemma 2B:
Reasoning: The unlock code for the puzzle box is 6. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: After successfully unlocking the puzzle box with the code obtained by multiplying 2 by 3, a new challenge appears on the screen inside the box. It tells you to multiply the previous code by 12 to get the final secret code to complete the puzzle. What is the final code?
Gemma 2B:
### Answer: 72
Expected answer: 72
Correct? Yes
Problem: After completing the previous challenge, another puzzle appears on the next screen inside the box. It instructs you to multiply 2 by 7 instead of 3. What number will you get by following this new instruction for the puzzle?
Gemma 2B:
### Answer: 14
Expected answer: 14
Correct? Yes
Problem: Peter has 6 different wallets and in each wallet, he has 9 dollars. If he stacks all the money in one wallet, how much money will be in that wallet?
Gemma 2B:
Reasoning: If Peter has 6 wallets, each with 9 dollars, then the total money in all the wallets is 6 * 9 = <<6*9=54>>54 dollars. ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: If Peter then puts all of the money from the one wallet into a piggy bank, how much money will be in the piggy bank?
Gemma 2B:
Reasoning: If Peter puts 9 dollars from each wallet into a piggy bank, then he will have 6 * 9 = <<6*9=54>>54 dollars in the piggy bank. ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: If Peter originally had 12 dollars in each of the 6 wallets instead of 9, how much money would be in the one wallet then?
Gemma 2B:
Reasoning: If Peter originally had 12 dollars in each of the 6 wallets, then the total money in all the wallets would be 6 * 12 = <<6*12=72>>72 dollars. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: A butterfly flaps its wings 9 times in one second. How many times does it flap its wings in 11 seconds?
Gemma 2B:
Reasoning: A butterfly flaps its wings 9 times in 1 second. Therefore, it flaps 9 * 11 = <<9*11=99>> times in 11 seconds. ### Answer: 99
Expected answer: 99
Correct? Yes
Problem: Now consider that the butterfly only flaps its wings 9 times in one second. How many times would it flap its wings in 4 seconds?
Gemma 2B:
### Answer: 36
Expected answer: 36
Correct? Yes
Problem: A plane travels at a constant speed of 12 miles per minute. How many miles would the plane cover in 6 minutes?
Gemma 2B:
Reasoning: The plane covers 12 x 6 = <<12 x 6=72>> miles in 6 minutes. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: If the plane's speed was instead 11 miles per minute, how many miles would the plane cover in the same time period of 6 minutes?
Gemma 2B:
### Answer: 60
Expected answer: 66
Correct? No
Problem: Josephine has 27 pairs of ice skates and wants to divide them equally among the 9 stores where she works. How many pairs of ice skates will each store receive?
Gemma 2B:
Reasoning: Josephine can divide 27 by 9 = <<27 ÷ 9 = 3>>3 pairs of ice skates for each store. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: In a different scenario, Josephine originally had 9 pairs of ice skates instead of 27 that she wanted to distribute equally among the 9 stores. How many pairs of ice skates would each store receive in this case?
Gemma 2B:
Reasoning: Josephine can divide 9 by 9 = <<9 ÷ 9 = 1>>1 pair of ice skates for each store. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Each soap factory produces 7 bars of soap every hour. If a factory remains operational for 11 hours, how many bars of soap are produced?
Gemma 2B:
Reasoning: The factory produces 7 bars/hour x 11 hours = <<7 bars/hour x 11 hours=77>>77 bars of soap. ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: Billy has 9 sets of kite with each set containing 3 kites. How many kites does he have in total?
Gemma 2B:
Reasoning: Billy has 9 sets of 3 kites each, so he has 9 * 3 = <<9*3=27>>27 kites in total. ### Answer: 27
Expected answer: 27
Correct? Yes
Problem: Billy decides to double his collection of kites. After doubling the initial amount, how many kites will he have in total?
Gemma 2B:
### Answer: 54
Expected answer: 54
Correct? Yes
Problem: Billy initially thought he had 9 sets of kites, but he actually had 11 sets. Given that each set contains 9 kites, how many kites does he really have in total?
Gemma 2B:
### Answer: 11
Expected answer: 99
Correct? No
Problem: In a fairy tale, a magical creature multiplies a number by itself and gets an outcome. If the magical creature uses the number 4, what will be the outcome?
Gemma 2B:
Answer: 4 Reasoning: 4 multiplied by itself is 4 * 4 = <<4*4=16>>16.
Expected answer: 16
Correct? No
Problem: There are 27 chairs and they need to be equally distributed among 3 rooms. How many chairs will each room have?
Gemma 2B:
Reasoning: Each room will have 9 chairs. ### Answer: 9
Expected answer: 9
Correct? Yes
Problem: At first, there were 12 rooms instead of 3 to distribute the 27 chairs into. How many chairs would each room have in this case?
Gemma 2B:
### Answer: 3
Expected answer: 9/4
Correct? No
Problem: A store stocks 56 toy cars uniformly over 8 shelves. How many toy cars are there per shelf?
Gemma 2B:
Reasoning: Each shelf has 56/8 = <<56/8=7>>7 toy cars. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: Now, imagine if the store decided to stock only one toy car per shelf instead, distributing 8 toy cars uniformly over 8 shelves. How many toy cars would be there per shelf?
Gemma 2B:
### Answer: 8
Expected answer: 1
Correct? No
Problem: In a restaurant, every pizza slice takes 6 minutes to cook and a full pizza has 3 slices. If the restaurant wants to make 3 full pizzas, how long will it take in total?
Gemma 2B:
Reasoning: 3 full pizzas x 6 minutes/slice = <<3 pizzas x 6 minutes/slice=18 minutes>>18 minutes. ### Answer: 18
Expected answer: 54
Correct? No
Problem: Arthur drives his car 7 hours each day for 4 days. How many total hours did Arthur spend driving his car over this period?
Gemma 2B:
Reasoning: Arthur drove 7 hours/day x 4 days = <<7 hours/day x 4 days=28 hours>>28 hours. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: Considering the previous problem, what if Arthur only drove his car for 2 hours each day for that same 4-day period? How many total hours did Arthur spend driving his car over this period?
