Math Resources – Page 14

Number Talks in the Classroom (Part 2)

November 29, 2016 by Beth Curran 3 Comments

From our previous post on Number Talks, we explained how to establish a safe and respectful classroom environment and shared examples of appropriate topics of Number Talks in Kindergarten through 5^th grade. Read Part 1.

Number Talks in Action

Environment plays a key role. Students should gather at a designated meeting area in the classroom away from writing materials or have writing materials tucked away if working at desks. I’ve allowed students to sit on top of desks just for this purpose.

The following outlines the flow of a Number Talk.

Teacher:	Students:
Teacher writes 27 + 18 on the board. “When you have found one way to solve it hold up your thumb. If you can think of a second way to solve it, add a finger.”	Holding up their thumbs if they have found a strategy to solve the problem. Adding in fingers for each additional strategy they come up with.
Teacher:	Students:
“Let’s share answers.” Teachers records all answers, right or wrong.	“48, 47, 45”
Teacher:	Students:
“Would anyone like to argue for or against one of the answers?” Teacher records strategies on the board as students share, and labels them with numbers and/or student names.	“I agree with 45 because I know I need to add 2 to 18 to make it 20, and I can get the 2 from the 27 which leaves me with 25 to add to 20, which makes 45.” “I disagree with 48 because you would need to add 30 to 18 to make 48 and you only have 27.” “I disagree with 47 because you would need to add 20 to 27 to get 47 and we only have 18.” “I also agree with 45 because I know that 20 and 10 makes 30 and 7 and 8 makes 15 and 30 and 15 is 45.” “I also agree with 45 because I know I need to add 3 to 27 to make it 30. I can get 3 from 18 which leaves me with 15 and 30 and 15 is 45.”
Teacher:	Students:
“It looks like we have 3 strategies that work to get us the answer of 45 and are able to disprove the other two answers. Can we all agree that 45 is the answers?” “If you had a similar problem to solve, show with your fingers, would you choose strategy 1, 2 or 3?” Teacher could use this time to discuss efficiency of strategies.	Students hold up 1, 2 or 3 fingers to choose their strategy of choice.
Teacher:	Students:
Teacher writes 38 + 23 on the board. “I want everyone to use strategy 3 (or other strategy of teacher’s or student’s choice) to solve this problem. “When I count down from 3, say the answer. 3-2-1…” Teacher clarifies any remaining confusion, if necessary.	Students holding up thumbs and fingers when they have solved the problem and say answer when prompted by the teacher.

Looking for a way to deepen number sense, build confidence and celebrate different ways of thinking? Then, give Number Talks a try! Please comment and share your experience.

Filed Under: Math Resources, Singapore Math Problems, Tales from the classroom, Training Tagged With: tales from the classroom

Number Talks in the Singapore Math Classroom (Part 1)

November 21, 2016 by Beth Curran 4 Comments

Mental math plays a huge role in the Singapore Math curriculum. By developing mental math strategies in your students, you are equipping them with strong number sense, a critical skill and goal for our students to reach by the end of middle school.

You can practice mental math in your classrooms with a Number Talk; a term coined by Sherry Parrish in her popular book, Number Talks: Helping Children Build Mental Math and Computation Strategies.

Establishing Rules and Roles for a Number Talk

For Number Talks to be successful, you have to establish some rules for respectful listening and productive criticism. All students need to feel safe to participate without feeling ridiculed.

Enlisting student help when generating rules allows students to take ownership of them and creates a classroom where the rules are more likely to be followed.

To generate rules for Number Talks you might ask:

What does it look and sound like when someone is being a good listener?

It’s equally important to teach students how to respond to each other in a respectful manner. In a recent post on Edutopia, Oracy in the Classroom, types of talk were artfully organized into 6 discussion roles.

During a Number Talk, students become the Builders, Challengers and Clarifiers, while the teacher plays the roles of the Instigator, Prober, and Summariser as he or she guides the discussion as the facilitator of the Number Talk.

What should we talk about?

In Kindergarten, Number Talks can focus on subitizing and connecting the pictorial to the abstract.

