Mathematics for Teaching Portfolio:

Mr. Heartwell

EDBE 8P29

During this math class, we went over the many different strands within the

Ontario math curriculum. We went over the five strands within the curriculum;

Number Sense and Numeration, Measurement, Geometry and Spatial Sense,

Patterning and algebra, and Data Management and Probability. Each strand was

then reinforced by our colleagues; going over fractions & decimals, integers,

proportional thinking, patterning & algebra, geometry, measurement, data

management & probability, and technology. All of these topics are covered within

the five strands of mathematics respectively, and the resources were collected from

our colleagues provided within their presentations regarding their topics.

The Big Ideas:

Number Sense and Numeration:

The first strand within the Ontario Math curriculum is Number Sense and

Numeration, which is overviewed within the grade levels 1-8. This strand includes

fractions, decimals and whole numbers, multiplication of fractions and decimals,

integers, and proportional relationships. Number Sense and numeration requires

understanding relationships, having an operational sense, and knowing

proportional relationships. It refers to a general understanding of numbers and

operations as well as the ability to apply this understanding to mathematical

judgments on the reasonableness of the answer

Measurement:

The second strand within this Ontario Math curriculum is measurement,

which can be demonstrated by the presented topic of measurement. This strand

includes metric units of area, volume, capacity, estimation, and the use of various

different tools. The main topic within this strand is measuring attributes, including

the area of an abject, and the volume of a prism. Measurement concepts and skills

are directly applicable to the real world, learning about the processes and units

involved in measurement.

Geometry and Spatial Sense:

The third strand within this Ontario math curriculum is Geometry and Spatial

Sense. This strand is concerned with understanding geometric properties,

relationships involving lines, triangles, polygons, and relating them to the Cartesian

planes. The most important topic I found was being able to make connections

between transformations and the real world. Geometric properties, relationships

and location and movement were the topics that our colleagues went over. Spatial

sense is the intuitive awareness of one’s surroundings and the objects in them.

Geometry helps us represent the geometrical properties of a shape, and their

relationships in space.

Patterning and Algebra:

The fourth strand was patterning and algebra, representing linear growth

patterns, using graphs, algebraic expressions, and equations. This strand requires

the student to recognize patterns and apply them to previous knowledge and a real-

world application. The students describe, and generalize patterns, building

mathematical models to simulate observable patterns.

Data Management and Probability:

Data management and probability requires the students to recognize,

describe, and generalize patterns and build mathematical models to simulate the

behaviour of a real-world application. The students had to connect with previous

knowledge and organize the information given, in order to find the mean, median,

and mode of the data. These students also had to organize the data given in order to

find the probability within a data set.

Mathematical Process

The mathematical process has the ability to support effective learning in

mathematics through:

- Problem Solving

- Reasoning and Proving

- Reflecting

- Selecting tools and computational strategies

- Connecting

- Representing

- Communicating

Problem Solving:

Central to learning mathematics. Learning to solve problems, through problem solving, connecting to the real-world. Students increase their opportunity to use critical-thinking-skills (estimating, and evaluating)

Reasoning and Proving:

A deeper understanding of mathematics by making sense of the learning. The process involves exploring, developing, making mathematical conjectures, and justifying their results

Reflecting:

Reflecting right after the students have completed an investigation. The students share their strategies, and defend their procedures they used.

Selecting Tools:

The students have a lot of tools to use, when solving mathematical processes. Students develop the ability to select the right tools, to perform particular math processes.

1. Number Sense and Numeration

2. Patterning and Algebra

3. Geometry and Spatial Sense

4. Measurement

5. Data Management and Probability

Connecting:

Refers to experiences that allow students to make connections – to see how concepts and skills of one strand of math are related to another.

Representing

Students represent their mathematical ideas and relationships and model situations using concrete materials, pictures, and diagrams to understand mathematical concepts.

Communicating:

The process of expressing mathematical ideas and understanding orally, visually, writing, using numbers and symbols, graphs and words.