Gemma 2B:
### Answer: 2 hours
Expected answer: 8
Correct? No
Problem: If each blanket requires 6 yards of yarn for one section, and each finished blanket is made up of 5 such sections, how many yards of yarn do you need to create one blanket?
Gemma 2B:
Reasoning: Each blanket requires 6/5 = <<6/5=12>>12 yards of yarn. ### Answer: 12
Expected answer: 30
Correct? No
Problem: A bus travels at a speed of 7 miles per hour. How many miles will the bus travel after 6 hours?
Gemma 2B:
Reasoning: The bus will travel 7 * 6 = <<7*6=42>>42 miles after 6 hours. ### Answer: 42
Expected answer: 42
Correct? Yes
Problem: Following the previous scenario, consider that the bus was actually traveling at a speed of 10 miles per hour, not 7. How many miles would the bus have travelled after 6 hours in this case?
Gemma 2B:
### Answer: 60
Expected answer: 60
Correct? Yes
Problem: Superhero Starlight has a power level that is the product of multiplying 3 by 5. What is Starlight's power level?
Gemma 2B:
Reasoning: Starlight's power level = 3 * 5 = <<3*5=15>>15. ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: Superhero Starlight, after completing her special power-up training, can now increase her initial power level by three times. If her initial power level was the product of multiplying 3 by 5, what is her new power level after the power-up training?
Gemma 2B:
### Answer: 45
Expected answer: 45
Correct? Yes
Problem: Considering that Superhero Starlight initially had a power level that was the product of multiplying 3 by 5, let's imagine if her initial power level was actually the product of multiplying 3 by 6. What would her initial power level be in this scenario?
Gemma 2B:
### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Jessica has a backpack that when you measure one side, is 10 inches long. What is the area of one side of Jessica's backpack assuming it is a perfect square?
Gemma 2B:
Reasoning: The area of a square is calculated by squaring the length of one side. 10 inches = 10 inches, so the area of one side of Jessica's backpack is 10 inches x 10 inches = <<10x10=100>>100 square inches.
Expected answer: 100
Correct? Yes
Problem: Captain Sparrow found 36 gold doubloons. He wants to divide it equally among his 3 crew members. How many gold doubloons will each crew member get?
Gemma 2B:
Reasoning: Each crew member will get 36 ÷ 3 = <<36 ÷ 3=12>>12 gold doubloons. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: Suppose Captain Sparrow had initially found 36 gold doubloons, but this time he wants to divide them equally among 7 crew members, not 3. How many gold doubloons will each crew member get now?
Gemma 2B:
Reasoning: Each crew member will get 36 ÷ 7 = <<36 ÷ 7=5>>5 gold doubloons. ### Answer: 5
Expected answer: 36/7
Correct? No
Problem: A robot factory produces 5 robots each hour. If the factory increases its output to twice this amount, how many robots will it produce each hour?
Gemma 2B:
Reasoning: The factory produces 5 * 2 = 10 robots each hour. ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: In the previous problem, the robot factory increased its output to twice its original amount, making 10 robots each hour. If the factory were to then multiply this new hourly output by the same amount they were originally making each hour (5 robots), how many robots would the factory make every hour?
Gemma 2B:
### Answer: 50
Expected answer: 50
Correct? Yes
Problem: In the previous problem, the robot factory was originally making 5 robots each hour. However, if the factory were to increase its output to six times the original amount instead, how many robots would it produce each hour?
Gemma 2B:
Reasoning: The factory would produce 5 * 6 = 30 robots each hour. ### Answer: 30
Expected answer: 30
Correct? Yes
Problem: If one bike wheel has a radius of 81 / 9 units, and the height of a certain signpost is 9 times this radius, what is the height of the signpost?
Gemma 2B:
Reasoning: The height of the signpost is 9 * 81 / 9 = 81 units. ### Answer: 81
Expected answer: 81
Correct? Yes
Problem: If one bike wheel still has a radius of 81/9 units, but now the height of a certain bike rack is only 6 times this radius, what is the height of the bike rack?
Gemma 2B:
Reasoning: The height of the bike rack is 6 * 81 / 9 = 48 units. ### Answer: 48
Expected answer: 54
Correct? No
Problem: On a sunny day, Jamie took some time to swing on a tree. He swung 11 times in every minute and he spent 1 minute swinging. How many times did Jamie swing in total?
Gemma 2B:
Reasoning: Jamie swung 11 times in every minute for 60 minutes. So, Jamie swung 11 * 60 = <<11 * 60=660>>660 times in total. ### Answer: 660
Expected answer: 11
Correct? No
Problem: James has 9 robot toys and he buys the same amount again. How many robot toys does he have now?
Gemma 2B:
Reasoning: James started with 9 toys, and he bought the same amount again, so he now has 9 toys. ### Answer: 9
Expected answer: 18
Correct? No
Problem: A farmer has 11 chickens and each chicken lays 7 eggs in a week. How many eggs do the chickens lay in total in a week?
Gemma 2B:
Reasoning: The number of eggs laid in a week = 11 chickens * 7 eggs/chicken = <<11 chickens * 7 eggs/chicken=77>>77 eggs. ### Answer: 77
Expected answer: 77
Correct? Yes
Problem: The farmer from the previous problem sells each egg for 1 dollar. How much money does the farmer make in a week by selling all the eggs?
Gemma 2B:
### Answer: 77 dollars
Expected answer: 77
Correct? Yes
Problem: In the previous problem, if the farmer only had 2 chickens instead of 11, and each chicken still lays 7 eggs in a week, how many eggs would the chickens lay in total in a week?
Gemma 2B:
### Answer: 14 eggs
Expected answer: 14
Correct? Yes
Problem: In an enchanting forest, a certain type of tree grows 4 centimeters each day. If it only grows half of this amount each night, how many centimeters does the tree grow overnight?
Gemma 2B:
Reasoning: If the tree grows 4 cm/day, then it grows 4/2 = 2 cm each night. Therefore, the tree grows 2 cm overnight. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: The enchanted tree that has been growing in the forest doesn't stop there. Overnight, it grows half of its daily growth rate, which is 4 cm. If this overnight height is multiplied by 10, how long is the final growth of the tree over these 10 nights?
