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.

An activity from Education.com

I was contacted recently by Education.com requesting that I post one of their hand-on activities. Since a component of blogging I truly value is supporting others on a similar journey, I decided to agree !

If you like the activity, you may want to check out their website, they have many more www.education.com/resources/math/


Activity : Tip the Scales for Estimation
Fifth Grade Math Activities: Tip the Scales for EstimationOkay, checking addition problems can be boring. Solving a math problem twice can be tedious. But finding the total weight of a group of family members can be hilarious, especially if your child is calculating and estimating the weight of a diverse group of subjects, like an 8 lb. cat, a 22 lb. toddler, and a 180 lb. grandpa!
  • Bathroom scale
  • Paper
  • Pencil
  • Family members

What You Do:

  1. Have your child record the weight of several willing family members. Have a scale available, if needed. These family members can include parents, siblings, grandparents, aunt and uncles, cousins and pets.
  2. Ask your child to add up the weights of all the participants to find the total number of pounds the group weighs.
  3. Using estimation, have your child check to see if his calculated results are reasonable. Suggest to your child that he first estimate the weight of each individual to the nearest ten pounds or five pounds. This is especially important if the individual is a pet. Sometimes it’s hard for kids to estimate the weight of adults. If your child’s estimation is not reasonable, suggest a more reasonable number. Then ask him to add all of the estimated numbers together.
  4. Have your child compare his estimation to his calculation. Discuss the use of estimation to verify, or check, calculations. Give examples of how this tool can be helpful in real world situations. If you’d like to extend the activity, start thinking about multiplication and division. How many cats would weigh the same a grandpa? How many baby sisters would weigh the same as Dad? Have fun calculating the numbers, and with your family, too!

For more activities:  www.education.com/resources/math/

 


Misconceptions in math

If you have visited this blog for a while, you may have noticed my continuous quest in helping children deepen their understanding in math. I share here what I do as a parent with my own children, hoping that it could help other parents as well. At home, I use games, math discussions,  explorations of word problems, etc. But I also try to identifying any misconceptions they may have in their learning.

Example.

My son Tom, 5, has learned how to count by Fives and Tens, while playing hide-and-seek with older kids.

– “Ten, Twenty, Thirty, Forty, Fifty, Sixty, Seventy, Eighty, Ninety, One hundred ! Ready or not, here I come !”.

I was quite surprised, initially, to hear him count by Ones, Fives, and Tens, as it is not a concept often mastered at a young age. So one day, as he was playing with his cars, I asked him if he could count them.

– “Sure !”, he said, pointing one car at a time, “One, two, three, four, five, six, seven, eight, nine, ten !”.

– “Could you count them by five?”, I asked

– “Sure !”, and pointing one car at a time as he did while counting by Ones, he counted : “Five, Ten, Fifteen, Twenty, twenty-five, thirty, thirty-five, forty, forty-five, fifty !”.

– “Could you count them by Tens ?”, I asked

– “Sure ! Ten, Twenty, Thirty, Forty, Fifty, Sixty, Seventy, Eighty, Ninety, One hundred !”, pointing again one car at a time.

He could root count by Ones, by Fives, by Tens up to a hundred and more. But he did not understand that counting by Fives means counting by groups of five, counting by Tens means counting by groups of tens. For him, it was just three independent ways of counting. You have ten cars when you count by Ones, fifty when you count by Fives, a hundred when you count by Tens. But since you “usually count by Ones”, you have ten cars. Seems logical in Tom’s world.

With Tom, 5, a discussion is usually the best way to assess his understanding, with a “tell me about what you are doing”, or “what does it mean to …”. With Rosie, 8, I like to use pretend-playing : she is the teacher, I am the child. I do not do it often during the school year, but Summer break is a fun time to do so. And since Summer break starts tomorrow… you should hear more about it pretty soon.

Stay tuned !

 


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 !