Thoughtful problems are used in grades 1 through 5, designed specifically to practice mental math strategies that have been introduced in class.

In Kindergarten, show an image like this and ask, “How many dots do you see?”

In first grade, show an image like this.

Or a problem like this to practice addition strategies.

18 + 5 =

In second grade, start with a problem like this to practice addition strategies.

57 + 14 =

Or this, to practice adding a number close to 100.

97 + 33

Or this, to practice subtraction strategies.

43 – 28 =

In third grade, start with this to practice mental math with multiplication.

14 x 3 =

Or this to practice mental division.

42 ÷ 3 =

In fourth grade, start with problems like these to build on strategies learned in the previous grades.

499 + 137 =

138 – 56 =

In fifth grade, start with problems like these to continue to build on strategies learned in the previous grades.

1388 + 2983 =

29 x 7 =

135 ÷ 5 =

Give some of these a try and check back soon for the next installment of Number Talks in the Singapore Math Classroom.

Look for Part 2 next Monday!

Filed Under: Math Resources, Singapore Math Problems, Tales from the classroom, Training

Journaling in the Singapore Math Classroom

October 13, 2016 by Beth Curran 1 Comment

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:

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):

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.

_____________

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

Filed Under: Math Resources, Tales from the classroom Tagged With: math journals, Singapore Math curriculum, tales from the classroom

Math On-A-Stick: New Favorite at Minnesota State Fair

September 2, 2016 by Cassy Turner Leave a Comment

$math-on-a-stick$ Those who talk to me for any meaningful amount of time usually are quick to detect an accent, and most can attribute it to the Upper Midwest. I’m a native of the Twin Cities, and “How to Speak Minnesotan” is the most widely lent title in my sizable collection of books.

I love to return home anytime (yes, even in winter), but especially at this time of year when the Minnesota State Fair is open for a 12-day run.

Minnesota State Fair is the oldest, best most incredible fair in USA

https://t.co/zLptVMw4Tp

— Andrew Zimmern (@andrewzimmern) August 28, 2016

Fate or Coincidence

$MN State Fair: Cheese Curds$ This year, four Minnesota schools booked training in mid- to late-August, giving me the opportunity to visit “The Great Minnesota Get-together” for the umpteenth time! Yes, I was excited to see Bob’s Snake Zoo (where I worked a long, LONG time ago) and the 4-H displays, the Miracle of Birth barn and Machinery Hill, and to dine on BOTH cheese curds and the fresh, roasted corn on the cob.

But this year, I couldn’t wait to visit a new attraction: Math On-A-Stick*, the brainchild of educator Christopher Danielson. Inspired by the Fair’s literacy-oriented “Alphabet Forest,” Danielson approached the Minnesota State Fair Foundation to ask about hosting a similar experience with a focus on mathematics. The Foundation liked the idea and Math On-A-Stick debuted at the 2015 State Fair. Here’s a short description from the Fair’s website:

The Math On-A-Stick experience is a welcoming space where kids and grown-ups can explore fun math concepts at the fair. Play with geometric and reptile-shaped tiles to create designs and patterns. Sort, count and look for what’s the same and what’s different in groups of colored eggs on captivating cards. Take a break from the hustle and bustle of the fair to enjoy a shapes or numbers book

It was wonderful to spend time at Math On-A-Stick with Christopher, volunteers staffing the exhibit and especially children so engaged by all the hands-on activities available.

Below are some images showing kids (and adults) digging into math.

$Math On-A-Stick: Lizards$ Math On-A-Stick: Lizards

$Math On-A-Stick: Pentagons$ Math On-A-Stick: Pentagons

$Math On-A-Stick: Tiles$ Math On-A-Stick: Tiles

$Math On-A-Stick: Spiral$ Math On-A-Stick: Spiral

$Math On-A-Stick: Danielson$

Cassy with Math On-A-Stick Mastermind, Christopher Danielson

Christopher Danielson is host of the Talking Math With Your Kids website and author of the forthcoming book, Which One Doesn’t Belong? (Of which I have pre-ordered and am anxiously checking the mailbox for.)