Gemma 2B:
### Answer: 40 cm Reasoning: The tree's growth over 10 nights is half of 4 cm/day, which is 2 cm. Therefore, the final growth of the tree over 10 nights is 2 cm x 10 = 20 cm.
Expected answer: 20
Correct? Yes
Problem: The enchanted tree that was previously growing at an overnight rate of 4 cm changes its growth pattern. Now, it starts to grow at a rate of 10 centimeters each day, but it still grows only half of this amount each night. How many centimeters does the tree now grow overnight?
Gemma 2B:
### Answer: 5 Reasoning: The tree grows 10 cm/day, so it grows 10/2 = 5 cm overnight.
Expected answer: 5
Correct? Yes
Problem: In a laboratory experiment, a group of 77 mice are divided equally among 11 cages. How many mice would be in each cage?
Gemma 2B:
Reasoning: Each cage would have 77/11 = <<77/11=7>>7 mice. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: After having divided the mice among the 11 cages, the scientist realized that she made a mistake and originally there were only 77 mice but some of them were counted twice. After correcting for this mistake, she realized that she actually only had 77 / 2 mice. How many mice did the scientist have originally?
Gemma 2B:
### Answer: 38
Expected answer: 77/2
Correct? No
Problem: Sally makes earrings. She needs 35 beads to make a set of earrings, but she divides this amount by 5 to make each individual earring. If she wants to make 8 earrings, how many beads will she need in total?
Gemma 2B:
Reasoning: If Sally needs 35 beads to make 8 earrings, then she needs 35 ÷ 8 = <<35 ÷ 8=4.375>>4.375 beads for each earring. Therefore, Sally will need 8 × 4.375 = <<8 × 4.375=33.4>>33.4 beads in total. ### Answer: 33.4
Expected answer: 56
Correct? No
Problem: Brenda has 9 apples and wishes to divide them equally amongst her 9 friends, so each friend receives the same amount. How many apples will each friend get?
Gemma 2B:
Reasoning: Brenda will divide 9 apples equally amongst 9 friends, so each friend will receive 1 apple. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: In a new scenario, Brenda has 9 apples but this time she only wants to divide them evenly among her 2 closest friends. Given this change, how many apples will each friend receive now?
Gemma 2B:
Reasoning: Brenda will divide 9 apples equally amongst 2 friends, so each friend will receive 4.5 apples. ### Answer: 4.5
Expected answer: 9/2
Correct? Yes
Problem: In a circus, a tightrope is set 10 feet off the ground. A stuntman wants to do a daring stunt - he wants to walk from one side of the tightrope to the other. The tightrope is five times the height above the ground. What distance will he need to walk to complete his stunt?
Gemma 2B:
Reasoning: The stuntman needs to walk 10 feet up to the top of the tightrope and then 5 times that distance down to the other side. 10 feet up = 10/5 = 2 feet 5 times 2 feet = 10 feet ### Answer: 10
Expected answer: 50
Correct? No
Problem: The length of one side of a square is equal to the result of dividing 30 by 6. What is the total area of the square?
Gemma 2B:
Reasoning: The side length is 30/6 = <<30/6=5>>5 cm. The total area is equal to the side length squared, which is 5^2 = <<5^2=25>>25 cm². ### Answer: 25
Expected answer: 25
Correct? Yes
Problem: The length of one side of a square is equal to the result of dividing 30 by 6. The total area of the square is found by multiplying the length of one side by itself. Now, if we multiply this area by 3, what will be the new value?
Gemma 2B:
### Answer: 150
Expected answer: 75
Correct? No
Problem: In the original problem, the length of one side of the square was found by dividing 30 by 6. Now consider a new scenario where the length of the square is instead found by dividing number 12 by 6. What would be the total area of this new square?
Gemma 2B:
### Answer: 36
Expected answer: 4
Correct? No
Problem: A certain star emits 7 particles every second. If this continues for 8 seconds, how many particles does the star emit in total?
Gemma 2B:
Reasoning: The number of particles emitted in 8 seconds is equal to the number emitted per second multiplied by the number of seconds. Number of particles emitted in 8 seconds = 7 particles/second x 8 seconds = <<56 particles>>56. ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: If the first star, instead of emitting particles for 8 seconds, only emits particles for 5 seconds, how many particles will then it emit?
Gemma 2B:
Reasoning: The number of particles emitted in 5 seconds is equal to the number emitted per second multiplied by the number of seconds. Number of particles emitted in 5 seconds = 7 particles/second x 5 seconds = <<35 particles>>35. ### Answer: 35
Expected answer: 35
Correct? Yes
Problem: A shoe factory can create 24 shoes in three hours. If the factory runs for five hours, how many shoes will be produced?
Gemma 2B:
Reasoning: The factory can create 24 shoes in 3 hours, so in 5 hours, they can create 24*5 = <<24*5=120>>120 shoes. ### Answer: 120
Expected answer: 40
Correct? No
Problem: A unique species of butterfly only lives for 5 days in each month. Considering this fact, how many days total does the butterfly species live in a span of a year, which is 12 months?
Gemma 2B:
Reasoning: The butterfly species lives for 5 days in each month, so it lives for 5*12 = <<5*12=60>>60 days in a year. ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: Considering the same unique species of butterfly, but now in a different region it only lives for 5 days each week instead of per month. How many days total does the butterfly species live in a 7-week span?
Gemma 2B:
### Answer: 7*5=35
Expected answer: 35
Correct? Yes
Problem: In fairy land, one ordinary mushroom provides food for 10 fairies for a day. If a magic mushroom can provide food as 4 ordinary mushrooms, how many fairies can a magic mushroom feed for a day?
Gemma 2B:
Reasoning: A magic mushroom can provide food for 10/4 = <<10/4=2.5>>2.5 fairies for a day. Therefore, a magic mushroom can feed 2.5 fairies for a day.
Expected answer: 40
Correct? No
Problem: A river is flowing at a rate of 4 kilometers per hour. How far can the river flow in 10 hours?