LEARNING ACTIVITY PRESENTATION

Topic: FractionsGrade Level: Grade 7 and upMathematics curriculum strand: Number sense, Numeration and Patterning.Content Expectation: Adding and subtraction of simple fractions and representing the growing pattern relationship (Page no. 97)Process Expectation: (Page no. 98)

1. Problem solving- Develop, select, apply, and compare a variety of problem-solving strategies as they pose and solve problems and conduct investigations, to help deepen their mathematical understanding.

2. Reasoning and Proving: develop and apply reasoning skills (e.g., recognition of relationships, generalization through inductive reasoning, use of counter-examples) to make mathematical conjectures, assess conjectures and justify conclusions, and plan and construct organized mathematical arguments.

Source: Nelson- Making Math Meaningful to Canadian Students, K-8. Chapter 11, Activity 11.14Date: October 2nd. 2015Name: Anjali Sharma

This activity is designed to explore sums and differences of fraction that form a pattern. I worked with different types of neighboring and related fraction and found that, they were forming patterns with numerators and denominators.

Type 1: Neighboring fraction- 12,1

3 ,14 ,1

5 ,16 ,1

7 ,18 . Addition of these fractions creates a pattern

where, numerator and denominator increase by 2.

Type 2: Fractions with common denominator -28 , ,

38 ,

, 48 ,

, 58

, 68

, 78On Addition,

numerator increases by 2.

Type 3: Denominator of 1st fraction is numerator of next fraction- 12

, 23 ,3

4, 4

5 ,56

, 67

, 78 . On

adding, numerator remains same and denominator increases by 2.

Type 4: Improper fractions:32 ,4

3 ,54

, 65 ,7

8. Addition shows interesting results. Here,

numerator increases by 4 and denominator by 2.

Reflection:This presentation was a great way to explore fractions, with common denominators. This presentation was also a good way to organize fractions from lowest to greatest.

DecimalsMaking Math Meaningful to Canadian Students, K-8: Marian

SmallOctober 2nd, 2015, Mariska Ceci

Target Grade Level: Grade 4/5Curriculum Strand: Number Sense & Numeration

Activity 12.4 (pg. 285, text by Marian Small)Students can colour designs on a decimal grid and give the design a decimal value. Students can also be given a value and asked to draw something to match it. Today we will be using 3 colours to create our designs from the initial decimal value and each colour needs to be given its own decimal value.100 square grid = 1 wholeFor example: Pumpkin Drawing in 0.72 of a whole

- Orange = 0.60, Green = 0.02, Black = 0.10 Total = 0.72 of a whole

Expectations:Gr. 4 (pg. 66- 67, Curriculum)- decimal numbers to 10ths, demonstrate understanding of magnitude by counting forward & backward by 0.1, addition & subtraction of decimal numbers to 10ths- Demonstrate an understanding of place value in whole numbers & decimal numbers for 0.1 – 10 000, represent, compare & order decimal numbers to 10ths using a variety of tools

Gr. 5 (pg. 78 -79, Curriculum) – decimal numbers to 100ths, counting backward and forward by 0.01

- Demonstrate & explain equivalent representation of decimal numbers using concrete materials & drawings (0.3 = 0.30)

Reflection:This presentation was a great way to engage the students, catering to the visual, kinesthetic, and oral learners. The colouring activity was a great way to get the students engaged within the activity, and learning process.

IntegersJulia Chamberlain

October 9, 2015

Minds On: Introduction• Use a large-scale deck of cards to introduce integers and represent and order integers

by comparing them to real life tools/manipulatives. • Deck of cards: Black cards are negative and reds are positive Ace is low and equal to 1

and Jokers counts as 0.• The line simulates the number scale we use for integers and helps for visual learning

and hands on, minds on involvement activity.

Activity: Integro (Activity 14.6 in Making Math Meaningful. Ch.14, pg 327)Rules:• In groups of 2 or 4, a student shuffles and deals cards equally to their group (Using

only numbers 2-10 and Aces -- Reds cards are positives, Black cards are negative, Aces are 1, Remove face cards and jokers)

• In a round, each player places one card face up on the table.• The first person to call out the sum of the cards wins all the cards in the turn. These

cards go into the players bank pile. • Tied players play additional rounds until someone wins.• When a player runs out of cards, the player shuffles his or her bank pile and continues

playing. If the player’s bank is empty the player is out.• The game ends when one player has won all the cards.

