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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Description of Student
My student is 8 years old and is currently in 3rd grade. She has always been a fast learner and grew up being tutored. She did many activities such as piano, dance, swim, and tutor before COVID. Her mom is very serious when it comes to school and homework, so Esther has been doing good in school. She is a lot better in math than in english because her mom and older sister are able to help. In math, she is very good at showing her work and explaining her thoughts step by step. When I was her teacher, I saw that she had a little bit of trouble with word problems because she didn’t know what to use to get her answer. She would end up guessing, but now as she gets older she’s starting to understand that in all means to add, is left means to subtract etc.
Esther is now learning how to multiply and divide. The curriculum is a lot slower than I remember, because by second grade I had my multiplication table memorized and we were tested on it weekly. I found that the strategies they use are different and are more about showing work than doing mental math. She’s very used to showing her work, so she finds it harder to memorize everything. I saw that she likes to draw everything out, which takes a while but at the end she does get the correct answer. It’s interesting to see how much the curriculum has changed since I was in school. I think Esther makes a good math student and she improves everyday. She practices a lot and always tries her best to completely understand the material. There are times when she will rush to just get it done, but she will still make sure that she is solving the question correctly.
Victoria has full pencil case for the first day of school. Mom have bought her 12 pack of markers, but she share 5 markers with her classmate for the school project. How many markers does Victoria has have now for her school project?
Type of question: Separate (Result Unknown)
Solution
12-5= ?
Victoria has 12 markers , she share (minus) 5 and will equal to 8 markers left.
Students can use cubes, they can also draw a picture of the markers, or use actual markers to show having 12 and taking away 5
Word Problem: Ayla took 15 minutes to walk to the bus stop from her house. She then rode the bus to her school. Ayla arrived at her school and she took 40 minutes to get there since she left her house. How many more minutes did she took riding the bus to her school?
->This word problem would be a Join: Change Unknown question because we need to add how many minutes together in total Ayla had taken to get to her school. The change is unknown since we only know how long Ayla took to walk to the bus stop, but we don’t know how long Ayla rode the bus for to get to her school. The question would show out as 15+__=40, and to solve this word problem, we can draw out small circles as a strategy. First, we draw out 15 circles + ? = 40 circles, and then in the total of 40 circles, we can cross out 15 circles to see how many circles are left by counting them. This shows subtraction, and students can see what circles they have left. They can also recount them and include the 15 circles, to show addition where both equals to 40. It would show both the relationship between addition and subtraction.
Great work, Alison. This could certainly be a join problem, but I might also classify it as a part-part-whole. As you prepare to introduce this problem to your students, you might want to prepare for both. I would also give students the opportunity to solve this problem with unifix cubes or another manipualtive of your choosing. What grade level are you planning this activity for? As it is currently written, it would probably be second grade, since the numbers are quite large.
Clare is learning to swim. She is told that in order to do butterfly, she needs to do 2 small kicks and then one big one to bring her body out of the water. She does 6 big kicks to get to the other end of the pool, how many small kicks did she do? Rate, multiplication. The method I would have them put 2 counters in each of the 6 circles, and then count the circles. This allows them to clearly see that this is a multiplications since each circle is like a copy of itself multiple times. I would either doo it in work stations or have them draw it out on their own. (and the answer is 12 small kicks for every 6 big kicks)
Great work, Claudia. This is a very creative problem. I agree that it is a rate (or a proportion) word problem. I might suggest to students that they act out the problem if they get confused. This is because some of the language might be new to them. You might also want to show a video of someone doing butterfly kicks as a way to hook the students and help them understand. From there, it might be easier for them to draw out the problem.
Grade Level: Kindergarten or First weeks of First Grade
Linda has 3 notebooks. Her mom buys her 3 more notebooks. How many notebooks does Linda have now?
Question type: Join: Result Unknown
Process of Working this out
3+3= ?
N N N + N N N = N N N N N N
3 + 3 = 6
Great work, Tasnim. In preparing to present this problem to students, you should think about what manipulatives you will have avaialble to allow students to develop a physical understanding of the structures of the problem.
