My Mathematics Digital Portfolio Marissa Di Camillo
Math Curriculum
The Ontario Curriculum Mathematics 1-8. Ministry of Education. Retrieved From: https://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
Number Sense and Numeration: Number sense refers to a general understanding of number and operations as well as the ability to apply this understanding in flexible ways to make mathematical judgements and to develop useful strategies for solving problems. In this strand, students develop their understanding of number by learning about different ways of representing numbers and about the relationships among numbers. Geometry and Spatial Sense: Spatial sense is the intuitive awareness of one’s surroundings and the objects in them. Geometry helps us represent and describe objects and their interrelationships in space. A strong sense of spatial relationships and competence in using the concepts and language of geometry also support students’ understanding of number and measurement. Spatial sense is necessary for understanding and appreciating the many geometric aspects of our world. Insights and intuitions about the characteristics of twodimensional shapes and three-dimensional figures, the interrelationships of shapes, and the effects of changes to shapes are important aspects of spatial sense.
Data Management and Probability The related topics of data management and probability are highly relevant to everyday life. Graphs and statistics bombard the public in advertising, opinion polls, population trends, reliability estimates, descriptions of discoveries by scientists, and estimates of health risks, to name just a few. In this strand, students learn about different ways to gather, organize, and display data. They learn about different types of data and develop techniques for analysing the data that include determining measures of central tendency and examining the distribution of the data.
Measurement: Measurement concepts and skills are directly applicable to the world in which students live. Many of these concepts are also developed in other subject areas, such as science, social studies, and physical education. In this strand, students learn about the measurable attributes of objects and about the units and processes involved in measurement. Students begin to learn how to measure by working with non-standard units, and then progress to using the basic metric units to measure quantities such as length, area, volume, capacity, mass, and temperature. Patterning and Algebra One of the central themes in mathematics is the study of patterns and relationships. This study requires students to recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of real-world phenomena that exhibit observable patterns. Young students identify patterns in shapes, designs, and movement, as well as in sets of numbers. They study both repeating patterns and growing and shrinking patterns and develop ways to extend them. Concrete materials and pictorial displays help students create patterns and recognize relationships. Through the observation of different representations of a pattern, students begin to identify some of the properties of the pattern.
Integers Julia 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.
My reflection: Julia’s activity is one that still stands out to me even after seeing all of the rest of my peers’ presentations. She made a great lesson, and created a deck of cards that were really big where the class can easily see and enjoy manipulating them. Her card game activity was quite challenging so I would use it with older grades that are more experienced with addition and subtraction.
Decimals
Making Math Meaningful to Canadian Students, K-8: Marian Small October 2nd, 2015, Mariska Ceci Target Grade Level: Grade 4/5 Curriculum 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 whole For example: Pumpkin Drawing in 0.72 of a whole - Orange = 0.60, Green = 0.02, Black = 0.10 à 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)
My reflection: Mariska had a fun activity that was cross-curricular with math and art. By using given numbers we were told to draw a picture of a pumpkin on grid paper. Using specific colours we then filled in the boxes that added up to the certain decimal number for that assigned colour. This activity taught us how to see decimal numbers from a whole, and how we can represent them in different ways. I would use this activity for younger students’ as it was not too complex of an activity.
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.66 Demonstrate an understanding of simple multiplicative relationships involving unit rates, through investigation using concrete materials and drawings p.68 Describe 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.68 Determine and explain, through investigation, the relationship between fractions (i.e., halves, fifths, tenths) and decimals to tenths, using a variety of tools p.68 Activity 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?’
My reflection: The idea of this activity is really good and if used properly can have a great outcome to it. However, in this particular lesson the presenter was given us numbers that could not work with his activity causing a lot of confusion among the class. He ended up changing the activity, which made it a simpler task (instead of increasing a picture by half its size we simply doubled it). Overall, the main concept this activity is getting to is great and demonstrates proportional reasoning really well. If done properly, this activity could be a great learning experience for the students.
