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Tuesday, 13 November 2018

Math Tools

By Julie Julian, Instructional Coach
Guided Math & Running Record, CRC Session with Dr.Nicki Newton




Math tools help students scaffold their thinking. All learners should be able to access them at any given moment, regardless of grade level.

“Good problem solvers usually construct a representation of the problems to help them comprehend it “(van Gardener & Montague, 2003), but representing mathematical information visually does not come naturally to most students. Visual representation should be explicitly taught and then practiced using a variety of tools.

Both hands-on manipulatives and virtual tools:

·        Help convey concepts
·        Help visualize mathematical ideas
·        Model number relationships

Classroom Manipulatives

Manipulatives Tip Sheets http://www.edugains.ca/newsite/math/manipulative_use.html
The tip sheets for each of the listed manipulatives include a description of what they are, how they can help students, how many are recommended and sample activities. Unfortunately, many of the weblinks at the bottom of these PDF files aren’t active, but the tip sheets themselves are very helpful.

Geoboards (pdf)
Tangrams (pdf)

Beaded Number Line

Have each student created a 100-bead beaded number line alternating colours every 10 beads This can be used for counting, skip counting, place value, rounding, adding, subtracting, number patterns, multiplication, division, and decimals.















Virtual Manipulatives

There are lots of fantastic interactive virtual math tools and apps for Smartboards, computers, tablets, and phones.

Graph Paper:

Number Frames:

Cuisenaire Rods:

Fractions:

Geoboards:

Number Line:

Rekenrek (number rack):

Pattern Shapes:

Wednesday, 7 November 2018

Problem Solving in Math


By Darla Milford, Instructional Coach
Running Record, CRC Session with Dr.Nicki Newton


Real World Connection:

Problem solving in math should not be taught separately from the mathematical skills, processes, and understanding.  In fact, according to Dr. Nicki Newton, everything ‘math’, should be attached to the real world with a story attached to it.   In order to intellectually engage our students in math, it is essential we approach problem solving from a real world context with personalization being key.  

On Dr. Newton’s Guided Math Blog, she quotes Bailey saying students “don’t care how many apples
Bob gave to Suzy. They’re much more interested in things like music, video games, movies, trading
cards, money, and friends” (Bailey, 2002, p. 61) so make it personal!!!

Here are some sites with engaging problems ready to use with your own students:



Cue Words/Keywords
We often fall into the trap of teaching our students to pick out ‘cue words’ or ‘keywords’ within a
problem to figure out the answer.  Some of these words may include ‘how many in all’ referring to
addition or ‘what is the difference’ suggesting subtraction. This strategy is essentially a quick ‘trick’
to help students solve the problem but it is important not to focus entirely on keywords without
considering the contextual information within the problem.  Focusing on words alone takes away
from the mathematical reasoning and understanding that is required in higher level or multi-step
problems students will encounter as they move forward in math.


Here’s an example:

Joe has 8 marbles, which is 2 times more than his brother. How many marbles do they have
altogether?

If kids focus primarily on key mathematical vocabulary, it may lead to a misunderstanding that the
term ‘times’ means that we multiply 8 X 2, when, in fact, if you read the problem in context you will
figure out that you already know that Joe has 8 marbles but you need to figure how many marbles
Joe’s brother had before adding these numbers together to get our answer.

Joe-8 marbles
Brother-½ of Joe’s 8 marbles = 4
So,
8+4=12 marbles altogether












Open-Ended Problem Solving
Dr. Nicki Newton emphasizes that math is best learned in contextual situations and that it is
important to provide opportunities for kids to demonstrate their mathematical understanding through
the use of ‘Open’ word problems.  ‘Open’ word problems are just that, open-ended, with a variety
of questions that could be asked as well as proven.  She suggested using a ‘3 Reads Protocol’
reading strategy to help make the problem more about the math than the reading  component.

Here’s an ‘Open’ problem example using the ‘3 Reads Protocol’ Reading Strategy.

The Smith Family Vacation Problem

The Smith family went on vacation. They drove 201 km on Monday, 177 km on Tuesday and 99 km
on Wednesday.

Write a story problem that includes the information given with an answer that makes sense.

When using this strategy, which can be used for whole group or guided math instruction there are 3
steps:

  1. Begin by reading the problem altogether out loud.

     2) Reread the problem altogether again, this time, unpacking the math.

     3) Read the problem a 3rd time and have students create possible problems linked to the  
information and have them figure out the answer.

Here is an interesting article about open-ended questions and the value in having students write their
own problems to increase engagement and metacognition.  

Dr. Nicki Newton’s authentic approach to teaching math problem solving in real world contexts makes

sense.  When students are connected to their learning and they can see the implications in the world
around them, they become much more invested.  Make sure you check out Dr. Nicki’s blog and if you
have any questions about her material, be in touch with the Instructional Coach in your building!

Thursday, 1 November 2018

What Exactly is Math Fluency Anyways?

Written by Shelly Read, Curriculum & Instruction Facilitator
"Guided Math and Running Records" session with Dr. Nicki Newton through CRC

A few years ago, as part of our curriculum redesign journey, I had the opportunity to meet with math professors from the University of Lethbridge to discuss student learning. The conversation centred around their valid concern that students were struggling in university math courses, mainly due to a lack of number fluency. As Bjorklund et al found back in 1990, “student brains are exhausted with these ‘small things’ and so can't work on the more complex problems”. This conversation has stuck with me and is one lens I use when designing math with a focus on conceptual learning. Although we know not ALL students go to university,  we also recognize the importance of understanding numbers in our everyday lives and the world of work.


So, what are these ‘small things’ that provide evidence that students know and understand
the ‘basics’ of basic facts?


