When we learn about new things, we can follow an inquiry cycle, just like we do in our Units of Inquiry.   

When we start finding out about a new concept or skill, it is important not to rush into solving things with formulas. To ensure we have a good understanding, we begin using concrete materials, move on to drawing pictures and creating models and then we begin to use abstract symbols to solve problems and apply our understanding to the real world.

Most of us have heard of skills like multiplying and dividing, but that does not mean that we have mastered how to do it. 

We show more understanding if we can apply our knowledge to the everyday problems that come up in our day to day lives. ​

Tuning In

Mind Map - Create a mind map to show what you already know. Do your mind map in pencil (and date your work), so that you can add to, or change things as you find out more.

Power Up Bar - Use the self and teacher assessment sheets to show what you think your understanding is. Have you just heard about it, or have your practiced or mastered a that skill? Do not colour in the whole pyramid, unless you are prepared to demonstrate your understanding for your teacher and peers. 

Video Explanation - With the iPads, you can either film yourself using tools, or talking about, or writing on a white board, explaining what you know about your math understanding.

Finding Out

Researching Online - There are many different places online to learn about particular concepts and skills - BrainPop, BrainPop Jr, YouTube, MathisFun, etc. When we are doing any kind of online research, it is important for us to use the same process we always do. We should write down what we already know, add what we have learned, try our best to apply our understanding, write down any further questions, and, of course, site our sources. 

Try using our Standard Websites and YouTube channels to find the information you need and if you find another site that you think is a great resource, add it to the class list.

The Template below can be printed out, or you can make a copy and save it into the Math Folder on your google docs and then share it with your teacher, friends and parents.
Khan Academy Videos and Hints - Khan Academy is not just a great place to go and practice what you already know. It is a great place to go and learn new things as well. I find that watching the videos is a great start. If it is a skill I know a little bit about, I can fast forward the video to the part that helps me. If it's something that is new to me, I can rewatch the video over and over until I finally understand. The hints are also helpful when you're new to a skill. Careful when using them though, as they will interrupt your streak. Watching the videos will also help add to your point total.

Learning from an Expert - There are many experts around us - and this include more than just the teachers. Some of our friends may know a lot about a subject and they may be such experts that they are also comfortable teaching and answering questions. Some of our experts may have even filmed videos and put them onto their blogs for us to view. 

Concrete

Below are a list of Concrete Tools that you can use to help you when solving problems. This is not all the tools that are out there, but it is amazing how these tools have so many uses.
Calculator

- mostly used for assisting with computation
- more complex calculators can help with more complex mathematical problems
Ruler / Tape Measurer

- wide range of rulers used for measuring different lengths
- tools include metre stick, trundle wheel, tape measurer, etc. ​
Cuisenaire Rods

- used for problems with fractions and can assist in bar modelling 
- can also be used with problems involving the four operations and finding divisors
3D Shapes

- can be used to help categorize and name various shapes
- can be used to find volume and measure edges, surface area and to count faces
Base 10 Blocks

- helpful for understanding place value
- used as concrete tool for four operations
Scale

- wide range of scales used for measuring different weights and masses
- tools include, balance scales, and pressure scales
Fraction Circles

- used for problems with fractions 
- can also be used with problems involving ratios and percentages
Pattern Blocks

- can be used to help categorize and name various shapes
- useful for patterning, measuring, tangrams, etc.
Cards

- wide range of games can be played using cards
- useful when discussing probability
Clocks

- helpful for measuring times (stopwatches) and for solving problems
- calendars and timelines can also be used ​
Compass

- used for drawing and measuring circles
Unifix Cubes

- helpful for solving problems that involve area and volume
- can also be used for counting or fractions
Dice

- wide range of games can be played using dice
- useful when discussing probability
Protractor

- measuring tool, used to help measure angles
Paper

- always a helpful tool for recording problems
- can also be used for problems to do with shape, symmetry, measurement, etc.
GeoBoards

- helpful tool for creating geometric shapes, calculating perimeter and area, and for testing lines of symmetry
Rekenrek

- tool used to help visualize and become comfortable with numbers within 20
- helpful for seeing patterns, adding and subtracting, and seeing missing values
Counters