Description about a student in my life
I have saw a student which was first grade in China, she was fear to study math, because she thought she was stupid in math. For each math exam of math, she always got low grades, and her parents were disappointed. But her parents didn’t give up on her. Her father has a friend who is a teacher. They invited him home and taught their daughter math. The teacher asked her why she chose “8” not “3” in a multiple choice question, she answered “because ‘8’ is more pretty than ‘3’.” I still feel funny when I recall this thing. Yes, the little girl is me. I don’t remember what the teacher’s expression looked like at that time, but he told my parents that I was not stupid, but my attention was not focused on studying when he left.
In China, people will not say you are stupid directly in front of you, but will quietly comment on you behind your back. My parents criticized me after the teacher left, because they thought I was joking while studying. Looking back now, I just didn’t understand the meaning of the questions. I knew how to calculate the operation of numbers, but I didn’t understand why some text questions should use addition instead of subtraction? Today I did Task 2. and these questions are very simple for me now, but they were difficult for me when I was in first grade. Until now, I still think that 8 is fatter than 3, which is the correct answer for me to select a pretty number who doesn’t understand the problem.
I don’t know when I started to like mathematics, maybe it was when I got a high score. When parents know that I have got good scores, they will be very happy and praise me, then I will also be very happy. As for when I suddenly understood the topic, I don’t remember it anymore. It seemed to be sudden, and it seemed to be a long process.
This is a beautiful description. Thank you so much for sharing. I hope that we can help you develop a deeper understanding of mathematical relationships so that you can help your students as well.
Ajani has 19 different Lego pieces. 8 Lego pieces are blue, and the rest are other colors. How many Lego pieces are not blue?
This question is a Part -Part Whole Problem (Part Unknown). This problem can be for 1st graders who are learning how to solve word problems by drawing pictures, and identifying what the question is asking.
Whole 19
Part 8 Part ?
8 + ? = 19
To solve this problem, students can use manipulatives such as actual Lego pieces, a Number 20 number line, or cubes.
Answer: 19- 8 = 11 or 8 +11= 19
Very nice job, Stephanie. It is especially helpful that you write about providing a number of different manipulatives to the students. Also, it seems that you are prepared to have students solve this problem as either a subtraction problem or an addition problem.
Target Grade Level: 2nd Grade
Joey needs fifty-five dollars to buy a new pair of shoes. He earns thirty-nine dollars over the weekend at his part-time job at a family diner. How many more dollars does Joey need in order to afford the new pair of shoes?
This is a compare problem where students must find the difference between the two quantities presented.
There is a multitude of strategies students may use to find the difference, the first one being breaking apart numbers to subtract. Students can break apart fifty-five into fifty and five, and thirty-nine into thirty, five, and four, to break the question down into smaller, easier to solve ones. Another strategy may be regrouping for subtraction, where students can model base ten blocks to allow for the visualization of converting a ten into ones. Finally, students may add to find the difference, where they begin at the smaller quantity (39) and count up to the larger quantity (55) on a number line.
Nice work, Danny. It is helpful that you included a number of different strategies that students might use to solve the problem. You might also want to think about ways in which students might understand this problem as an addition problem, such as 55 = 39 + ___.
In my teaching career, there is only one student I should be able to describe her as perfect. She is making very constant progress in all subjects. Her desire for learning is very surprised by me. In daily school life, she always actively asks me what the next learning task is after completing a task. Even if I think that she has completed the additional learning tasks today, she will still actively look for tasks that have the purpose of learning. For example, one day I asked her to complete the practice questions of addition. After receiving the skills of how to solve the addition problem, she completed the remaining practice questions very efficiently and found another technique to complete the practice questions. After completing the math exercises, she asked me what the next learning task was. I said you go find a toy to play with because you have completed the learning task today. My eyes followed her until I saw her consciously picking up the phonics task to practice.
Thank you for including this beautiful description of your student. 🙂
The word problem I chose was “Five families are planning to share 53 bags of vegetables from a community garden. How many bags will each get?”. This word problem was equal groups partitive, and group size unknown. This word problem will be good for 4th-grade students.