LEARNING ACTIVITY PRESENTATION – Anjali Sharma
Topic: Fractions Grade Level: Grade 7 and up Mathematics 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 11.14 Date: October 2nd. 2015 Name: 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-
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, , , , , , . Addition of these fractions creates a pattern where,
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numerator and denominator increase by 2.
Type 2: Fractions with common denominator -
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, , , , , On Addition, numerator increases by
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2. Type 3: Denominator of 1st fraction is numerator of next fractionnumerator remains same and denominator increases by 2. Type 4: Improper fractions:
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, , , , . Addition shows interesting results. Here, numerator
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increases by 4 and denominator by 2.
My reflection: This presentation did a great job talking about adding fractions. By showing us the patterns the sets of fractions made allowed us to comprehend the material easier. I was able to visualize the answers. She also made it very clear about the different types of fractions and how the numerator or denominator would change upon adding them. I would definitely use this activity for students who are just learning how to add fractions and learn about the different types.
8P29 - Mathematics Presentation Date: October 9th 2015, Name: Zach Dekker, Topic: Adding and Subtracting Integers Grade Level: Grade 7, Curriculum Strand: Number Sense and Numeration Content Expectations: Quantity Relationships ● Identify and compare integers found in real-life contexts ● Represent and order integers, using a variety of tools Operational Sense ● Add and subtract integers, using a variety of tools Process Expectations: 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. Reasoning and Proving: Develop and apply reasoning skills to make mathematical conjectures, assess conjectures and justify conclusions, and plan and construct organized mathematical arguments. Reflecting: Demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem. 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 problems. Communicating: Communicate mathematical thinking orally, visually, and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions. Activity: Coin Toss Have the students toss a coin ● If the coin lands heads, they gain a point (+1) ● If the coin lands tails, the lose a point (-1) After the students have tossed 20 times, they indicate their final score Ask how many tails someone whose final score is (-2) or (+5) etc., could have tossed and why Activity Source: Small, M. (2013). Computational Strategies: Operations with Whole Numbers. In L. Taylor-Atkins (Ed.), Making Math Meaningful to Canadian Students, K-8 (2nd ed., pp. 327). Toronto, Canada: Nelson Education.
My reflection: This coin toss game was very fun and interesting to learn about adding and subtracting integers. It also taught us about odds since it was a 50% chance to land on heads or tails. This game was very useful in keeping track of a score using integers, and seeing the number go up or down depending on the toss of the coin.
Tim D’Anna
Grade 4 Math Problem: Estimating and Measuring Length Activity 17.2 with Modifications
Corresponding Strands: Measurement and Geometry and Spatial Sense (pg. 8/9) (measuring using a ruler and visualizing lengths) Grade 4 Measurement 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) 1. 2. 3. 4. 5.
Estimates (in M/CM)
Actual Height (in M/CM)
The mathematical processes • problem solving • reasoning and proving • reflecting • selecting tools and computational strategies • connecting • representing • communicating 30CM = 11.8 Inches My reflection: I thought this game was very good to test estimation skills based on measurement of an object that is not present. By using people and a measurement that is not usually used to describe the height of a person, it added an extra complexity to it. The activity was very fun to be apart of and definitely taught me a useful lesson based on measurement. I would use this activity in my placement to demonstrate how accurate or inaccurate our estimation skills are.
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, striaght 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/ segements 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.
My reflection: This activity was a good introduction to 2 dimensional polygons. If I were to use this activity it would be for younger students who are just learning how to categorize various shapes. This activity was very simple and basic which is why I would not use it with older more advanced students.
Reflections - Geometry and Spatial Sense By: 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 paper o The first flip will be vertical – leave 3 boxes between the shape and the line of reflection o The second flip will be horizontal – leave 5 boxes between the shape and the line of reflection o 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
Original
My reflection: This activity was the one I presented to the class. I thought the activity was suitable for the intermediate grades as the content related to grade 7 and 8 curriculum. The activity was fun to participate and allowed for students to learn through many learning styles. I would definitely use this activity in my placement or future as an educator.
