Category Archives: Word Problems

Exploring word problems throughout Summer

Summer break is here, and we are back to exploring word problems regularly.

Here is a good source of word problems if you want to do the same:

South Dakota Booklet

As always with our math journeys (e.g. Time 4 Fractions or WedWordPro), I simply invite my child Rosie, 8, to solve a problem in a meaningful way to her (Cognitively Guided Instruction, Carpenter et al, 2014), and share her thinking out loud. Drawing a visual representation on paper to make sense of the problem, using manipulatives (e.g. buttons, Legos®, Base Ten block, flashcards to fold and cut, etc), writing an equation and solving the problem using a strategy of her choice, it is up to her, I just listen 🙂

Enjoy !


Reference

  • Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014). Children’s Mathematics, Second Edition: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.

Exploring fractions with “The doorbell rang” by Pat Hutchins

You may know the author Pat Hutchins and her books for young children, such as Rosie’s Thedoorbellrangwalk, Changes changes, Clocks and more Clocks, etc. I bought a few when my children Rosie and Tom were younger, and “The doorbell rang” was one of them. I had almost forgotten about them, until I recently heard Rosie, second grade, say:

“I recognize this book ! We read it in math today !”

So we read it again. The text is attractive as it includes predictable sentences that young children enjoys repeating out loud. And for older kids, the story opens the door to math. Ma made cookies for her two children, Sam and Victoria to share (equally). The doorbell rings, and two more children, Tom and Hannah come and share the cookies. As the doorbell keeps riging, more children come to share the cookies, until twelve children have to share the twelve cookies.

As I was reading the story, Rosie modeled it. She used flashcards to represent the cookies, similarly to what she has been doing with Time 4 Fractions.

  1. At the beginning of the story, Sam and Victoria gets 6 cookies each. How many cookies has Ma baked?
  2. Now that they have to share the 12 cookies among 6 children, how many cookies does each child get?
IMG_0041

6 children sharing 12 cookies equally: each child gets 2 cookies

But a fun activity we added was to twist the story a little, and work not only with whole numbers, but also fraction. You may want to give it a try. I just let my child make sense of the problem, whether using paper to cut, or buttons to count, or the base Ten Blocks. Sometimes, she connects her model to symbols she has learned at school. But the goal is to let her make sense of the problem.

  1. What if Tom does not want any cookie, i.e. three children share the twelve cookies, how many cookies does each child get ?

  2. What if Peter does not want any cookie, i.e. five children share twelve cookies many cookies does each child get ?

  3. What if Tom, Peter and Victoria do not want any cookie i.e. nine children share twelve cookies many cookies does each child get ?

IMG_0042

9 children sharing 12 cookies: each child gets 1 whole cookie, and 1/3 of a cookie (or equivalents)

I always look for opportunities for my children to have fun exploring problems, and make sense of them.  “The doorbell rang” sure is a neat book to create such opportunities.

Give it a try ! I am here if you have any questions !


WedWoPro #14 – Last one !

Every Wednesday, I give a chance to my child to explore a word problem a way that makes sense to her. And every Wednesday, I share the word problem, and my experience with you, so you can do the same ! Click here  to start from the beginning ! Hope you join us !

Here comes WedWoPro #14, that will end our journey for a little while. I don’t know if Rosie is getting tired with the end of the year but I think it is time to take a little break in word problems to come back even stronger once Summer break starts.


WedWoPro #14 – Last one

Today, you are the teacher ! Write a word problem, and I will solve it !


Sharing my experience:

Here is what I had to solve :

“Once upon a time, 6 butterflies came to have an ice-cream at a friend’s house because it was very hot outside. 4 more came at the friend’s house to have ice cream.

How many butterflies were there in total?

One butterfly left. Then, 3 more left. Then, 3 more left again.

How many butterflies were still at the friend’s house?”

I love doing this kind of task, and opening the door to creativity. It always lead to fun discussion. Today, it gave us a chance to discuss again how to select information that was necessary to solve the problem (e.g. 6 butterflies, 4 more, etc)  vs the information that was not (e.g. it was very hot outside). It was also a fun way to model how I would solve the problem, and share my reasoning, by pretending to be the kid.

Until next time !

 

 


WedWoPro #13 – Few more days !

Every Wednesday, I give a chance to my child to explore a word problem a way that makes sense to her. And every Wednesday, I share the word problem, and my experience with you, so you can do the same ! Click here  to start from the beginning ! Hope you join us !

Here comes WedWoPro #13. We will be working with time for another week. Just to show Rosie that time is not only about minutes and hours. A one-step problem.


WedWoPro #13 – Few more days !

Rosie was very excited. Soon, his grandma would come to visit.

  • “I can’t wait to see her tomorrow ! “
  • “I can’t wait to see her  ! Just 2 more days !”
  • “I can’t wait to see her ! Just 3 more weeks !”

If today is Wednesday, April 13, when is Grandma coming ?


Here is the .pdf if you want to print it out (WedWoPro13).