Consolidation:Integers start to show up in the Ontario curriculum in Grade 7 and are a part of the Number Sense and Numeration stream. By the end of grade 7 students have the overall expectation to, “represent, compare, and order numbers, including integers,” and also, “demonstrate an understanding of addition and subtraction of fractions and integers, and apply a variety of computational strategies to solve problems involving whole numbers and decimal numbers.” Their specific expectations are to, “represent and order integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines)” as well as, “add and subtract integers, using a variety of tools (e.g., two-colour counters, virtual manipulatives, number lines).” This activity would ideally be used in grade 7 classrooms, where they are first being introduced to integers and how they can be represented in addition and subtraction.

Reflection:This presentation was one of the most engaging projects that I have participated in. It was a great presentation regarding a number line, being related to cards. It was a great way to use cross-curricular expectations within the classroom.

Proportional Reasoning

October 23rd, 2015 Mathieu Carrière Activity Target Grade: 4-6

Source of activity: Making Math Meaningful to Canadian Students, K-8

A couple points on proportional reasoning:

-The essence of proportional reasoning is the consideration of number in relative terms, rather than absolute terms. -Ratios are not introduced until grade 6, although they are introduced in informal ways earlier on. Example 1: Kindergarten teachers will say there are 2 eyes for every person. They are using the ratio 2:1 Example 2: A grade 2 or 3 teacher might ask how many wheels are on 5 bicycles. The students will use the ratio of 2:1 to solve the problem.

Curriculum expectations for Grade 4 Number Sense and Numeration:

Compare and order fractions (i.e., halves, thirds, fourths, fifths, tenths) by considering the size and the number of fractional p.66Demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings p.68Describe relationships that involve simple whole-number multiplication (e.g.,“If you have 2 marbles and I have 6 marbles, I can say that I have three times the number of marbles you have.”) p.68Determine and explain, through investigation, the relationship between fractions (i.e., halves, fifths, tenths) and decimals to tenths, using a variety of tools p.68Activity 13.7, p.311-For a grade 4 class, I would tell students to enlarge the picture so that it is twice as high and twice as wide.-For a grade 6 class, I could ask questions such as ‘What is the ratio of the pumpkin’s eyes?’ and ‘What is the new ratio of the pumpkin, if you enlarge it by half of its original ratio?

Reflection:

This presentation was a great way to relate integers to whole-number multiplication. This presentation demonstrated a great way to use personal-experiences, and reflections on the real-world.

Maddison Furtado 27th November 2015

Proportional Thinking: Ratios + Equivalent Ratio’s

Integrating Technology into the Classroom

Target Grade Level: Grade 6 & 7

Overall Expectations:

Grade 6 & 7 Number Sense and Numeration Pg. 88, 99

"Demonstrate an understanding of relationships involving percent, ratio and unit rate."

Specific Expectations: Proportional Relationships

"Represent ratios found in real-life contexts, using concrete materials, drawings, and standard fractional notation” (89)

"Determine and explain, through investigation using concrete materials, drawings, and calculators, the relationships among fractions,

decimal numbers, and percents” (89)

• “Determine, through investigation, the relationships among fractions, decimals, percents, and ratios” (100)

Source of Activity: Math Play Ground: An Educational Website that Includes a Variety of Math Activities and Videos

http://www.mathplayground.com

Activity: Ratio Stadium

There will be a ratio presented at the bottom center of the screen.One needs to identify the equivalent ratio, from the options presented, in order to increase the speed of the bike. If the wrong answer is chosen, the speed will decrease.

Answer as many questions as you can to win the race!

