Due Sunday, September 12th:
Share one word problem that you wrote today. Identify the type of word problem that you wrote (join, compare, etc.) and then describe the strategies that might be used to solve your word problem.
Here is a link to the worksheet to help you organize your thoughts.
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I apologize for the late response! I was confused about the due dates!
Question: Daisy had 6 strawberries for a snack. Her sister Katy gave her 2 more strawberries. How many strawberries does Daisy have now?
6+2=__
For first grade, join problem, result unknown
I would ask students what are strategies they would use to solve this problem. Then I would have students use counters, drawings, and unifix cubes, or a number line. I would have them use different colors for unifix cubes, counters, or drawings to differentiate between 6 and 2.
A word problem that I came up with was Sammmy has to go to Long Island city for a birthday. It takes her 10 minutes to get there on the train and 30 minutes to get there on a bus. How many more minutes does it take her on a train than on a bus? The equation is 30-10=? This is a comparison problem for 1st graders. To help them I would use a bar model. Another way to teach the students would be to give them manipulatives to solve the problem such as counters that have 2 sides, yellow and red. I would start off with 10 counters on the yellow side and then go up to 30 using the red side and this will help the students see the difference.
Great work, Uzrah. The numbers might be a little big for first graders, but I love the options that you will provide to help them solve the problem. I think that the compare problem would be easier to model with the equation 30 = 10 + ___. Nice work.
Question: Jemma has 12 books, she goes to the book store and buys 5 more books. How many books does Jemma have now?
Join problem and result unknown, 1st grade
Solving: I would show the students a few ways to solve this problem, we would use a number line and place our fingers on the 12 and count up 5, where they will reach 17. Another way would be by using props like the one cubes, where students will count 12 and add 5 cubes and count it all together. If there aren’t props in the classroom, students can draw 12 dots in one box and 5 dots in one box and students will count all the dots.
Great work, Rashmit. This is an appropriate problem for first graders and I like the different options that you have provided. Be sure to give students the opportunity to solve the problem using their own strategies before you show them how to do it. That will be more meaningful for them.
Word problem: Eliana has 10 flowers that she picked from her mom’s garden. She gives some flowers to her brother Jadiel. She is then left with 6 flowers. How many flowers did she give to her brother Jadiel?
Equation: 10 – ____ =6
This problem is a separate (take from) word problem: change unknown. Students can use blocks to solve this problem. They can stock ten blocks together. Then start removing some until they reach 6 blocks. They will then count the number of blocks removed and that will give them the answer.
Angelie has 8 books. Her mom takes 5 back to the library. How many does she have left?
8-5=? (3)
This type of problem is separate (take from). The result is unknown.
I can show my students how to solve this problem by using manipulatives such as counters and unifix cubes. Students can also do drawings. They can draw 8 books or just small squares and cross out five of them to find how many are left. If they do not want to draw that, they can simply draw circles and follow the same steps.
Great work, Stephanie. This is a separate problem with the result unknown. I think that giving students the opportunity to work with counters and unifix cubes is great. Just make sure that they have the time and space to try out their own methods before you show them how to solve the problem. Their strategies may surprise you.
Work Problem:
Nick has 4 remote control cars. Angela gave him 2 more for his birthday. How many remote control cars does Nick have altogether?
This is a join problem where the result is unknown. The student can use a visual to solve this problem. They can draw out 6 circles representing the remote control cars, and then they can draw another 4 circles representing the ones that he was given. The student can then count all the circles that they drew on their paper to find the unknown result. The student can also use a number line to solve this problem.
Nice work, Angela. What grade are you thinking about for this problem? It seems like kindergarten, based on the numbers and the relationship. Think about how you might introduce new models to help students deepen their understanding of the relationship between addition and subtraction.
My example problem: “Julio had twenty-four baseballs. He put them into buckets containing six baseballs each. How many buckets did Julio use?”
This problem would fall under the category of “Number of groups unknown” (Quotative division). The students solving the problem would know the total number of baseballs and would know that one bucket contained six baseballs. They would be solving for how many buckets were used with an equal number of baseballs inside of each bucket. I would use math manipulatives for this problem. I would begin with maybe small cubes and give them twenty-four. They can use real buckets or containers, or draw circles on the paper. They should then put six cubes in a circle or bucket and then continue to move the cubes in groups of six until they have all the cubes in buckets. They would have a total of four buckets. They can write out the problem as such: 24/6=? (=4)
Great work, Victoria. What grade are you thinking about for this problem? Perhaps third grade? Also, you want to think about what models you might push your students to think about in the coming days and weeks.