Gemma 2B:
Reasoning: The rate of flow is 4 km/h, so in 1 hour, the river can flow 4 km. In 10 hours, the river can flow 4 km/h x 10 h = <<4 km/h x 10 h=40 km>>40 km of water. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: If the speed of the river were instead 4 kilometers per hour for 2 hours, how far would the river flow within these 2 hours?
Gemma 2B:
Reasoning: The speed of the river is 4 km/h, so in 2 hours, the river can flow 4 km/h x 2 h = <<4 km/h x 2 h=8 km>>8 km of water. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: A slide is double the height of Ava who is 12 feet tall. How tall is the slide?
Gemma 2B:
Reasoning: The slide is double the height of Ava, which is 12 feet. The slide is 2 * 12 = <<2 * 12=24>>24 feet tall. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: Following up on the last problem: If Ava decides to triple the height of the slide that is double her height, how high will the new slide be?
Gemma 2B:
Reasoning: The new slide will be 3 * 24 = <<3 * 24=72>>72 feet high. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: In the previous problem, Ava was initially considering a slide double her height when she was 12 feet tall. However, let's say Ava is actually 11 feet tall. In that case, how high would the slide be if it was still double her height?
Gemma 2B:
Reasoning: If Ava is 11 feet tall, the slide would be 2 * 11 = <<2 * 11=22>>22 feet high. ### Answer: 22
Expected answer: 22
Correct? Yes
Problem: There's a tap which fills a tank at a rate of 2 liters per minute. How much water will be in the tank after 9 minutes?
Gemma 2B:
Reasoning: The tank initially contains 2 liters, and the tap fills it at a rate of 2 liters per minute. Therefore, after 9 minutes, the tank will contain 2 + 2*9 = <<2+18=20>>20 liters of water. ### Answer: 20
Expected answer: 18
Correct? No
Problem: Fred received 12 letters in one week and he reads them evenly over 3 days. How many letters does he read per day?
Gemma 2B:
Reasoning: Fred received 12/3 = <<12/3=4>>4 letters per day. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: Fred received 11 letters in one week instead of 12. If he still reads them evenly over 3 days, how many letters does he read per day now?
Gemma 2B:
Reasoning: Fred received 11/3 = <<11/3=3.7>>3.7 letters per day. ### Answer: 3.7
Expected answer: 11/3
Correct? No
Problem: A toy car factory produces 8 cars every hour 24/7. If the factory runs for 12 hours a day, how many cars will it produce in one day?
Gemma 2B:
Reasoning: 8 cars/hour * 24 hours/day = <<8 cars/hour * 24 hours/day= 240 cars/day>>240 cars. ### Answer: 240
Expected answer: 96
Correct? No
Problem: If baby Lily got 44 toys divided evenly among her 4 cousins, each cousin would get 'i' number of toys. If we multiply 'i' by 5, how many toys would that represent?
Gemma 2B:
Answer: 220 Reasoning: If each cousin gets 'i' number of toys, then 44 ÷ 5 = <<44 ÷ 5=8.8>>8.8 cousins will get 8 toys each.
Expected answer: 55
Correct? No
Problem: Mike has $9 and he wants to divide it equally among his 3 children. How much money will each child recieve?
Gemma 2B:
Reasoning: Mike will divide $9 equally among his 3 children, which is $3 each. ### Answer: $3
Expected answer: 3
Correct? Yes
Problem: If each of Mike's children decided to save the money they received from their father every month for a year, how much money would each child have saved by the end of the year?
Gemma 2B:
Reasoning: Each child would save $3 per month for 12 months, which is $36 in total. ### Answer: $36
Expected answer: 36
Correct? Yes
Problem: If Mike had $11 instead of $9 and he still decided to divide it equally among his 3 children, how much money would each child receive now?
Gemma 2B:
### Answer: $3.33
Expected answer: 11/3
Correct? No
Problem: If a cow produces 72 liters of milk in 12 days, and you need to find out how much milk it produces in a day, then use this amount to calculate how much milk the cow will produce in 12 days.
Gemma 2B:
The amount of milk produced in 1 day = 72/12 = <<72/12=6>>6 liters.
Expected answer: 72
Correct? No
Problem: On a map, 30 miles is represented as 10 inches. How many miles does 1 inch represent?
Gemma 2B:
Reasoning: 30 ÷ 10 = <<30 ÷ 10=3>>3 miles. 1 inch represents 1/10 of 3 miles, which is 0.03 miles.
Expected answer: 3
Correct? No
Problem: A truck has 8 tires. If each tire can carry a load of 8 tons, how much total load can the truck carry when all tires are fully loaded?
Gemma 2B:
Reasoning: Each tire can carry 8 tons, so the truck can carry 8 * 8 = <<8*8=64>>64 tons when all tires are fully loaded. ### Answer: 64
Expected answer: 64
Correct? Yes
Problem: If the truck with all the tires fully loaded is carrying cargo weighing the same as the total load the tires can handle, what would be the total weight being carried by the truck?
Gemma 2B:
### Answer: 64 tons
Expected answer: 64
Correct? Yes
Problem: In the previous scenario, each tire was capable of carrying a load of 8 tons. But what if each tire was only capable of carrying a load of 3 tons? How much total load could the truck carry then when all tires are fully loaded?
Gemma 2B:
### Answer: 32
Expected answer: 24
Correct? No
Problem: If you have 4 fruits and each fruit provides 1 cup of juice, how many cups of juice can you get in total?
Gemma 2B:
Reasoning: 4 fruits x 1 cup of juice/fruit = <<4 fruits * 1 cup of juice/fruit=4 cups of juice>>4 cups of juice. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: If instead you started with just 1 fruit, how many cups of juice would you be able to make?
Gemma 2B:
Reasoning: 1 fruit x 1 cup of juice/fruit = <<1 fruit * 1 cup of juice/fruit=1 cup of juice>>1 cup of juice. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Sara has a box of colored pencils, and she has 5 colors. If she has 5 of each type, how many colored pencils does Sara have in total?
Gemma 2B:
Reasoning: Sara has 5 identical colored pencils. ### Answer: 5
Expected answer: 25
Correct? No
Problem: In a word, each letter corresponds to a point in a game. If you have a 12-letter word, how many points will you get if each letter corresponds to 1 point in the game?