Because I teach students to solve this problem, I will list some keywords to distinguish which operation they need to use. （Key Words
Addition：Sum, And, More, Increased by ；Subtraction：Less, Difference, Decreased by：Multiplication：Of, Product, Times；
Division：Each, Per, Quotient, Shared, RationIn ）This problem we can see there have some keywords such as share and each. Then we will know this problem. We need to use the division operation to solve it. After we knew which operation we would use, I would ask students to find all the numbers in the problem. Students used to look at the Arabic numerals in the problem, but they will often ignore the number written in English. Like this problem, there is a number written in English and a number written in Arabic. The last procedure will be to taking these two numbers using the division operation to solve the problem. 53➗5= 10.6
Great work, Shiqi. I think that it’s great that you chose a word problem that has a remainder, which is an important challenge for students to engage with. Since this problem is vocabulary-rich, rather than talking about keywords, it might be helpful for students if you act out the problem with them, and/or provide pictures to show students what is happening in the problem. These strategies are especially helpful for emergent bilingual students but will help all students in the class. (Keywords can be deceiving for students, so you want to move away from teaching in this way.)
There are 10 birds sitting on a tree branch. A loud noise scares some of them away. Now there are 4 birds left. How many birds flew away?
10-__=4
(6)
This is a separate change unknown problem. You start off with ten and are left with four in the end. To visually represent this, you can start off with ten bird figures and set four aside to represent the four birds that stayed. Then you would count the other birds which are the birds that flew away.
Description of student:
My student is a six year old in first grade. He comes from a Spanish speaking family and is able to communicate in both Spanish and English. He struggled when learning how to read but he learned how to count and do simple addition and subtraction problems at an early age. He has two older sisters, one in third grade and another in seventh. He uses his fingers to count and is at grade level, academically.
Great work, Joselyne. I especially like the context of the word problem. Thank you for attaching your description of your student. Since this student is in first grade, you will want to push him towards larger numbers (within 20). Also, you’ll want to think about what next steps you will want the students to take.
Jonathan takes five books to school in the morning. He bought 3 of the books to his peers. How many books did he left?
This question is part – part – whole. We will use the total numbers of books subtract the the number that bought to peers.
5-3=?
5-3=2
I would solve this problem by drawing 5 circles, and then drawing three of them with cross to show that they gave away, and ask students how many circles without cross which means how many books left.
Great work, Shan. I would probably classify this problem as a separate problem with the result unknown. I would begin by offering students manipulatives so that they can act out what is going on in the world problem. This is easier for students than a picture, especially for their first experiences in kindergarten.
There are 20 marbles in a jar and five friends want to play with them. In order for them to receive a fair amount of marbles, how many marbles will each person get? This word problem is an equal group where the group size is unknown. One strategy to solve this is to draw out 20 circles that represent the marbles and group them equally into five groups. The word problem written out would be 20/5=?
Nice problem, Jesselli. Would this be a fair share (partitive) or measurement (subtraction) word problem? Though drawing circles is helpful, you might want to give students manipulatives of some kind – maybe even 20 marbles and some cups – so that they can work with the objects physically. This should help students develop a feel for what division of this type really means. From there, students can begin to draw out circles and distribute them to five bigger circles – one for each student.
Question: Lucas went strawberry picking and picked 10 strawberries. When he showed his mom, she said 3 of the strawberries were moldy and threw them away. How many strawberries does Lucas have left?
This is a part- part- whole question. There are two parts and a missing whole.
The answer to this question is 7 strawberries. Students would write the equation 10-3=? and would use counters or a picture to get the answer, 7.
This question would be for 1st graders. 1st graders usually start the school year with simple questions like this to develop a sense of how to subtract and what to do and then move onto to more difficult equations with larger numbers.
Nice work, Katherine. I especially like the context that you created with the moldy strawberries. I would probably classify this problem as a separate problem since the 3 strawberries are moldy and need to be thrown away. I think the counters are a great manipulative to use with the kids. You might want to think about the next steps that you would want the kids to take, such as drawing a model or writing an equation.
Noah is a six year old student in the first grade. He is Asian and has one older brother in the fifth grade. He loves Spiderman and anything Marvel. He enjoys doing fun activities and can stay occupied if the activity interests him enough. Noah loves going outside and exploring nature. He loves running around. He is very social and loves talking. He loves making new friends and can talk for days if he wants. Noah is very quick to help his classmates. If one of them is feeling sad or gets hurt, he’s always the first to go and help or comfort them. He’s very caring and accommodating to others. He’s very eager to answer questions even if he doesn’t know the answer sometimes. Sometimes he gets frustrated when he is unable to answer because the teacher doesn’t call on him, but once you explain that other students need a chance to share too, he’ll be less upset.