- helpful if they are clear plastic as they can be used with tens frames or hundreds charts
- as with the bears, they can be used for a lot of purposes, such as counting and grouping
Bears

- anything that can be counted, really (counters, money, shells, buttons, etc.)
- can be used for grouping, counting, creating arrays
​- useful with tens frames
Hundreds Chart

- finding patterns in numbers from one to a hundred
- can also be used with things like the counters to help look for patterns
​- helpful for helping with skip counting
Fraction Tiles

- like the fraction circles, these are helpful when visualizing parts of a whole
- can be used to visualize equal fractions and adding or subtracting fractions
Money

- useful tool for practicing addition and subtraction in the real world
- can be used for problem solving activities and open ended questions
MIRA Mirro
​
- for use when discussing lines of symmetry
- excellent for helping see mirror images and getting a better sense of shape and space
Tens Frame

- the perfect tool for making tens and discussing numbers to tens and twenty
- can be used along with other math tools like counters or bears 
Spinner
​
- all kinds of different spinners can be made or used
- useful when discussing probability
- good for number games
Sorting Circles

- as the name suggests, these are great for sorting and making venn diagrams
- useful when discussing changes in attributes or when creating large circles
Attribute Blocks

- different from pattern blocks as there are specific shapes and sizes
- useful for finding out about how shapes can change and looking at the features of shapes
Tangrams

- excellent for creating shapes and seeing how shapes go together
- many purposes when building and creating 

Pictorial

Drawing Pictures - Sometimes just drawing a picture of the information that we have been given is helpful when solving problems. The pictures that we draw do not need to be to scale, or even realistic. If I want to share 15 items between three friends, I can draw three stick men, and draw circles underneath each one to represent the items. If I want to build something, I can draw a picture at a smaller scale to show what it will look like. I can draw clocks, blocks, angles, buildings, shapes... you name it, I can draw it. Drawing pictures can be extremely helpful when solving problems.

Bar Modelling - Anytime we use a picture to represent something else, we are using a technique widely used in mathematics. With Bar Modelling, we draw a bar, or a series of bars, to help us solve many different problems involving the four operations, fractions and ratios. Many questions will be used throughout the year that relate to bar modelling and can be found in both the games section and in the links relating to the four operations and fractions.

Abstract

Khan Academy - The following tools are useful for practicing different questions in an abstract manner. Khan Academy is a useful tool because it supplies you with instant feedback, and gives a wide variety of questions that relate to the same skill. Make sure to sign up your teacher, friends and parent as your coach, so that they can see what you are working on and what you need help with. 

Prodigy - Prodigy is a very fun game that also involves a great deal of mathematical learning and understanding. Battle with other students and collect pets as you work on specific skills assigned by the teacher. This game is great to play on the laptop, or on your iPad. ​Like Khan Academy, make sure you sign up with the Class Code, so that your teacher can track your progress.

Applying

Problem Solving - Most math problem we see come in our day to day lives, but some we might not see. Sometimes we will see something, or hear something, and it will fill us with questions. Sometimes these questions have solutions that we can "Google," but sometimes, they are questions that can only be solved by using a bit of math.
3-Act Problem Solving Approach - One method for solving problems is called the three act problem solving approach. The three acts are detailed below:

Act One: 
What questions come to mind? 
​
Act Two:
What information is important in helping us solve the problem? 
What do we need to know? 
How can we solve this in the easiest way possible?

Act Three:
What is the answer to the question?
What if...?
​
Reflecting - When we learn about a new skill or concept, it is important that we reflect on what we have learned in order to deepen our understanding and to plan and our next steps. To reflect on some of the skills that you will learn throughout the year, use the reflecting template below.
Problem Solving Techniques - There are many different versions of math problem solving strategies, like the RUCSAC Method to the right, but most of them involve the same basic principals. 

1. Read / Listen to the Problem 
2. Turn the question into a statement
3. Find the important information
4. Model or create an algorithm
5. Solve and fill in the statement 

Trying using either of these two problem solving approaches when problems arise that you are trying to solve.