What is a ratio?A ratio is a way to compare quantities

Example:

Part 1: Pineapples Part 2: Apples

-----------------Total: All the Fruit Together-----------------

Ratio of Pineapples to apples: 2 to 3 , 2:3 , 23

Ratio of Apples to Pineapples: 3 to 2 , 3:2 , 32

Ratio of Pineapples to total amount of fruit: 2 to 5 , 2:5 , 25

Ratio of Apples to total amount of fruit: 3 to 5 , 3:5 , 35

Reflection:Maddison did a great job on bringing manipulatives and visuals to the presentation to extend student engagement. Relating fractions to bunches of pinapples was a great way to extend student understanding to the real-world.

Patterning

Activity Target: Grade 4

Source of Activity: Making Math Meaningful to Canadian Students, K-8

Curriculum Expectations for Grade 4 Patterning and Algebra:

Overall Expectations:

Describe extend and create a variety of numeric and geometric patterns make predictions related to the patterns, and investigate repeating patterns involving reflections;

Demonstrate and understanding of equality between pairs of expressions, using addition, subtraction and multiplication (73)

Introduction to Patterning:

Core: the shortest part of the pattern that repeats itself

Core

Repeating Patterns are also sometimes described using a letter code ie. AAB

Multi-Attribute Patterns: patterns that contain more than a single attribute ie. color, shape, size etc.

Activity 22.5:Ask Students to choose a criterion from the list below for creating a pattern:

Color Pattern: ABCShape Pattern: ABB

Use three colors of counters to create a pattern Create a repeating pattern that has a core of three elements Create a growing pattern where the 10th term is 100 Create a pattern that grows but not by the same amount each time Create a shrinking pattern where the 4th number is 16

Reflection:This presentation on patterns was a great way to use the manipulative, to represent patterns. It made the students use the shapes to represent a pattern. Overall, a great presentation

Julian Foglia Geometry- 2-D shapes intro

1) what is a polygon?

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Give examples:

2) Properties of polygons and different types:

Triangles- they are classified in terms of their relationship to their sides... The length of the size, the angles of each side etc.--> in the text, they mention the types of triangles:

Quadrilaterals- they are 4-sided polygons. Most common are squares and rectangles however there are many other types.

-Students must understand what properties are in polygons. They are, the traits and characteristics of each shape; angle, straight sided, curves etc. Students must list the properties of the triangles and the other shapes given.

From there we can teach them what different types of lines/ segments there are in geometry.

Parallel lines- Lines that do not meet and run in the same direction.

Intersection- the lines meet at a single point. Perpendicular- The lines intersect, but they only meet at a right angle.

Reflection:I really enjoyed this presentation, drawing polygons on the graph paper provided. This way the students can visually see a 2D or a 3D shape on graph paper. It was a great visual for the visual learners to learn from

Reflections - Geometry and Spatial SenseBy: Marissa Di Camillo

Activity Target Grades: 6 and 7

Curriculum Expectations: Grade 6 – Create and analyse designs made by reflecting, translating, and/or

rotating a shape, or shapes, by 90 degrees or 180 degrees (Pg. 93) Grade 7 – Create and analyse designs involving translations, reflections,

dilatations, and/or simple rotations of two-dimensional shapes, using a variety of tools (e.g., concrete materials, Mira, drawings, dynamic geometry software) and strategies (e.g., paper folding) (pg. 104)

Source of Activity: Making Math Meaningful to Canadian Students, K-8 – Page 397

What is a flip/ Reflection? A flip (or reflection) can be thought of as the result of picking up a shape and

turning it over. A flip is always made over a line called the flip line or line of reflection. This line

can be place horizontal, vertical or slanted. What is a transparent Mirror?

A transparent mirror is a useful tool for performing reflections. By placing the mirror in front of a shape, you can see the flip image when you look through the plastic at the other side.

Activity 16.8 – Flips (Reflections)Ask students where to put the mirror on the original shape to create the two images.

First practice flips and reflections using the provided shapes and graph papero The first flip will be vertical – leave 3 boxes between the shape and the

line of reflectiono The second flip will be horizontal – leave 5 boxes between the shape and

the line of reflectiono The third flip will be slanted – leave 2 boxes between the shape and the

line of reflection

Using the provided shapes with the graph paper, figure out where the line of reflection would be

3D Geometry: Representing Reflection:This presentation was a great way to visually represent reflections on the board, and as an activity. Involving the mirra was a great way to make sure the students can visually see the reflection, without getting the question wrong.