Gemma 2B:
Answer: 12
Expected answer: 12
Correct? Yes
Problem: You have decided to play 8 rounds of the same game. If you continue to use the same 12-letter word in each round, how many points will you accumulate in total from all the rounds?
Gemma 2B:
Answer: 12
Expected answer: 96
Correct? No
Problem: You decide to change your strategy in the next game and instead use a 9-letter word. If each letter still corresponds to 1 point, how many points will you get in this game?
Gemma 2B:
Answer: 9
Expected answer: 9
Correct? Yes
Problem: Jake has 7 crates, each containing 7 bottles of water. How many bottles of water does he have in total?
Gemma 2B:
Reasoning: Jake has 7 * 7 = <<7*7=49>>49 bottles of water in total. ### Answer: 49
Expected answer: 49
Correct? Yes
Problem: Jake decided to not drink any of the water just yet and stored all the bottles in his garage. After leaving the bottles in the garage untouched, how many bottles does Jake still have?
Gemma 2B:
Reasoning: Jake started with 7 bottles and did not drink any, so he still has 7 bottles in his garage. ### Answer: 7
Expected answer: 49
Correct? No
Problem: A piano has 4 legs. If there are 2 pianos in the music room, how many legs are there in total?
Gemma 2B:
Reasoning: There are 4 legs in each piano, so there are 2 * 4 = <<2*4=8>>8 legs in the music room. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Considering from the previous question, what if each piano only had 3 legs instead of 4. With 2 pianos in the music room, how many legs would there be in total?
Gemma 2B:
### Answer: 12
Expected answer: 6
Correct? No
Problem: A keyring holds 2 keys but each keyring must be split between two people. How many keys does each person get?
Gemma 2B:
Reasoning: Each person gets 2 keys. ### Answer: 2
Expected answer: 1
Correct? No
Problem: Javier has 9 crates of bottles. Each crate contains 6 bottles, how many bottles does Javier have?
Gemma 2B:
Reasoning: Javier has 9 x 6 = <<9x6=54>>54 bottles. ### Answer: 54
Expected answer: 54
Correct? Yes
Problem: Javier decided to pack more bottles into his crates. Now, each crate contains 8 bottles instead of 6. How many bottles does Javier have now with his 9 crates?
Gemma 2B:
Reasoning: Javier has 9 x 8 = <<9x8=72>>72 bottles now. ### Answer: 72
Expected answer: 72
Correct? Yes
Problem: A shirt costs 10 dollars. If 1 dollar equals 1 euro, how much does the shirt cost in euros?
Gemma 2B:
Reasoning: 10 dollars = 10 euros. ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: Following the previous question: if the exchange rate changes and now 1 euro equals 1 dollar, how much will the shirt cost in dollars now?
Gemma 2B:
### Answer: 10
Expected answer: 10
Correct? Yes
Problem: After the price changes, the shirt now costs 9 dollars. If 1 dollar equals 1 euro, how much does the shirt cost in euros now?
Gemma 2B:
### Answer: 9
Expected answer: 9
Correct? Yes
Problem: If a plant grows 12 flowers each month, how many flowers will it grow in 5 months?
Gemma 2B:
Reasoning: A plant grows 12 flowers each month, so it will grow 12 * 5 = <<12 * 5=60>>60 flowers in 5 months. ### Answer: 60
Expected answer: 60
Correct? Yes
Problem: A beach ball is being blown up to be twice the size of its original size of 3 feet in diameter. What will be the diameter of the beach ball after it is blown up?
Gemma 2B:
Reasoning: The diameter of the beach ball will be 3 * 2 = <<3*2=6>>6 times its original diameter. The diameter of the beach ball after it is blown up is 3 feet * 6 = <<3 feet * 6=18>>18 feet.
Expected answer: 6
Correct? No
Problem: A farmer has a total of 24 tomatoes. He wants to equally divide them into 4 boxes. How many tomatoes will there be in each box?
Gemma 2B:
Reasoning: Each box will have 6 tomatoes, as 24 ÷ 4 = 6. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: The farmer then decides to combine all the tomatoes from the 4 boxes back into one large container. How many tomatoes will there be in the large container?
Gemma 2B:
Reasoning: Each box has 6 tomatoes, so 4 boxes have 4 × 6 = <<4 × 6=24>>24 tomatoes in the large container. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: In a different scenario, if the farmer had decided to equally divide the 24 tomatoes between only 2 boxes instead of 4, how many tomatoes would have been in each box then?
Gemma 2B:
### Answer: 12
Expected answer: 12
Correct? Yes
Problem: John wants to go out playing with his scooter. He travels a certain distance "B" which he calculates as half of 16. When he gets tired, he multiplies the distance "B" he traveled with 6 to find out the total distance "X" he traveled back and forth in his playing area. What is the total distance "X" he traveled?
Gemma 2B:
Reasoning: B = 1/2 * 16 = <<16/2=8>>8. X = B * 6 = 8 * 6 = <<8*6=48>>48. ### Answer: 48
Expected answer: 48
Correct? Yes
Problem: In the previous situation, John multiplied the distance he traveled with 6. But this time, he decides to ride his scooter for a bit longer. Instead of multiplying by 6, he now multiplies the same initial half of 16, distance "B", by 8 to find out the new total distance "X" he traveled back and forth. What is the new total distance "X" he traveled?
Gemma 2B:
### Answer: 48
Expected answer: 64
Correct? No
Problem: Lisa has a favorite TV show that she likes to watch, which happens to be 8 minutes long per episode. If Lisa decides to watch 2 episodes back-to-back without any breaks, how long will she be watching her favorite TV show in total?
Gemma 2B:
Reasoning: Lisa will be watching 2 episodes back-to-back, which is 8 minutes/episode x 2 episodes = 16 minutes. ### Answer: 16
Expected answer: 16
Correct? Yes
Problem: Now, imagine Lisa spent 5 days over the course of a week doing the same routine of watching 2 episodes back-to-back of her favorite TV show, which is 8 minutes per episode. How long in total did she spend watching her TV show over those 5 days?
