Graphing the Holidays

Teaching between Thanksgiving and the winter break can be a challenge. How do you keep your students engaged in meaningful math learning while embracing the season? Introducing graphing and data analysis might just be the answer.

Imagine starting your day in first grade with a question about favorite holiday treats. Students can answer the question and instantly you have meaningful data that can be organized into a tally chart, picture graph, or bar graph for students to analyze. Or, students can build a bar graph with post-it notes as they make their choices. Then, spend some time analyzing the results.

Ask 5th graders if they traveled over Thanksgiving break. If so, how far? Now use this data to find mean, median, and mode, or to create a histogram for students to analyze. Or, chart the temperatures over the course of a couple of weeks and use this data to create a line graph.

Third and fourth graders could tally the number of candles in their homes for the holidays and use this data to create a line plot. Fourth graders can use their line plots to explore finding the median.

Planning a holiday party? Survey the students on what should be served and what activities should be included. Students can present the findings in a graph and use the results to determine how much and what needs to be donated or purchased to make the party a success.

The holidays are a great time to share family traditions. Why not use that information to meet some graphing and data analysis standards?

For other ideas to keep students engaged in learning read Mental Math Breaks from December 2017.

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Word Problem Wednesday – Alice, Betty, & Cassie

Word Problem Wednesday was such a hit, we’re going to continue throughout the year with one problem a month.

Our problem this month comes courtesy of a 5th grade teacher who was excited that for the first time, her students understood and easily modeled this problem from the Teacher’s Guide for Primary Mathematics US Edition 5A.

Alice, Betty, and Cassie have $70 altogether. The ratio of Alice’s money to Betty’s money is 1 : 3. Cassie has $10 more than Alice. What is the ratio of Alice’s money to Betty’s money to Cassie’s money?

Submit your solutions by the end of the month!


The last problem was taken from the Dimensions Math 3A Textbook. (Click to learn more about this recently released curriculum):

Shirley Davis shared her algebraic bar model solution:

 

How did you do?

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Students Love Singapore Math!

Last May, third graders at a school in Minnesota wrote me some letters. Their school started with a Singapore Mathematics curriculum in the fall and they were just completing their first year working with the materials. I’m told that students weren’t “required” to write these.  😁

Enjoy!

 

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Throwback Thursday – Journaling in the Singapore Math Classroom

Over the summer, we thought it would be fun to run some of the most popular posts from the past. Journaling in math class has become quite popular. We’d love to hear your successes or challenges with math journals!


Journaling in the Singapore Math Classroom

Originally published 10/13/2016

Communicating mathematically is a critical skill and goal for all of our students to reach by the end of middle school. In fact, Common Core Standards for Mathematical Practices, MP3, states that students will, “Construct viable arguments and critique the reasoning of other.”

Singapore’s Ministry of Education would tell you that there’s nothing Singaporean about Singapore math.  When developing their highly successful math curriculum, they took theory and ideas from mathematicians and educational theorists around the world and put them into action.

What should a math journal look like?

I have attended many workshops and make-and-take sessions on planning and preparing for student math journals.  Many have focused on setting up the student journal with a contents page and tabs to divide the journal into “notes,” “vocabulary” and “practice problem” sections.  While this will create a journal that looks really nice, what I have found to be most effective (and one that I actually use in the classroom) is taking a simple composition or spiral bound notebook and beginning on the first page.  Students make their first journal entry of the school year on page one and continue with entries on subsequent pages. Less is more!

Here’s what a journal entry page might look like:

journal-photo

The journal entry number just grows as the year progresses.  We might come up with the title as a class, or students can create their own.  The problem in the problem box can be copied by students or printed out for students to paste in their journals.

What should students put into journals?

There are four basic types of journal entries; investigative, descriptive, evaluative and creative.

Investigative: Students explore a new concept, solve a problem and make connections to prior learning.

  • Example: Three friends share a sleeve of cookies.  Each sleeve holds 32 cookies.  If each friend eats ¼ of the sleeve, how many cookies do they eat altogether?

Descriptive: Students describe or explain a concept or mathematical vocabulary.

  • Example: Use pictures, numbers and/or words to explain a polygon.

Evaluative: Students argue for or against a strategy or solution to explain why they think an answer is right or wrong, explain their choice of strategies or justify the most efficient strategy.