A word problem that I wrote was: Jim bakes twenty cupcakes for the school bake sale. Jim had baked four more cupcakes than Sally. How many cupcakes did Sally bake? This is a compare problem where the smaller quantity is unknown. This problem would be for first graders, one of the strategies that can be used to help them solve the problem would be the use of a number line. Having the kids start at twenty and count backwards 4 numbers to get their answer. The equation for this problem would be _+4=20 or the students can view it as 20-4=_
Great work Tatiana. I would start by introducing unifix cubes to the students so that they can use them to compare Jim’s cupcakes to Sally’s. That should help the students see the difference. It might be easiest to model if the equation is ___ + 4 = 20.
The word problem I created was: Ari has 6 boxes of crayons. Within each box there are 5 crayons. How many crayons does Ari have in total? This word problem is an equal groups problem where the total is unknown.
The steps used to solve this problem are: 6 boxes of crayons multiplied by 5 crayons= 30 crayons in total. (6×5)=30
Another strategy that can be used is drawing 6 pictures of crayons box, adding in 5 dots within each and counting them, or using an array chart by setting it up as 6 boxes going down vertically and 5 boxes going horizontally for 6 rows. Each way of solving this problem gives you a total of 30.
This word problem can be given to students between the grades of 2nd-5th.
Nice work, Michelle. I really like how you are looking to introduce an array model. You might also want to introduce a number line to the students as well. You could also draw the boxes and have students put five unifix cubes in each of the boxes and see how many crayons there are altogether. Then, you can connect the groups to the number line or the array model. The goal is to move from counting individual pieces to counting groups and then representing groups. I think this problem is best for third grade students.
Winnie the Pooh has 15 cookies. Tigger has 5 cookies. How many times as many cookies does Pooh have than Tigger?
This is a comparison multiplication problem with the multiplier unknown. 5x?=15
Strategies that will be helpful in solving this problem include a bar model, the fair share model, number line, or counters.
I imaged this for be for 3rd graders and included strategies that relied more on models than manipulatives.
Very nice job, Rabia. I think that providing unifix cubes as manipulatives would help as well. That way students could see how many groups of five fit into 15.
The one-word problem that I came out with today is:
Joey baked 16 cupcakes and gift them to her neighbor. She has only 8 cupcakes left when she comes back. How many cupcakes did she gift to her neighbor?
This would be a join: change unknown or a separate: change unknown problem. The students can be using the unifix cubes, based ten-block, or draw out the picture in order to solve the problems by 8+y=16 or 16-8=y.
Great job, Justine. I would classify this as a separate problem. The change is unknown. I think the idea of unifix cubes is great. You might want to push the students to start to model this problem in some way. What grade are you planning this for? Based on the numbers, it seems like first grade.
One word problem I wrote today was, Lisa has 5 crayons and her best friend Alex gives her 4 more crayons. How many crayons does Lisa have in total now? This is a join problem with the result unknown. I can show students how to solve this question by using counters in the tens box to show the end result. I will show them 5 counters and then add 4 more to show them 9 counters in total.
Nice work, Millennia. This is a problem for kindergardeners? Think about how you would push their thinking with next steps. Also, be sure to give students the opportunity to solve the problem in small groups before showing a procedure to them.
One word problem I wrote was: Jane has 21 different types of dog treats and wants to share them equally with her 3 dogs. How many treats does each dog get? This would be an equal groups division problem specifically partition division. One way students can solve this problem would be using manipulatives such as things like little bears. They could have three little piles and hand each dog one. Another way to solve this problem would be to draw three dogs or circles and then mark a tally in each one till they get the number 21.
Very nice job, Janetta. Is this a problem for third graders? Think about what next steps you might introduce to the students to push their thinking a bit.
My word problem is:
Kacey is looking out the window and sees 12 cars pass by. If 6 more cars pass by, how many cars will she see in total?
This is a part-part whole problem with the result unknown. It is a join problem. This question would be for the younger grades, most likely 1st grade. Some strategies that can be used to solve this problem are using manipulatives such as, diagrams, counters, and cubes. Students can use these manipulatives to represent the cars in the word problem. After students draw/ count 12 cars and 6 cars, they can count them all together to get their solution of 18 cars. I can also try to break down the numbers with them. For example, we can first solve what 2+6 equals to and then we can determine what 1+0 equals to.