—

*The Minnesota State Fair is famous for the variety of food (and other things) served On-A-Stick: more than 90 vendors [link: http://www.mnstatefair.org/find/food/index.html?category=40&keywords=&-search=Search] offered such items this year.

Filed Under: Math Events, Math Resources Tagged With: Math Events, news

“Summer Math” Suggestions to Boost Student Understanding

June 23, 2016 by Beth Curran 4 Comments

School is out and summer is calling, but for many teachers and administrators, summer is a time to take stock and plan and budget for next year.

As a teacher, this is a glorious time of year, but also one of worry. I worry about my students. I worry about those who needed extra support throughout the year understanding and retaining math concepts. How will they fare next school year? Will they regress over the summer months if they don’t do any math work?

There are three categories of students who benefit most from summer math work:

Those who have struggled all year and maybe never quite achieved mastery on those critical grade level concepts,
those who easily forget concepts, and
those whose math confidence could use a boost.

With a Singapore Math program, there aren’t many ready-made options to pick up at the local bookstore. Books that are available focus heavily on procedural understanding rather than underlying math concepts. So what’s a teacher to do?

Aside from recommending tutoring, I have found a couple of options that seem to meet my needs as a teacher and the needs of my students.

Workbook Work

For those looking for a paper and pencil option, I recommend the Extra Practice books from Singapore Math’s Primary Mathematics series. Students should work at the grade level just completed (a rising 3rd-grade student should do summer work in the 2^nd grade Extra Practice book).

The Extra Practice books offer parents and/or tutors “Friendly Notes” at the beginning of each unit that explain how to re-teach concepts in a way that is familiar to the student. The notes are followed by practice pages that give parents sample problems appropriate for practicing the concepts and the student an option of working through problems independently. Best of all, they include an answer key in the back so parents can check work and students can re-work problems, if necessary.

These books are written to cover a year’s worth of concepts; I am by no means suggesting that a child complete the entire book over the summer. Teachers recommending this book will need to tailor the tasks to meet each student’s needs. This can be as simple as highlighting the contents page to include units or pages that you would like the student to complete over the summer keeping those critical concepts in mind.

Another option for summer work can be found in online programs. I have come across three online options for concept practice; Primary Math Digital, it’s twin Math Buddies and a program new to the US market, Matholia.

Online Options

Primary Math Digital (Free 15-day trial) and Math Buddies (Also a free trial) are backed by Singapore Math’s Primary Mathematics and Math in Focus series. Both offer students video tutorials that can be viewed by the student (and parent) an unlimited number of times. These videos are scaffolded to follow the pictorial and abstract progression of learning.

Teachers can assign videos, practice and assessment tasks f $Math Buddies$ or students to complete over the summer at their own pace. The practice pages can be a little challenging to navigate, but with some initial guidance, students should be able to complete the tasks independently.

Both programs require the school to purchase annual student and/or teacher accounts to gain access to the library of lessons. There are Homeschool accounts available. Expect a price tag of around $30 per student depending on the number of accounts purchased.

Another, more affordable option new to the US market is Matholia. Matholia was developed by two teachers from Singapore and has been used by teachers and students in Singapore as well as several other countries. This program also includes a library of video tutorials, practice and assessment tasks as well as fact fluency tasks and games.

The videos are easy to understand and are also strategically scaffolded for student understanding. The practice and assessment tasks are intuitive and easy for students to navigate. As with the other programs, teachers can assign tasks for students to complete over the summer.

Matholia also requires the school to purchase annual student accounts (teacher accounts are free) but is much more affordable at just $8 per student.

Don’t forget the concrete…

I can’t go without saying that any of these options will give students practice, but struggling students need more than just extra practice working through math problems. They need more time in the concrete phase of learning using manipulatives; base-ten blocks, place value chips, model building with connecting cubes or paper strips, fraction strips or circles, etc. So, please, consider not only sending these students home with books and login IDs but also with a bag of manipulatives for hands-on learning and practice.

Now…back to dreams of lazy mornings and time to relax and recharge. Have a great summer and rest assured that your students will be prepared for the next grade with a little summer math work.