Gemma 2B:
Reasoning: 5 days x 8 minutes/episode = 40 minutes. ### Answer: 40
Expected answer: 80
Correct? No
Problem: In a twist, one day Lisa decided to watch a different TV show, which is 12 minutes long per episode. If she watches 2 episodes of this show back-to-back without any breaks, how long will she be watching this different TV show in total?
Gemma 2B:
Reasoning: Lisa will be watching 2 episodes back-to-back, which is 12 minutes/episode x 2 episodes = 24 minutes. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: Jane has 1 blanket and John has 3 times as many blankets as Jane. How many blankets does John have?
Gemma 2B:
Reasoning: John has 3 * 1 = <<3*1=3>> blankets. ### Answer: 3
Expected answer: 3
Correct? Yes
Problem: Consider the starting point of the previous problem where Jane had 1 blanket and John had 3 times as many blankets as Jane. Now, suppose that Jane initially has 6 blankets instead of 1. In this new scenario, how many blankets does John have initially?
Gemma 2B:
Reasoning: If Jane initially has 6 blankets, then John initially has 3 * 6 = <<3*6=18>>18 blankets. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: John has $28 which he wants to divide equally among his 7 children. How many dollars will each child receive?
Gemma 2B:
Reasoning: John divided $28 by 7 = <<$28 ÷ 7=4>>4 dollars each child will receive. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: If John originally had $10 instead of $28, and he still wanted to divide it equally among his 7 children, how much would each child receive now?
Gemma 2B:
Reasoning: John divided $10 by 7 = <<$10 ÷ 7=1.43>>1.43 dollars each child will receive now. ### Answer: 1.43
Expected answer: 10/7
Correct? No
Problem: A tailor uses 2 meters of fabric to make one shirt. He uses double the fabric for the shirt's lining. If the tailor wants to make 5 shirts with lining, how many meters of fabric will he use for the lining?
Gemma 2B:
Reasoning: The tailor uses 2 meters of fabric for one shirt, so he uses 5 * 2 = <<5 * 2=10>>10 meters of fabric for the lining. ### Answer: 10
Expected answer: 20
Correct? No
Problem: Kate owns a scooter shop. She sells 1 scooter every day. How many scooters will she sell after 8 days?
Gemma 2B:
Reasoning: Kate sells 1 scooter every day, so after 8 days, she will sell 1 x 8 = <<1 x 8=8>> scooters. ### Answer: 8
Expected answer: 8
Correct? Yes
Problem: Continuing from the previous situation, after selling 1 scooter a day for 8 days, Kate decides to hold a grand sale for 8 more days where she sells the same number of scooters she sold in the previous 8 days every day. How many additional scooters will she sell during this grand sale?
Gemma 2B:
### Answer: 8
Expected answer: 64
Correct? No
Problem: Let's revise the original situation. Instead of selling 1 scooter a day, let's say Kate was actually selling 7 scooters a day for 8 days. How many scooters did she sell in this period?
Gemma 2B:
Reasoning: Kate sold 7 scooters a day for 8 days, so she sold 7 x 8 = <<7 x 8=56>>56 scooters in this period. ### Answer: 56
Expected answer: 56
Correct? Yes
Problem: In a forest, one tree produces 10 seeds each year. How many seeds does the tree produce in 1 year?
Gemma 2B:
Reasoning: The tree produces 10 seeds each year, so in 1 year, the tree produces 10 seeds. ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: Now imagine that the tree actually produces 12 seeds each year instead of 10. How many seeds does the tree produce in 1 year?
Gemma 2B:
Reasoning: The tree still produces 10 seeds each year, regardless of the number of seeds it produced the previous year. ### Answer: 10
Expected answer: 12
Correct? No
Problem: The sun shines 12 hours in a day and a scientist wants to divide it into 6 equal parts for an experiment. How many hours are there in each part?
Gemma 2B:
Reasoning: Each part will have 12/6 = <<12/6=2>>2 hours of sunlight. ### Answer: 2
Expected answer: 2
Correct? Yes
Problem: A group of 12 friends decided to split into smaller groups to play a board game. If they want to have exactly 3 friends in each group, how many groups will there be?
Gemma 2B:
Reasoning: If there are 12 friends, we can choose 3 friends from 12 in 12C3 ways. There are 12C3 = 40 different ways to choose 3 friends from 12. Therefore, there will be 40 groups of 3 friends each.
Expected answer: 4
Correct? No
Problem: Emma and her friends are building sandcastles on the beach. Each sandcastle uses 6 buckets of sand, and they build 4 sandcastles. Each bucket of sand has 3 shovels full of sand in it. How many shovels of sand do they use in total?
Gemma 2B:
Reasoning: Emma and her friends used 4 sandcastles * 6 buckets/castle = <<4 sandcastles * 6 buckets/castle=24 buckets>>24 buckets of sand in total. ### Answer: 24
Expected answer: 72
Correct? No
Problem: Jenna is making bracelets for her friends. Each bracelet requires 12 beads and she has a total of 8 bracelets to make. How many beads will Jenna need in total?
Gemma 2B:
Reasoning: Jenna needs 12 beads for each bracelet, so she will need 12 * 8 = <<12 * 8=96>>96 beads in total. ### Answer: 96
Expected answer: 96
Correct? Yes
Problem: After reconsidering, Jenna decided to only make 7 bracelets instead of 8. Now, how many beads will Jenna need to make the bracelets?
Gemma 2B:
Reasoning: Each bracelet requires 12 beads, so Jenna needs 12 * 7 = <<12 * 7=84>>84 beads in total. ### Answer: 84
Expected answer: 84
Correct? Yes
Problem: Penny has 66 milliliters of toothpaste in a new tube. If she uses 11 milliliters for each brushing, how many times can she brush her teeth with the new tube of toothpaste?
Gemma 2B:
Reasoning: Penny can brush her teeth 66 ÷ 11 = <<66 ÷ 11=6>>6 times with the new tube of toothpaste. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: If Penny started using 9 milliliters of toothpaste for each brushing instead of 11, how many times could she brush her teeth with the new tube of toothpaste?