Great work, Ashley. I would not introduce adding by place value to such young children ( 1 + 0 and 2 + 6) because many first graders are not ready for this way of understanding. Instead, how about offering them base-ten frames or a rekenrek so that they can start to move towards place value understanding independently.
Casey has 5 lollipops. Her teacher gave her 3 more lollipops for helping her peers. How many lollipops does she have altogether?
Type of problem: Join/ Addition
Equation: 5+3=y, y= how many lollipops does Casey have
This problem is catered towards kindergarten or 1st grade depending on the students math ability. The students will be able to use things like cubes or a number line to solve this problem. Students will also be able to use their fingers which is why I chose those numbers. Lower elementary school would be able to solve this question.
Great reasoning Nathalia. Thank you for including why you choose the numbers that you did. Now, think about what you would do if students either struggled to solve this problem or flew through and need more of a challenge.
A word problem that I came up with is:
Lisa has four-star stickers on her notebook and five-star stickers on her laptop. How many star stickers does she have altogether?
This problem is a join problem for first-graders. A strategy that I might use to solve the word problem is using drawing pictures. I would draw a notebook with four-star stickers on it + a laptop with five-star stickers on it =? Another strategy I can use to solve this problem is using counters. The red counters can represent the four-star stickers and the yellow counters can represent the five-star stickers.
Nice work, Christine. I would say that this is probably a part-part-whole problem since there is no movement happening with the change. Since you are writing this for first graders, you might be able to push them with either bigger numbers (sums greater than ten) or show them a modeling strategy or have them work towards grouping with a ten-frame.
A word problem that I came up with is: Adam has 7 toy cars and his mom buys him 4 more toy cars. How many toy cars does Adam have now? This word problem is a part-part whole problem where the total is unknown. One of the ways that I would show how to solve this problem is have cubes and then visually show that there are 7 ‘toy cars’ and then we add 4 more ‘toy cars’.
Great Joanna. It could also be seen as a join problem, with the result unknown. So, be prepared for students to interpret the problem that way.
What grade would this be for? How did you choose the numbers?
Think about next steps that you would take as well.
Problem: Leon has 6 more watermelons than Christy. Leon has 10 watermelons. How many watermelons does Christy have?
My problem is a compare problem for first-grade students, students should previously know what is mean by more than in order to solve this problem. This problem includes a smaller quantity unknown since the 10 is the bigger amount and we need to find the smaller quantity from the difference of the bigger amount. If the students are using cubes to solve the problem, basically they will have to take out 6 cubes first and see how many cubes are left to make a 10. In this case, students will use the addition strategy to solve the problem, 6 +_ = 10. However, students can also see this problem in another way, because more than can means subtraction as well. So they can first grab 10 cubes for Leon, and then since Leon has 6 more than Christy, they can cross out 6 cubes to see how many cubes are left for Christy. (10 – 6 =?).
Fantastic work, Liufen! You tried a really challenging problem and described it nicely. What would be the next steps that you would push students towards? Perhaps a bar model?
The word problem I chose to share is: Sebastian has 9 Oreos and 7 Chips Ahoy!. How many cookies does he have? This problem is a part-part-whole problem where the whole is unknown. The strategies that can be used to solve this are counters, drawings, unifex cubes, number frames. When using the cubes the student can select a specific color to represent the Oreos and chose a different color to represent the Chips Ahoy!. This will help them see the different parts (cookies) in the problem and when put together (9 + 7) help them solve it (9 + 7 = 16).
Great work, Lissette. I think it’s a great idea to use the ten frame with this problem. What grade is this for?
one word problem i wrote today was: Jessica had some coins. Vanessa gave her 5 more. Now, Jessica has 12 coins. How many coins did Jessica have to begin with? it is a join problem where the initial quantity is unknown. one of the strategies that can be used is visual drawing. the student completing this assignment can draw out 12 coins and cross out the 5 coins that vanessa gave her to get the total of 7 coins.
Nice work, Caralyn. This can be a challenging problem for students. I would suggest starting with manipulatives and not introducing a problem like this until students have a firm grasp of the different models and relationships between numbers.