ShapesNicole Horlings

November 6, 2015

Activity Target Grade: 4

Source of Activity: Making Math Meaningful to Canadian Students, K-8

What does it mean to be able to represent a shape?- By demonstrating that they are able to create or draw a shape, students show that

they have visualizations skills and a good grasp of spatial sense. - Being able to conceptualize a shape and accurately draw it is important for

students to understand the relationship between 2-D and 3-D objects. - A real life example that demonstrates the importance of conceptualizing and

representing shapes is an architect who makes blue prints for buildings and needs to understand what those 2-D blue prints will look like when they become 3-D buildings.

Curriculum expectations for Grade 4 Geometry and Spatial Sense: Overall expectation:

- construct three-dimensional figures, using two-dimensional shapes (p. 71)

Specific expectation: - construct skeletons of three-dimensional figures, using a variety of tools (e.g.,

straws and modelling clay, toothpicks and marshmallows, Polydrons), and sketch the skeletons (p. 71)

Activity 15.13, p. 360

- “Use balls of clay for vertices and sticks for edges to build the skeleton of a 3-D shape” (p. 360).

- Instead of clay, I will be using mini marshmallows for this activity - I will make the students create a cube using their tooth picks and marshmallows

- Once the students have created their cubes, I will ask them to record how many edges and vertices there are

- I will also ask the students what the angles that the cube has are called

- As an extra challenge if there is time, I will hand the students a sheet of isometric paper, and have them draw an image of the cube where 3 faces of the cube are visible.

Reflection:This presentation was really fun. It however was extremely difficult to draw a 3D object on the isometric paper. Once I did this, I got a 3D shape that looked like an optical illusion. I would have used normal graph paper, so the students would not be confused.

Tim’s Presentation: My Instructions:  

1) Introduce topic (measurement of length). Length is one-dimensional. 2) Length is: assigning a qualitative or quantitative description of size to an object

based on particular attributes. In simple terms - measurements are markers that we use every day to help describe the dimensions of a particular thing (i.e. CN Tower is 553M, Toronto is about 110KM from St. Kits)

3) You’ll notice something about the measurements I just gave you: they’re widely known. They’re like benchmarks. Sometimes what we use to measure are standard measurement units, other times they are contextual (i.e. that truck weighs as much as a whale). Not perfect, but still get a sense of how much the truck weighs.

4) Standard measurements are used to simplify and clarify communication of size of objects and simplifies measurements. In other words – if we didn’t have CMs, Ms, KMs, etc… it would be difficult for us to tell others how far we are talking about.

5) You’ll notice one more thing: we are dealing in metres and centimetres; imperial (US, Liberia, Myanmar) (Wikipedia)metric (everywhere else). Who here thinks of their weight in pounds? Their size in feet & inches? (2m)

Task:1) Have five students come to the front and stand against the board (30s)

2) Line up from shortest to tallest, then estimate how tall they are in CM or M/CM (gave you a hint at the bottom of the page with inch conversion). Draw a line on the board with names while people estimate. (2m)

3) Have all students sit down; give students who volunteered a chance to estimate heights just from line on board and without a human to help them visualize); in meantime ask students to explain how they got their estimates (visualization, prior knowledge?) or ask them to describe what they see. (3m)

4) Ask for five volunteers to measure the lengths in CMs, write it on the corresponding line with their name (2m)

5) Who thinks their estimates were close? Not close? Why do you think I wanted you to estimate first? (in the real world you don’t

have a tape measure, can be quicker, what’s more important: the time it takes to measure or exact measurement?).

Do you think it was more difficult for volunteers to estimate the lengths based on the lines on the board rather than seeing a person?

Do you think it would have been more difficult to estimate height if we didn’t line them up shortest to tallest? Why

Reflection:Tim’s presentation was a great way to use a real-world application of measuring objects. It was a great representation of reflecting back on the size of every day objects. Overall, a great presentation.