Gemma 2B:
Reasoning: If Penny started using 9 milliliters of toothpaste, she would be using 9/11 = <<9/11=0.82>>82% as many milliliters of toothpaste per brushing. Therefore, she could brush her teeth 66 ÷ 0.82 = <<66 ÷ 0.82=78.5>>79 times with the new tube of toothpaste. ### Answer: 79
Expected answer: 22/3
Correct? No
Problem: Vanessa has 4 bunches of grapes and each bunch has 11 grapes. How many grapes does Vanessa have in total?
Gemma 2B:
Reasoning: Vanessa has 4 bunches of grapes, each with 11 grapes. So, she has 4 * 11 = <<4 * 11=44>>44 grapes in total. ### Answer: 44
Expected answer: 44
Correct? Yes
Problem: If Vanessa only had 4 bunches of grapes and each bunch had 5 grapes instead of 11, how many grapes would Vanessa have in total then?
Gemma 2B:
Reasoning: If Vanessa had 4 bunches of grapes with 5 grapes each, she would have 4 * 5 = <<4 * 5=20>>20 grapes in total. ### Answer: 20
Expected answer: 20
Correct? Yes
Problem: Mary has a length of fabric measuring 6 yards. She needs 6 yards of fabric to make a skirt. How many skirts can she make with the fabric she has?
Gemma 2B:
Reasoning: Mary can make 6 ÷ 6 = <<6 ÷ 6=1>> skirt with the fabric she has. ### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Mary used her 6 yards of fabric to make a skirt. Each skirt she makes, requires 6 yards of fabric. She decides to make as many skirts as skirts she already made (i.e., she wants to multiply the number of skirts by the number of skirts she already made). How many skirts will Mary have made in total?
Gemma 2B:
### Answer: 1
Expected answer: 1
Correct? Yes
Problem: Mary now has a new length of fabric that's 7 yards long. Keeping in mind that each skirt requires 6 yards of fabric, how many skirts can Mary make with the new fabric she has?
Gemma 2B:
### Answer: 1
Expected answer: 7/6
Correct? No
Problem: Jordan has 9 card packs and each pack contains 1 card. If he decides to double the total number of his cards, how many cards will Jordan have then?
Gemma 2B:
Reasoning: If Jordan has 9 card packs with 1 card in each pack, then he has 9 cards. If he decides to double the total number of his cards, then he will have 2 * 9 = <<2*9=18>>18 cards. ### Answer: 18
Expected answer: 18
Correct? Yes
Problem: Following up from the previous question, if Jordan decides to again double the total number of cards he has, how many cards will Jordan end up with at that point?
Gemma 2B:
### Answer: 36
Expected answer: 36
Correct? Yes
Problem: Following up from the previous question, if originally Jordan had 5 card packs instead of 9, and he still decided to double the total number of his cards, how many cards would Jordan have then?
Gemma 2B:
Reasoning: If Jordan had 5 card packs initially, then he would have 5 cards. If he decided to double the total number of his cards, then he would have 5 * 2 = <<5*2=10>>10 cards. ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: A wizard casts a magic spell that lasts 60 minutes. However, his wizard staff can only channel the spell for 6 equal periods of time before it needs a 1-minute break to recharge. How long is each period of the spell?
Gemma 2B:
Reasoning: Each period is 60/6 = <<60/6=10>>10 minutes. The wizard's staff can channel the spell for 6 periods, each lasting 10 minutes. ### Answer: 10
Expected answer: 10
Correct? Yes
Problem: In the magical world, a donezal is a unit of time equal to 10 wizard staff channeling periods. If every wizard staff channeling period lasts as long as the spell in the previous problem, how much time does one donezal represent?
Gemma 2B:
Reasoning: One donezal is equal to 10 minutes. The spell lasts 60 minutes, so one donezal represents 60/10 = <<60/10=6>>6 minutes. ### Answer: 6
Expected answer: 100
Correct? No
Problem: In a new experiment, the wizard decided to divide the same 60-minute spell into only 4 equal periods before the wizard staff needs to take a break. How long does each period of casting last now?
Gemma 2B:
Reasoning: Each period is 60/4 = <<60/4=15>>15 minutes. The wizard's staff can cast the spell for 4 periods, each lasting 15 minutes. ### Answer: 15
Expected answer: 15
Correct? Yes
Problem: A drummer hits his drum 11 times per minute. How many times does he hit the drum in 8 minutes?
Gemma 2B:
Reasoning: 11 times per minute is equivalent to 11/60 = 0.1777 times per second. In 8 minutes, he hits the drum 0.1777 * 8 = <<0.1475>>14.75 times. ### Answer: 14.75
Expected answer: 88
Correct? No
Problem: John is packing for a trip and realizes that for each pair of pants, he needs 2 pairs of socks. If he plans to bring 22 pairs of socks, how many pairs of pants should he pack?
Gemma 2B:
Reasoning: John needs 22/2 = <<22/2=11>>11 pairs of pants. ### Answer: 11
Expected answer: 11
Correct? Yes
Problem: Now, John is reconsidering his packing strategy. Instead of packing two pairs of socks per pair of pants, he thinks he only needs to pack two socks for every pair of pants. If he sticks to this new strategy, how many pairs of pants should he pack for his 4 pairs of socks?
Gemma 2B:
Reasoning: John needs 4 pairs of socks * 2 socks/pair = <<4 pairs of socks * 2 socks/pair=8 socks>>8 socks for his 4 pairs of socks. ### Answer: 8
Expected answer: 2
Correct? No
Problem: If a pack of pens contains 8 pens and John has 5 packs, how many pens does he have in total?
Gemma 2B:
Reasoning: John has 5 * 8 = <<5*8=40>>40 pens in total. ### Answer: 40
Expected answer: 40
Correct? Yes
Problem: If, instead of 8 pens per pack, there were 6 pens per pack, how many pens would John have in total with his 5 packs?
Gemma 2B:
### Answer: 30
Expected answer: 30
Correct? Yes
Problem: Captain Blackbeard's pirate ship sailed for 60 hours and he divided the total hours equally among the 6 shifts. If each guard is expected to protect the ship for one shift, how many hours will one guard have to protect the ship?
Gemma 2B:
Reasoning: Each guard will be protecting the ship for 1/60 of a day, which is equivalent to 1 hour. ### Answer: 60
Expected answer: 10
Correct? No
Problem: John needs a rope. Every meter of the rope costs $5. If John needs a 6-meter long rope, how much will it cost him?