Back to blogging

Thanks for your patience, dear readers. The break gave me the opportunity to reflect on the purpose of this blog, and topics to share in the coming weeks/months. I am pleased to be back in the game.


And now what?

Hey there,

You may have noticed that I haven’t posted a lot  for a while.  I enjoyed updating our project Time 4 Fractions, but I need time to reflect on how to support further math instruction at home. I graduated in December with my M.Ed. in Math Elementary Education, and hopefully, a new chapter will open up soon, still connected with the topic of this blog.  So I will be back. In a little while. Until then…


Update Ending Time 4 Fractions – Problem #12 – Sharing cereal bars

My daughter and I went on a 12 week-journey last year to explore Fractions. We are doing it again this Fall/Winter. I am updating the posts, in case you want to join us this yearClick here if you want to know more about the journey and the previous problems.

Here comes our last Equal Sharing problem !


Time 4 Fractions –  Problem #12 – Sharing cereal bars

Level Yellow – 2 people want to share 1 cereal bar so that each of them gets the same amount. How many cereal bar would each get?

Level Orange – 3 people want to share 1 cereal bar so that each of them gets the same amount. How many cereal bar would each get?

Level Red – 5 people want to share 3 cereal bars so that each of them gets the same amount. How many cereal bar would each get?


Invite your child to either model the problem (with paper and scissors for instance) and/or represent the problem with a picture. If your child has learned about fractions at school, invite him/her to connect symbols to the model or picture. And as always, invite your child to share his/her reasoning with you !

The problem will lead to a answer of each person getting 1/2 of a cereal bar (level Yellow) , 1/3 of a cereal bar (level Orange) or 3/5 of a cereal bar (level Red).

problem12

Level Red – Child’s sample

This is the last problem. What can you do now ?

The goal of T4F was to provide children with opportunities to explore fractions at home, so they have stronger foundations to build up on when they study fractions at school. This is our last problem, but it does not have to be the end of our journey. The set of problems was designed to provide a wide range of answers, to explore halves, fourths, thirds, fifths and so on, so do not hesitate to go back to these problems and provide one regularly to your child, until your child figures out that “a thing shared by b people is a/b” (Empson & Levi, 2011, p25).  For instance, Problem 12, Level Orange, leading to an answer of 1/3 would be an instructive step towards Problem 8, Level Red, that leads to an answer of 2/3.

The level of difficulties can be seen as follow (Epson & Levi, 2011):

  • Equal Sharing problems that lead to a whole number (i.e. Problem 8, Level Yellow)
  • Equal Sharing problems that lead to an answer that is more than one, with the children having to decide what to do with any left over they may have (first in halves, e.g. Problem 8, Level Orange, or Problem 9, Level Yellow, then fourth e.g. Problem 9, Level Orange)
  • Equal Sharing problems that lead to an answer that is less than one (first with halves or fourths e.g. Problem 12, Level Yellow, then thirds, e.g. Problem 8, Level Red, Problem 12, Level Orange, and so on)

I am including a table summarizing the problems and set of numbers we have exploring so far, I thought it might help.

Problem Level Number involved
Problem 8 – Sharing paper Level Yellow 2
Level Orange 2 1/2
Level Red 2/3
Problem 9 – Sharing bananas Level Yellow 2 1/2
Level Orange 1 1/4
Level Red 4/5
Problem 10 – Sharing apples Level Yellow 1 1/2
Level Orange 2 1/4
Level Red 4/6
Problem 11 – Sharing clay Level Yellow 3 1/2
Level Orange 1/2
Level Red 3/8
Problem 12 – Sharing cereal bars Level Yellow 1/2
Level Orange 1/3
Level Red 3/5

Hope you enjoyed our T4F journey ! As always, I  appreciate any feedback you may have. Comment, or email at journey2helpchildrenwithmath(at)gmail.com.


Reference

Empson, S. E., and Levi, L. (2011). Extending Children’s Mathematics: Fractions and Decimals. Portsmouth, NH : Heinemann. ISBN-13: 978-0325030531.