There are four pillars around math fluency that teachers should consider:


  1. Automaticity
  • Can students recall the answer instantaneously or do they have to stop and
think?
  • As a general rule, automaticity is answering in 2-3 seconds without thinking
about it or hesitating.
  • No actual timer should be used by the teacher.

  1. Accuracy
  • Teachers should consider both a student’s oral and written responses.
  • Does the student self-correct if they provide an incorrect answer?
  • Be aware of counting strategies a student may use to solve facts mentally,
such as finger counting or counting in their head.


  1. Flexibility
  • Flexible thinking about numbers reveals a student’s depth of understanding.
  • Does the student have a variety of strategies at their disposal?
  • Teachers and students, as mathematicians, should know the names of the
strategies they are using.


  1. Efficiency
  • Students have a repertoire of strategies to choose from and choose the best
one for the situation.

  • Students may have more developed strategies but often resort back to simple
methods.

  • Both the teacher and the student should monitor progress and use of the most
appropriate strategies.


Together, these four criteria are used by students when they develop their individual
mathematical disposition. Having math talks with individual students is invaluable, as it
“provides teachers with a richer portrait of who they are helping to learn.” (p. 17)




In her book, Math Running Records in Action,Dr. Nicki Newton has created a framework
teachers can use to assess basic fact fluency that goes beyond memorization or speed and
instead helps to make students’ thinking visible by providing evidence of the child’s
computational thinking. “Designed to go way beyond merely capturing answers, these
assessments reveal how students are arriving at solutions, where they are breaking down,
and how they feel about themselves in the context of math. Ask yourself, can a timed test
do all that?” (page xiii)

Monday, 29 October 2018

Math Thinking Routines at your Fingertips!

Written by Lindsay Brooks, Instructional Coach
Workshop: “Guided Math Instruction & Running Records” with Dr. Nicki Newton


"Routines must be student-centered and student-friendly."
(Sanchez, 2010)


Once students learn“Math routines” they become quick to begin and practice! They allow students tohang out with numbers and get on friendly terms with them throughout the day, week and year!

Do a series of energizers and daily routines that build skills throughout the school year like:
→ number talks
→ number of the day
→ fraction of the day
→ decimal of the day
→ calendar math etc.

What they are:
Math routines or “energizers” are a way to get the whole class involved in developing number sense. The routine means students can perform it independently. They are meant to be low floor, high ceiling so there is multiple entry points for all learners.

There are a variety of different types of routines that can be used to help with the following:


1) Build Number Sense
2) Build Vocabulary
3) Build Conceptual Knowledge
4) Build Mathematical Modeling Skills
5) Build Procedural Fluency
6) Build Strategic Competence
7) Build a Strong Mathematical Disposition



Math Routines can be used any time once the students are familiar with them and are usually QUICK lasting 5-10 minutes.

They offer the opportunity for FLEXIBLE grouping and can be set up in a variety of ways including:

  • individual, 
  • partner, 
  • small group  
  • whole class



A favourite daily routine “Counting Around the Room”-
Dr. Nicki’s Guided Math Blog

Counting around the room can be really fun and works in all grade levels.
The count differs according to the grade level. In the primary grades you are counting by 1’s, 2’s 5’s and 10’s.  In the upper elementary grades you are counting by multiples, fractions, decimals and percents.
Remember that the FOCUS is on the relationships of the numbers!
So for example, count around the room by 5’s and then by 10’s.  Ask the students to talk about what they noticed. Have the students count by 2’s and then ask them where they think they will land if they count by 4’s given the relationship between those two numbers.  Have the students count by 1’s and then ask them where they think they will land if they count by halves.

Here are a few questions to consider about this routine:

1. What are your scaffolds, so everyone has a way into the activity and can experience success?
2. Is your numberline out, visible and accessible?
3.  Does everyone have their own number line?
4.  Is your numbergrid out, visible and accessible?
5.  What other models and tools might the students use to access the count?
More Energizers...
Rule of the Day.  The teacher states a rule like:
  • Doubles
  • Doubles Plus One
  • Half Facts
  • Ten More
  • Ten Less
  • Multiples
Playing the game: The teacher says a number and the students have to answer following the rule.  For example, if the teacher said, the rule is “Half Facts” the starter number is 20 then students would say 10, 5, 2.5 depending on the grade level.  If the prompt is doubling and the starter number was 50 the students would say 100,200,400 etc. This can be a fun, energetic, academically rigorous game that gets students very flexible with math facts.  Look at your math curriculum and pick your rules based on what the students need to know!
Think Math! logoSee Think Math! For more
1. Half It!  Teacher gives an even starter number.  Kids verbally toss it around the room- each child halving it until you get to the first odd number.  So for example,
Starter number 20 – Trevor says 10 – Lisa says 5 – we stop.
Starter number 200 – Michael says 100 – John says 50…they keep going till they can’t go anymore
Starter number 1/2 – Troy says 1/4 – Trina says 1/8 ….
2. Double It!   Teacher gives a starter number and kids verbally toss it around the room…this time doubling the number.
3.  Number Line It! –  Draw an unlabeled number line and then have the students plot numbers. Teacher says…draw a numberline…start it with 500 end it with 1000…write where 650 is…write where 899 is….
Teacher says…draw a numberline…start with 2/3 and end with two and a half…write where one and a half goes…write where 1 and 3/4 goes… write where 2 goes
A few other Recommended Resources:
***In many cases you have to copy the link and paste it into the url because it is a pdf and it won’t hyperlink.***


Dr. Newton is also an active pinner (https://www.pinterest.com/drnicki7/) and

Tweeter @drnickimath