3D Geometry: Representing Shapes Nicole 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.
My reflection: This presentation was a great way for students to work with their hands and build 3 dimensional shapes. I also liked how Nicole used isometric paper and got us to draw a cube that was 3 dimensional. I would definitely use this activity in the future, as it is a great way for students to visualize various shaped and all of the sides/ faces they have.
Algebra- Brett Arnott Target Grade Level: 5/6 Overall Expectations Recognize and represent algebraic relationships between a group of numbers Be able to write an equation representing that relationship What is Algebra? (Page 620) Algebra is generalized thinking about numerical relationships and how numbers change. Moving from patterning to algebra is a natural progression. Algebra is essentially associating a relationship rule with a pattern. Example: Take the pattern 4, 7, 10, 13, 16… Looking at this as a pattern we see the pattern as being adding 3 to each value Thinking algebraically, we can see it is multiplying its position in the pattern by 3 and adding 1 o (3n+1) when n = It’s position in the pattern § 3(1)+1 = 4 § 3(2)+1 = 7 In Algebra it is important to know the difference between variables and constants. Variables are symbols used to represent unknown or changing values used in expressions. Constants are the values in the equation that don’t change. Guess My Rule (Activity 22.10): Work in your group to determine the relationship between the input number and the output number in the table. Once you do that, try and come up with an equation to associate with that relationship (Like we did above). There is more than one solution to each combination. Input Output Relationship Equation 1 4 2 5 3 10 6 3 12 5 Extension: Now try to do the same thing for these patterns in the table. Pattern Relationship Equation 4, 8, 12, 16, 20… 3, 10, 31, 94… 1, 4, 9, 16, 25, 36…
My reflection: This presentation had a good idea, but the way it was presented was somewhat confusing. If done correctly the activity allowed the learners to create patterns using algebraic equations. This activity is more appropriate for higher-level students in grades 5 and 6 or even higher, as the equations could become progressively harder. Overall the activity is very well thought out, but should be done with caution as to give the correct numbers in the pattern, and not to confuse the students.
Patterning – Kelsey Potts 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. Color Pattern: ABC Shape Pattern: ABB Activity 22.5: Ask Students to choose a criterion from the list below for creating a pattern: • • • • •
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
My reflection: This activity was a fun way to express patterning through both colours and shapes. It allowed the learners to create more difficult patterns by combining both characteristics and making a pattern that is both shape and colour oriented. This activity was very fun to participate in, and easy to work through, as the only materials needed were the manipulative patterning shapes. Overall, I would definitely use this activity in my future, most likely with the younger grades just beginning to learn more complex patterns.
Data Management and Probability – Asma Malik Bar Graphs Activity: 19.4 (modified), page 527 of Making Math Meaningful to Canadian Student, K-8 textbook Grade: 4/5 Overall 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 2 1 2 3 4 5 6 7 8 9 10 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).
My reflection: This presentation was a great way to express the difference between single and double bar graphs. It allowed us to see why one would be used over the other and how to graph our information on a double bar graph. The activity using the dice is a great way to show students to track, collect, and graph data on their own. I would definitely use this activity in my future career.