  • Example: Which of the strategies discussed in class today would you use to solve 245 – 97?  Why?

Creative: Students write their own word problem or create their own number puzzle.

  • Example:  The answer is 465 lbs.  What’s the question?

Here’s a sample student  journal page (click on image to enlarge):

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When should I ask students to make journal entries?

Journaling can be a very effective tool to develop communication skills in your students.  Depending on the type of entry, you could incorporate journaling into many parts of your math day.  Open a class with an investigative entry to engage students.  Consolidate learning and reflect on thinking with a mid-lesson descriptive or evaluative entry.  Enrich students with a creative entry for early finishers of independent practice.

The benefit of journaling for the teacher is it provides a concrete formative assessment.  By evaluating student responses, you can determine their readiness to handle a new task and check for understanding of concepts.  Student journals also provide a great launching point for discussion at parent-teacher conferences.

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Check out a resource from a previous post: Singapore Math and Math Journal Writing

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Throwback Thursday – Learning from the East: The benefits of persistence

Over the summer, we thought it would be fun to run some of the most popular posts from the past. When I re-read a post from the past I always take away something different because I am in a different place with my own experience. Perhaps you are as well!


Learning from the East: The benefits of persistence

Originally published 1/13/13

Elementary Math class in Singapore by Cassandra Turner, Singapore Math Teacher, Trainer, CoachWorking with schools, teachers, and parents over the last five years, I’m often asked whether cultural differences can explain why Singapore’s students have led the world in international math standings for 15 years while US students rank no better than mid-pack.

When I visited Singapore in 2007, I learned how the country decided to focus on building strong Singaporean citizens beginning with their earliest education.  The country’s mathematics curriculum (Primary Mathematics) was developed in the early 1980s with this goal in mind. At that time, Singapore’s students were mediocre at math. Within a few years after the launch of the second edition of Primary Mathematics, Singapore’s students topped the international TIMSS study.

To me, it’s quite easy to attribute much of Singapore’s Math success to changes in how it approached education, including, most importantly, the new curriculum. Could Singapore’s culture have changed dramatically between 1984 (when Singapore’s students were ranked 16th of 26 in the Second International Science Study) and 1995 (when they ranked first in the TIMSS study)?

Today, much attention is paid to “Tiger Mothers,” who, in the words of the Economist,

“load their cubs down with extra homework and tuition to make them excel at school.”

This trend seems more recent; it’s also one which, remarkably, Singapore’s current Prime Minister wants to curtail (http://www.economist.com/node/21563354).

A more subtle consideration concerns expectations; how do parents and teachers ask students to engage in schoolwork?

I had a driveway moment this fall when NPR ran a story (http://www.npr.org/blogs/health/2012/11/12/164793058/struggle-for-smarts-how-eastern-and-western-cultures-tackle-learning) titled, “Struggle For Smarts? How Eastern And Western Cultures Tackle Learning.” The piece focuses on the importance of persistence to a student’s learning. Reporter Alix Spiegel cites several examples, then gets to the heart of the issue:

“For the most part in American culture, intellectual struggle in schoolchildren is seen as an indicator of weakness, while in Eastern cultures it is not only tolerated but is often used to measure emotional strength.”

Reporter Spiegel then chooses to NOT to choose between East and West. In this silence, though, I believe there is a teachable moment for those of us in the West.

In training sessions with teachers, it is not uncommon to encounter resistance when I advise (insist) that teachers give students the opportunity to really work on math problems. This can be a difficult skill for teachers to learn.

And if teachers are inclined to want to move their class along before giving students a chance to truly work the math, parents can worse. They are unaccustomed to and uncomfortable at seeing their children struggle, unable to finish their home enjoyment (aka homework). Parents sometimes can be too quick to either give their kids a pass (well, you have tried, haven’t you?) or demand an explanation of the teacher (why can’t my child do the homework?).

Here’s where I find that it’s critical to have laid the groundwork and properly set expectations. Teachers need patience (whew, do teachers ever need patience!). They must let their students work through problems, even if they end up struggling and having to start over. And parents need to appreciate that homework (honestly completed or struggled with) can be the best feedback loop for teachers.

Pointing at cultural differences to rationalize a lack of math proficiency in many of our students serves no one. Instead, I think there’s a lot to be gained by asking that western students work a bit more to earn some of the praise they frequently receive.

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