Grade 4 Math Problem: Estimating and Measuring LengthActivity 17.2 with Modifications

Corresponding Strands: Measurement and Geometry and Spatial Sense (pg. 8/9) (measuring using a ruler and visualizing lengths)

Grade 4 Measurements:Overall Expectation:- Estimate, measure, and record length, perimeter, area, mass, capacity, volume, and

elapsed time, using a variety of strategies (pg. 69)Specific Expectation: - estimate, measure, and record length, height, and distance, using standard units (i.e.,

millimetre, centimetre, metre, kilometre) (e.g., a pencil that is 75 mm long) (pg. 69)

Volunteers (shortest to tallest)

Estimates (in M/CM) Actual Height (in M/CM)

1. 2. 3. 4.The mathematical processes • problem solving • reasoning and proving • reflecting • selecting tools and computational strategies • connecting • representing • communicating

30CM = 11.8 Inches

Reflection:Measuring the height of our peers was a great way to use estimation skills. It was a real-world application of height, and the process was great to estimate first, and measure last. This presentation really sparked the creative, and intellectual process.

Victoria MedeirosFriday, November 27, 2015

TechnologyGrades 4-8 (Grade 5)

Geometry and Spatial Sense

Using technology to teach Geometry: Kahoot!

Process Expectations Selecting tools and computational strategies: select and use a variety of

concrete, visual, and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problem

Communicating: communicate mathematical thinking orally, visually, and in writing, using everyday language, a basic mathematical vocabulary, and a variety of representations, and observing basic mathematical conventions

Overall Expectations identify and classify two-dimensional shapes by side and angle properties and

compare and sort three-dimensional figure

Specific Expectations Geometric Properties

o distinguish among polygons, regular polygons, and other two-dimensional shapes

o distinguish among prisms, right prisms, pyramids, and other three-dimensional figures

o identify and classify acute, right, obtuse, and straight angleso identify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral),

and classify them according to angle and side properties

Kahoot! Kahoot! is an online tool that teachers can use to create online quizzes, discussions and surveys in order to assess student learning. It is a more fun and interactive way to assess learning than the traditional method of handing out a quiz. This would be best used at the end of a unit for Assessment of Learning. A teacher can design the questions, how many answers there are, how much time there is to answer and also if it is worth points. The teacher can make this game into a challenge like I will show today or simply use it as an assessment tool. Another great aspect is the website is free to use.

Visit it at: https://getkahoot.com/

Reflection:Using technology within the presentation was a great way to promote classroom inclusiveness. This presentation was a great way to promote classroom competitiveness, without making students feel left out.

Data Management and Probability

Bar Graphs

Activity: 19.4 (modified), page 527 of Making Math Meaningful to Canadian Student, K-8 textbookGrade: 4/5Overall expectations:

- collect and organize discrete primary data and display the data using charts and graphs, including double bar graphs

- read, describe, and interpret primary data and secondary data presented in charts and graphs

What is a bar graph?A bar graph is a diagram in which the numerical values of variables are represented by the height or length of lines or rectangles (bars) of equal width and equal space between them. Single bar graph: Double bar graph:

Activity: Choose a partner and each person roll a dice 10 times. Record your data and create a double bar graph using the data collected. Step 1: Each person take turns to roll the dice 10 times. Step 2: Record each person’s dice outcomes (i.e. Student 1 may roll a 3 and Student 2 may roll a 5) in the chart below.

# of Rolls Student 1 Student 212345678910

Step 3: Create a double bar graph using the data collected on the graph paper provided. (Do not forget to label the axes and have a legend).

References:Grade 5: Making a Double Bar Graph: Introducing the Concept. (n.d.). Retrieved November 18, 2015, from http://www.eduplace.com/math/mw/background/5/06a/te_5_06a_graphs_ideas.html

Small, M. (2013) 2nd Edition. Making Math Meaningful to Canadian Students, K-8. 2nd Edition, Toronto, Nelson.