Noah struggles with reading, but excels in math. He has trouble reading at a constant pace. He needs to stop to sound out a word on almost every page, however, he is able to comprehend what is going on and can answer questions about the book. Noah likes to write, but needs help once in a while to get his ideas flowing. He loves math, so he is very comfortable working independently and rarely asks for help. He’d rather complete the work himself than have someone helping him unless he doesn’t understand, which is rare. He is the most confident when it comes to math. Noah can follow along with what’s happening and all the information being provided to him. He tends to answer questions too quickly and makes careless mistakes, but when told to check his work again, he’ll catch his mistake.
Owen has 8 books and Mike has 15 books. How many fewer books does Owen have than Mike?
15-8=7
Owen has 7 fewer books compare to Mike.
This is a compare problem type. The students will be using subtraction to find the unknown difference. This exercise is for first graders.
The students can use math link cubes
Owen 8 yellow cube links and Mike 15 red cube links.
📕📕📕📕📕📕📕📕📕📕📕📕📕📕📕
📒📒📒📒📒📒📒📒 | | | | | | |
Great work, Sabina. I really like the pictures that you included. I think that it might be easier to model the problem as 15 = 8 + __. Just be prepared for students to interpret the problem in different ways. Also, think about what next steps you might take to push students’ thinking.
Amy only has 1 candy, she loves candy so much, but she thought that is too less for her, so she is sad. Her brother Tom gives some candy to her, she is happy because she has 15 candies now! So how much does Tom give to her?
The question is a join problem, the key point is: Does this question use subtraction or addition? The answer is 14. I will let students think about it : They gain candies or lose candies if they are Amy. By comparing two numbers “1” and “15”, the “1” means how many she had in the beginning, “15” means what she had in the end, therefore, students will know Amy gain more. 1+?=15, so the change is unknown.
I will solve this question with candies, which is a favorite for students of 2nd grade, so they will be interested to figure out this question.
Great work, Zhenyue. It is great that you took the time to create a context that would make sense to the students. What manipulatives would you provide to help students solve this problem? How would you push them to model this problem?
Chloe went apple picking with her family. She found 12 small apples and put them in her bag. After they were done, they got to go on a very fun but bumpy hayride. 3 of Chloe’s apples fell out, how many apples does she have left in her bag?
This is a part- part- whole problem where one part is unknown. This would be for second graders because they are subtracting the double digit whole number to one of the one digit parts to find the answer. A strategy that can be used for this problem are the ten frames. Two ten frames would be drawn and the student will then draw 12 circles to fill up the frames and then they can cross out 3 to count how many remain.
0 0 0 0 0 0 0 – – – – > 0 0 0 0 0
0 0 0 0 0 0 0 0 0
12-3=?
12-3=9
I couldn’t cross out in the comments, but it would like like that in a ten frame.
Very thoughtful problem Jenny. I think that this problem would be more appropriate for first graders, who are learning to add and subtract within 20. I like the use of a ten frame, though I doubt that students would choose that strategy themselves. It is much more likely that they would use manipulatives or even drawings at this stage. Just be prepared to connect their thinking to the ten frame.
Question: Aaron received a gift of many basketball cards on his birthday. He gives nine cards to his classmate, Joseph. Now, Aaron has thirty-nine cards. How many cards did Aaron start out with?
This question is Separate (Start Unknown). The answer is 48 because you add 39 and 9 together. One strategy to solve my problem would be drawing a stick figure picture with both Aaron and Joseph. For children to “see” the problem, I would have Aaron saying “Wow, I have a lot of basketball cards” and drawing him giving nine cards to Joseph (it can be a square shaped card with a number 9 or 9 cards). Aaron then says “I have 39 cards now.” From creating the picture, students will understand that they will have to perform addition to find out the answer. Another strategy would be to use basketball cards and have students pretend to be Aaron and Joseph, which will be an engaging activity.
Afterwards, in order to write the problem in an equation, they write it as: ? – 9 = 39 with the start being blank because the question asks for it then they see that nine cards were given away, which leads to a result of having 39 basketball cards.
