Category Archives: Word Problems

Solve & Share #1 – Confusing dimes !

Our journey “Solve & Share” will take us to exploring math tasks and sharing some reasoning out loud. I thought the following word problem would be a good way to start as it illustrates, I hope, how much you can learn about your child’s understanding in math by just listening to him/her.

The problem was from the South Dakota Booket I discussed previously (here). As always, my child Rosie, 8, could solve the problem in “any way that makes sense to her” (Carpenter et al, 2014). She could model the problem, with manipulative, a drawing  or a trial error approach, she could use counting strategies, or number facts. As always, it was up to her.

The problem was:

Kenata has 167 coins in her jar. 50 of them are dimes, and the rest are pennies. How many pennies does she have?

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I had seen Rosie solve problems that looked similar to me. Using counting strategies and number facts. And confidence.

With this one, she froze.

At some point, she drew the picture shown on the right, with not much conviction though. Used to the Base Ten Blocks and their representation on paper, she drew the 167 coins as 1 Hundred (i.e. the “gridded square” on the top ), 6 Tens (i.e. the tallies), and 7 Ones (the little squares). She wrote an equation with the unknown number : I was kind of expecting Rosie to finish up.

But she froze again.

She tried with smaller numbers, but it did not seem to help.

I suggested another strategy she had been using successfully in the past when she is stuck : change the story. We talked about pets, dogs and cats, instead of coins, dimes and pennies. Rosie did not have any issue to solve it.

But when she went back to the initial problem, she… froze again.

We went back to her drawing. At this point, however, I noticed through her explanation that the Tens in her jar no longer represented 10 coins but… 10 cents i.e. … 1 dime. No wonder why she was confused. Dimes and pennies are so often associated to cents in word problems, that she could not see them as just coins anymore.

I could have helped her, and said “Rosie! Your Tens represent Tens of coins, not Tens of cents!”.

But I did not.

Because I rarely do. Following the steps of Cognitively Guided Instruction (Carpenter et al, 2014), I prefer waiting that it comes from her, even if it requires an additional 5-10 minutes. Or more. But little step by little step, going back and forth from her drawing to the problem, from the problem to the drawing, she saw it. At some point, she saw where her confusion came from. And provided an answer of 117 pennies almost instantly. With a priceless expression on her face.

It may take time to let a child fully make sense of a problem, or a math concept. But, to me, as a parent as much as an educator, it seems so worth it.


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 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 !