  • Level Green:  Grandma is coming on Thursday, April 14.
  • Level Orange: Grandma is coming on Friday, April 15.
  • Level Red: Grandma is coming on Wednesday, May 4.

As always, invite your child to solve the level of his/her choice a way that is meaningful to him/her (Carpenter et al., 2014) !

Sharing my experience:

Well, Rosie’s grandma actually arrived TODAY from France. Too much excitement around here… Will have to update the post later !

A bientôt !

Reference:

  • Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014). Children’s Mathematics, Second Edition: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.

WedWoPro #12 – You have few more minutes !

Every Wednesday, I give a chance to my child to explore a word problem a way that makes sense to her. And every Wednesday, I share the word problem, and my experience with you, so you can do the same ! Click here  to start from the beginning ! Hope you join us !

Here comes WedWoPro #12. We will be working with time this week !


WedWoPro #12 – You have few more minutes !

Rosie was reading a book about unicorns and fairies. Soon, it will be time to get ready to go to School.WedWoPro12
Her daddy said:

  • “It is 7:00. In 30 minutes, it will be time to go to School.”
  • “It is 7:00. In 15 minutes, it will be time to go to School.”
  • “It is 6:50. If you read for 20 min, you will have 15 min left before it is time to go to School.”

What time does Rosie need to go to School?


Here is the .pdf if you want to print it out (WedWoPro12).

  • Level Green:  Rosie needs to leave at 7:30.
  • Level Orange: Rosie needs to leave at 7:15
  • Level Red: Rosie needs to leave at 7:25

As always, invite your child to solve the level of his/her choice a way that is meaningful to him/her (Carpenter et al, 2014)!

Sharing my experience:

Here came a loud “7:30!” as soon as Rosie finished reading the first level. OK, Rosie, but I want more… How did you figure it out?

So she started drawing a clock, the 2 hands, writing 1 to 12 on it.

What are these numbers for ? What about the hands? How would the big hand move in Level Green? How about the little hand? In Level Orange? How could you figure it out Level Red?  And so on. And so on.WedWoPro12b

Indeed, these 3 levels took us to a fun discussion on how clock works. So engaging that I will come up soon with a post dedicated to time…. Stay tuned, I should finally have more time to write on my blog  very soon.

Until next time !

Reference:

  • Carpenter, T., Fennema, E., Franke, M., Levi, L. and Empson S. (2014). Children’s Mathematics, Second Edition: Cognitively Guided Instruction. Portsmouth, NH: Heinemann. ISBN-13:978-0325052878.

WedWoPro #11 – Exploring symbols

Every Wednesday, I give a chance to my child to explore a problem in a way that makes sense to her.  And every Wednesday, I share the word problem, and my experience with you, so you can do the same! Click here  to start from the beginning ! Hope you join us !

There are so many posts I would like to add on my blog, with sooooo little time right now. Please bear with me  ! I have a whole plan in mind of fun math to do  once we switched gear to Summer.  But until then, I may coast a little. And just take the chance on Wednesdays to try different tasks with Rosie and Tom.

Today, we started from an equation, including the symbols =, < or >, to write a story that would match it.


WedWoPro #11 – Exploring symbols

Write a story that would match the equation below:

  • Level green :       2 + ___ = 7
  • Level orange :     5 + ___ < 10
  • Level red :            ___ – 16 > 12

Sharing my experience: 

Exploring Level Orange was quite fun, as the symbol ” < ” leads to several solutions. Rosie was quite intrigued by that. I need to keep that in mind, and provide her with more opportunities like this. Stay tuned !

Until next time !


WedWoPro #10 – Doing math outside !

Every Wednesday, I give a chance to my child to explore a problem in a way that makes sense to her.  And every Wednesday, I share the word problem, and my experience with you, so you can do the same! Click here  to start from the beginning ! Hope you join us !

Today was just  too beautiful to stay inside. I changed the plan I had in mind, and decided to do math… outside. And I am so glad we did, as my 4 year old son Tom decided to join us for the first time.


WedWoPro #10 – Doing math outside

Walk around the yard, pick up some material, and  invent a story that would lead to sharing the material equally.


I am not making a .pdf file this week, the goal is for the child to create his/her own equal sharing problem (i.e. “I have found 4 beautiful rocks. How could you and your brother share them so that both of you have the same amount ?”).

Sharing my experience:

Rosie started by picking 3 leaves, and sharing them among 2 Playmobils. “Once upon a time….And so on and so on… until…. “They had to share 3 leaves, so each one would get 1 leaf. They would cut the last leaf into 2 pieces that are the same size”.WedWoPro10a

That’s when Tom made his entrance. “I want to do math, too !”

Here came 4 pinecones. And 3 dinosaurs. A story of dinosaurs sharing nicely the pinecones.

Rosie: “Wait ! I know how I can solve the problem ! Each dinosaur gets one pinecone. And there is one pinecone left because I am not sure how to cut a pinecone”.

Tom: “Do you want a saw? We can cut the last pinecone in 3 pieces”.

The intuitivity young kids have in solving problems, away from symbolic,  is astonishing. Welcome aboard, Tom.

WedWoProb

Until next time !