Data Management & Probability – Mean, Median, Mode Activity Target Grade: Grade 6 & 7 Overall Expectations: • •
Grade 6: Connect and organize primary data, secondary data and display data using charts and graphs Grade 7: Compare experimental probabilities with the theoretical probability of two independent events
Specific Expectations: • •
Collecting and Organizing Data: o Collect data by conducting an experiment/survey Data Relationships: o Determine through investigation, the effect on a measure (ie. mean, median, mode)
What are Mean, Median, and Modes? • • • •
Mean = “Average number” or norm Median = The middle value Mode = Most frequent number Range = The difference between the highest and lowest numbers o Graphs are an easy way to organize data, so it is easy to understand
Activity: 20.10 Minds on: Data can be analyzed in a certain way to provide a sense of shape of the data, including how spread out they are (range, variance) and how they are centered
Using an understanding of data management, we can understand the relationship between mean, media, and mode with regards to a set of data. In your group: Explore the mean, median, and mode of data regarding shoe sizes within your table groups (regardless of gender) and discover the range. Record Data of Shoe Size Within your Group: Mean: Median: Mode: Range: My reflection: This presentation was a great example of expressing mean, median and mode. He showed us the material in a very realistic way that related to daily life. We learned why using mean, median and mode is important when analyzing data. I think this presentation was very well done, and the activity was very useful. Therefore, I would definitely use it in my future career to teach mean, median and mode to my students.
Victoria Medeiros Friday, November 27, 2015 Technology Grades 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 angles o 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/
My reflection: Using the website Kahoot would be a great way to implement technology into a math class. By using online testing that limits your thinking time, it allows the students to work on thinking quickly and logically. I would definitely use this website and activity in my classroom in the future. I think it is a great tool to utilize in not only math, but also every subject across the curriculum.
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 ,
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Ratio of Apples to Pineapples: 3 to 2 , 3:2 ,
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Ratio of Pineapples to total amount of fruit: 2 to 5 , 2:5 , Ratio of Apples to total amount of fruit: 3 to 5 , 3:5 ,
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! !
My reflection: The game that we played online called ratio stadium was very fun to play and also had a competitive aspect to it. This game taught students about ratios as well as equivalent ratios, which will help students to learn to write down the lowest one possible. The game was a great way to utilize technology and I can definitely see myself using this game in my future, along with all of the other great games we explored.
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Amberley Morris EDBE 8P29: Learning Activity Presentation Friday, November 27 , 2015 Number Sense and Numeration - Improper Fractions and Mixed Numbers Grade: 5 Content Expectations: Overall Expectations: ☼ read, represent, compare, and order whole numbers to 1 000 000, decimal numbers to thousandths, proper and improper fractions, and mixed numbers (pg. 78) Specific Expectations: ☼ represent, compare, and order fractional amounts with like denominators, including proper and improper fractions and mixed numbers, using a variety of tools (e.g., fraction circles, Cuisenaire rods, drawings, number lines, calculators) (pg. 78) Process Expectations: ☼ 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 ☼ Demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem ☼ 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 problems ☼ Communicate mathematical thinking orally, visually and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions Recall: 3 / 4 ← (3) Numerator & (4) Denominator New Terminology: Watch: “Improper Fractions and Mixed Numbers” video at https://www.youtube.com/watch?v=ggYdPef3Nuk ☼ Proper Fraction: the numerator is smaller than the denominators ☼ Improper Fraction: the
numerator is greater than the denominators ☼ Mixed Number: a whole number and a proper fraction together
Activity: Fun with Fraction Calculators ☼ Spend some time playing around with the mixed number to improper fraction calculator (http://www.calculatorsoup.com/calculators/math/mixed-number-to-improper-fraction.php) and the improper fraction to mixed number calculator (http://calculator.tutorvista.com/math/1/improper-to- mixed-fractions-calculator.html#) online, paying attention to the process (Hint: read the procedure for converting fractions beside the online calculator). Now trying converting a few on your own! ☼ In your groups, use these calculators to help you order these numbers from smallest to largest: ☼ When you think you have figured out the answer, have one member from each group write the answer on the board. The first team with the correct answer wins! ☼ Some questions to consider: which of the calculators did you use, and why? Do you find it easier to convert mixed numbers to improper fractions, or vice versa? Did using the calculators aid in your understanding of this topic? Why or why not? My reflection: This presentation had a great use of YouTube videos along with online mathematical tools such as an online calculator. Out of the two, I would prefer to use YouTube videos in my class rather than online calculators. I think the students should do the math on paper, but if they require the use of a calculator they can just use a handheld one, since technology is not always available to simply use it for a calculator.