Michael, I think that this is a very well-thought-out problem that will be challenging for students. Using pictures is a wonderful strategy that should help all children, and especially the emergent bilingual students that we spoke about reaching in class. You could also have the children act out the problem, which should be really fun and engaging for everyone. Since this is a problem where the start is unknown, you might want to make sure not to do it until students have a number of experiences with separate questions in which the change or the result is unknown. (In addition to join, compare and part-part-whole problems.)
Also, be ready to discuss the relationship between addition and subtraction.
Logan scored 512 points. Jessica scored 249 points. How many points did they score all together?
Join
512+249= ?
There were 761 points.
Hi Jasmine, you did a join problem with the result unknown. What grade level is this for? Why did you choose the numbers that you choose? What strategies do you anticipate children using to solve this problem?
Question: Sally was walking to school and picked 7 flowers. When she got to school, her friend gave her a few more flowers. Now, Sally has 10 flowers. How many more flowers did Sally’s friend give her?`
This question is join, change unknown. We are adding the number of flowers together, but the change (flowers her friend gave her) is unknown.
The answer to this question is 3 flowers. We would need to do 7+?=10. We know that 7+3=10.
I would solve this problem using small objects, such as flower stickers or counters. I would start off with 7 counters and then see how many more I need to add. Students can also draw pictures to solve this problem.
Great work Gianna. The strategy that you choose is very clear and students would benefit from using objects. Be prepared to talk to students about the relationship between addition and subtraction.
Word Problem:
Brandon weighed 137 pounds when he was 14. He weighed 100 pounds when he was 10. How many pounds did Brandon gain?
This is a join word problem. The answer could be found by doing subtraction. 137-100=37.
Description:
A student in my life is a little boy who is 5 years old. He is diagnosed as an autistic child on the spectrum and he is very interested in academics. He loves math and writing and his alphabet. The boy is a sensory learner and he loves to imagine. I noticed he uses his fingers to count and he taps on beat to music even though he dislikes singing and loud noises. This boy is very bright and is able to learn once he is lucid but he has just as many off days as good days which makes it hard for him to learn and complete tasks because he feels discouraged when he makes a mistake even though he is very smart and he picks and choses his friends wisely.
Rebecca, thank you for posting about the child in your life. He sounds wonderful. I look forward to talking more about strategies to help him and all children in your classes.
I think the syntax of this problem might be difficult for students. You might want to start with 100 pounds and then have the sentence about 137 pounds afterward. I agree that this is a join problem, but I think a more clear equation would be 100 + — = 137. This type of join problem is a change unknown problem, which you can use subtraction to solve, but maybe it is confusing to model in that way because nothing is being lost in the problem. Be prepared to speak with children about the relationship between addition and subtraction.
There are 10 bikes outside the school. 4 bikes are red, and the rest are blue. How many blue bikes are there?
10-4= _
4+__=10
(6)
This word problem is part-part-whole because you have set up the equation by ether having the total of how many bikes there are and then subtracting 4 away because we know there are 4 red bikes, and the rest is the result. One can also solve it by using the addition by setting up the equation by having 4 bikes already + X for the unknown, and equaling it to the amount we know =10.
Great thinking, Maria. What strategies do you expect students to use in order to solve this problem? What manipulatives would you make available for them in the classroom?
Good afternoon everyone,
School is back in session. Cynthia is reading her school supply list that teacher has provided. She needs a total of 12 pencils, she currently has 4. How many more pencils does Cynthia need to have a total of 12 pencils? The strategies we can use to solve is draw a total of 12 pencils then cross out 4 because that is currently how many pencils Cynthia has which will give you your total.
✏️ ✏️ ✏️ ✏️ ✏️ ✏️ ✏️ ✏️ (✏️ ✏️ ✏️ ✏️) = 12 – 4 = 8 Cynthia would 8 more pencils.
or
you can group 4 pencils together and 4 three times.
(✏️ ✏️ ✏️ ✏️ )(✏️ ✏️ ✏️ ✏️)( ✏️ ✏️ ✏️ ✏️)
4 + 4 + 4 = 12
Hi Dawn, You wrote this problem very conversationally, which I really enjoyed. What type of problem would you classify this problem as? I think it is a part-part-whole problem, with one of the parts missing. Therefore, I think that some students will say that the equation will be 4 + — = 12. Or will represent it in that way using manipulatives. What manipulatives will you have available for students? Think about how you would show them the relationship between addition and subtraction.