Gemma 2B:
Reasoning: To find the cost of the rope, we multiply the length of the rope by the cost per meter. 6 m * $5 = <<6 m * $5=$30>>$30. John will need $30 to buy a 6-meter long rope.
Expected answer: 30
Correct? Yes
Problem: Amelia has 42 gifts to distribute equally among her 7 best friends. How many gifts will each friend receive?
Gemma 2B:
Reasoning: Amelia divided 42 by 7, which gives her 6 gifts for each friend. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: In the previous scenario, Amelia was distributing gifts among 7 of her friends. But what if Amelia instead planned to distribute her 42 gifts equally among only 6 friends instead? How many gifts would each friend receive in this case?
Gemma 2B:
Reasoning: If Amelia distributed the gifts equally among 6 friends, she would give 7 friends 7 gifts each and 1 friend 6 gifts. ### Answer: 7
Expected answer: 7
Correct? Yes
Problem: A mother bear has 40 honey pots and she wants to evenly distribute them among her 8 cubs. How many honey pots will each cub receive?
Gemma 2B:
Reasoning: Each cub will receive 5 honey pots because 40 ÷ 8 = 5. ### Answer: 5
Expected answer: 5
Correct? Yes
Problem: If the mother bear had only 40 honey pots and wanted to evenly distribute them among her 10 cubs instead, how many honey pots would each cub receive now?
Gemma 2B:
Reasoning: Each cub will receive 4 honey pots because 40 ÷ 10 = 4. ### Answer: 4
Expected answer: 4
Correct? Yes
Problem: A penguin is diving into the sea. Initially, it took the penguin 28 seconds to reach a depth that is 4 times its own height. What is the square of the depth the penguin reaches in seconds?
Gemma 2B:
Reasoning: The depth the penguin reaches is 4 times its height, which is 4h. The square of the depth the penguin reaches is (4h)^2 = 16h^2. The square of the depth the penguin reaches in seconds is 16h^2 seconds. ### Answer: 16h^2
Expected answer: 49
Correct? No
Problem: A swing goes back and forth 10 times every minute. How many back and forth swings will the swing accomplish in 9 minutes?
Gemma 2B:
Reasoning: A swing goes back and forth 10 times every minute, so in 9 minutes, it will go back and forth 10 * 9 = <<10*9=90>>90 times. ### Answer: 90
Expected answer: 90
Correct? Yes
Problem: An elephant can eat 7kg food per hour. How much food will an elephant eat in 4 hours?
Gemma 2B:
Reasoning: An elephant can eat 7kg/hour x 4 hours = <<7kg/hour x 4 hours=28kg>>28kg of food in 4 hours. ### Answer: 28
Expected answer: 28
Correct? Yes
Problem: In the previous situation, what if instead of eating 4kg of food per hour, the elephant ate only 3kg of food per hour? How much food would the elephant eat in 4 hours then?
Gemma 2B:
Reasoning: An elephant can eat 3kg/hour x 4 hours = <<3kg/hour x 4 hours=12kg>>12kg of food in 4 hours. ### Answer: 12
Expected answer: 12
Correct? Yes
Problem: A dragon has 3 heads and each head has 8 eyes. How many eyes does the dragon have in total?
Gemma 2B:
Reasoning: A dragon has 3 heads, each with 8 eyes. So, the total number of eyes is 3 * 8 = <<3*8=24>>24. ### Answer: 24
Expected answer: 24
Correct? Yes
Problem: In addition to the 3-headed dragon, another dragon of the same kind joins it. Between the two dragons, how many eyes are there in total?
Gemma 2B:
### Answer: 48
Expected answer: 48
Correct? Yes
Problem: Suppose that each dragon instead had 11 eyes per head, not 8. How many eyes would one three-headed dragon have then?
Gemma 2B:
### Answer: 33
Expected answer: 33
Correct? Yes
Problem: A candle burns out at a rate of 2 hours per inch. If a candle is 3 inches tall, how long will it take for the candle to burn out completely?
Gemma 2B:
Reasoning: The candle will burn out completely when it is 3 inches high. The time taken for the candle to burn out can be calculated by dividing the total height of the candle by the rate of burning out per hour. Therefore, the time taken for the candle to burn out completely is 3 ÷ 2 = <<3/2>>2 hours. ### Answer: 2
Expected answer: 6
Correct? No
Problem: Charlie has 4 chocolates and decides to share half of them with his sister. Then he counts his remaining chocolates and decides to double the amount. How many chocolates does Charlie have now?
Gemma 2B:
Reasoning: After sharing half of 4 chocolates, Charlie has 4/2 = <<4/2=2>>2 chocolates. After doubling his remaining chocolates, he has 2 * 2 = <<2 * 2=4>>4 chocolates. So, Charlie has 4 chocolates now.
Expected answer: 4
Correct? Yes
Problem: Following from the last problem, Charlie then takes the amount of chocolates he has and decides to multiply it by 9 for a birthday party. How many chocolates does Charlie have now?
Gemma 2B:
### Answer: 36
Expected answer: 36
Correct? Yes
Problem: Following from the previous problems, let's consider a new scenario. This time, suppose Charlie only had 2 chocolates and again decided to share half of them with his sister. Then, he counts his remaining chocolates and decides to double the amount. How many chocolates does Charlie have now in this scenario?
Gemma 2B:
### Answer: 4 chocolates
Expected answer: 2
Correct? No
Problem: A castle has 36 towers and there are an equal number of towers on each of its 6 walls. How many towers are there on each wall?
Gemma 2B:
Reasoning: Each wall has 36/6 = <<36/6=6>>6 towers. ### Answer: 6
Expected answer: 6
Correct? Yes
Problem: Suppose the number of walls in the castle was incorrectly counted before, and there are actually 10 walls instead of 6. If the castle still has a total of 36 towers, how many towers would be on each wall in that case?
Gemma 2B:
Reasoning: Each wall would then have 36/10 = <<36/10=3.6>>3.6 towers. ### Answer: 3.6
Expected answer: 18/5
Correct? Yes