Reflection:This way of representing data collection within data management was a great presentation for bar graphs. With this visual representation was a great way to reinforce the mean, median, mode, by visually allowing the students to see these averages:

First Blog Post:

Weekly Report & Reflection

Reflection:Is there a negative viewpoint on mathematics?Overall I feel that there is an extremely negative viewpoint on mathematics. I feel this way because Math teachers often do not inspire their students, showing them the appreciation for math and instead teach the memorization steps of math. Often I feel like the Math teachers have a great concept on the understanding of the problem, but struggle with breaking down the steps and teaching the concepts. As a result of this, math students often feel like math is a foreign language, which they cannot orient themselves around.

How do I feel about mathematics?Growing up, My father was a math teacher so if I ever had a problem understanding a question I could come to him for help. I took Kumon when I was a child, and understood the basic high school math concepts, however when it came to grade 12 advanced functions/ calculus I was lost.

What strategies will I use in a J/I classroom to teach mathematics?After learning the many different styles of breaking down the math problems within the course EDBE 8P29, I would use the heuristic teaching style, allowing the students to discover or learn something themselves. I would provide the students the proper steps to complete the problem, however I would let them know there are many other ways to complete the problem.

What makes an excellent math teacher? I feel that an excellent math teacher goes over all 7 of the processes to solve a problem. These processes are; problem solving, reasoning & proving, reflecting, selecting tools, connecting, representing, and communicating.

Report:Areas of mathematics I will focus on?

The area I will focus on the most is the mathematical process. In J/I this process supports an effective learning style within mathematics. I will be particularly focused on the "Understanding the Problem", rereading and restating the problem. I will have to identify the information given and the information that needs to be determined. In this stage, most students have a problem understanding the problem, and in this stage it is extremely difficult to break down the problem into steps. I will have to talk about the problem and break it down for the students to understand it better.

Connections on Building Background:http://www.edugains.ca/newsite/HOME/index.htmlThe connection I made on this resource provided, was the revised Ontario curriculum on the Curriculum Document +. This resource was especially important when discovering the mathematical process, and the many overall and specific expectations regarding the curriculum, more specifically patterning and algebra.

Hialah Gardens. Google Images [Image]Retrieved from: https://hgms.files.wordpress.com/2014/03/math.jpg

Last Blog Post:

This week we learned about bringing technology within the classroom. The first presenter was Amberley, presenting Number Sense and Numeration, more specifically proper and improper fractions. She did a great demonstration on the

board, explaining mix numbers and explaining the different processes it takes to simplify the mixed number. I already had a strong previous knowledge regarding this topic. The group activity was ordering fractions from lowest to highest, with a list of proper, improper, and mixed numbers. What I noticed, was that I did a very different process than the majority of the class, making all the numbers mixed numbers, instead of changing the numbers too improper fractions.

Heartwell, 2015

The second presenter was Julian, presenting Geometry 2-D shapes, explaining what a polygon is:a plan figure bounded by straight line segments to form a closed chain. He handed out a bunch of pencil crayons, and were instructed to draw various shapes on graph paper. His presentation started with having students come up to the board and guess the various shapes he drew on the board. It has been a while for myself to go over my geometrical shapes, and I got a lot of them wrong. Julian then moved onto different styles of lines, parallel lines, intersecting lines and perpendicular lines.

Heartwell, 2015

The next presenter was Madison, on Proportional reasoning, Ratios + equivalent ratios, and integrating technology within the classroom. We were then asked to complete a game called ratio stadium , a game where you had to eat all of the equivalent ratios in order to move forward with the game. This was a fun game to get the class engaged, while learning the topic of equivalent fractions.

Kelsey Potts presented next, on the topic patterning. She did a great job on explaining the different types of patterning using shapes and letter sequences.

Heartwell, 2015

The last presenter was Victoria, who presented geometry using technology. She used the Kahoot, or an application that makes learning certain topics a game. She divided the class up into table groups, and the groups competed for royalty over the class. This was a great way to promote fair play, and was the most engaging way to promote classroom participation.

Thanks for listening

Reflecting back on my blog posts, I became more aware of the mathematical processes. As the weeks progressed, I included more pictures, and related more to the textbook. This process can be reflected by myself becoming a more reflective teacher, and improving myself as a teacher.