Math Portfolio Ms. Potts
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Table of Contents Big Ideas Mathematical Processes
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Activities: 1. Number Sense and Numeration
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2. Geometry and Spatial Sense
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3. Data Management and Probability
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4. Measurement
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5. and
Patterning Algebra
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Math Clip Art. 10 December 2015. Retrieved from: http://cleanclipart.com/math-clip-art/
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The Big Ideas 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 math- ematical judgements and to develop useful strategies for solving problems
Measurement Measurement concepts and skills are directly applicable to the world in which students live. Students learn about the measurable attributes of objects and about the units and processes involved in measurement
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. Patterning and Algebra Requires students to recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of realworld phenomena that exhibit observable patterns.
Data Management and Probability Requires students to recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of realworld phenomena that exhibit observable patterns.
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Mathematical Processes Problem Solving: By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect math- ematical ideas and to develop conceptual understanding. Reasoning and Proving: The reasoning process supports a deeper understanding of mathematics by enabling students to make sense of the mathematics they are learning. The process involves exploring phenomena, developing ideas, making mathematical conjectures, and justifying results. Reflecting: Good problem solvers regularly and consciously reflect on and monitor their own thought processes. By doing so, they are able to recognize when the technique they are using is not fruitful, and to make a conscious decision to switch to a different strategy, rethink the problem, search for related content knowledge that may be helpful, and so forth. Selecting Tools and Computational Strategies: Students need to develop the ability to select the appropriate electronic tools, manipulatives, and computational strategies to perform particular mathematical tasks, to investigate mathe- matical ideas, and to solve problems. Connecting: Experiences that allow students to make connections – to see, for example, how concepts and skills from one strand of mathematics are related to those from another – will help them to grasp general mathematical principles. Representing: Learning the various forms of representation helps students to understand mathematical concepts and relationships; communicate their thinking, arguments, and understandings; recognize connections among related mathematical concepts; and use mathematics to model and interpret realistic problem situations. Communicating: Communication is the process of expressing mathematical ideas and understanding orally, visually, and in writing, using numbers, symbols,
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pictures, graphs, diagrams, and words. Communication is an essential process in learning mathematics. Through communication, students are able to reflect upon and clarify their ideas, their understanding of mathematical relationships, and their mathematical arguments.
1. Number Sense and Numeration Adding and Subtracting Integers Zach Dekker October 9, 2015 Grade 7 Content Expectations: Quantity Relationships •
identify and compare integers found in reallife contexts
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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)
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If the coin lands tails, the lose a point (1)
6 • After the students have tossed 2 0 times, they indicate their final score Ask how many tails someone whose final score is (2) or (+5) etc., could have tossed and why
Adding & Subtracting Integers When adding or subtracting integers with like signs, add and keep the signs [8 + 4 = 12] [(2) + (5) = (7)] [(4) 5 = (9)] When adding or subtracting integers with unlike signs, subtract and keep the sign of the higher integer [(5)+3=(2)] [6+(3)=3] [4+(5)=(1)] When subtracting a negative, it turns into a positive and then follows one of the two rules above [7(3)=10 becomes 7+3=10] [(9) (3) = (6) becomes (9) + 3 = (6)] [(3) (8) = 5 becomes (3) + 8 = 5] Visually Representing Integers
7 I thought Zach’s activity was a lot of fun and very knowledgeable. He really went in depth with his explanation of how the unit signs can change when dealing with integers and his hand out was very helpful. I will definitely be using this in my class! It is extremely important to use visuals and the concept was easy to understand with the help of visuals.
Integers Julia Chamberlain October 9, 2015 Grade 7
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: 1. In groups of 2 or 4, a student shuffles and deals cards equally to their group (Using only numbers 210 and Aces -- Reds cards are positives, Black cards are negative, Aces are 1, Remove face cards and jokers) 2. In a round, each player places one card face up on the table. 3. 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. 4. Tied players play additional rounds until someone wins. 5. 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. 6. 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
8 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.
Julia’s presentation was very hands on and provided a great manipulative for students to understand how integers work by using oversized playing cards. I think it was a great activity to get students involved and it was fun for their entire class! I didn’t see much I could improve on with the activity because it was very organized and easy to understand.
Proportional Thinking: Ratios + Equivalent Ratio’s Integrating Technology into the Classroom Maddison Furtado November 27, 2015 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: 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!
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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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I thought Maddison’s activity was a great tool to use in the classroom to get students engaged. From my experience in placement, students generally are more focused and ready to learn when there is a game involved. However, I wouldn’t necessarily use this activity as a learning tool, but rather a fun activity to use at the end of a lesson to consolidate understanding.
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Proportional Reasoning Mathieu Carrière October 23, 2015 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?’
The activity was great because you can use a different image based on your student’s interests or holidays surrounding the lesson. However, I would make sure not to use an abstract image as some of us had difficulty understanding the assignment. I would start with a simple image such as a box and then move on from there to more difficult images
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Decimals Mariska Ceci October 2nd, 2015 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 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) This activity was great to also work in art into one subject by having students create an image by filling in the right number of squares for their decimals. Students could get extremely creative with this assignment and it can become very personalized for each student. I think it was a great activity to introduce a creative side to math, but it can be time consuming for each student to count up the amount of squares they need coloured if the decimal is 0.86 for example.
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Fractions Anjali Sharma October 2, 2015 Grade 7-8 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.
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. 1 1 1 1 1 1 1 , , , , , , . Addition of these fractions creates a 2 3 4 5 6 7 8 pattern where, numerator and denominator increase by 2. Type 1: Neighboring fraction-
Type 2: Fractions with common denominator -
2 , 8,
3 4 5 6 7 , , , , On Addition, numerator increases 8, 8, 8 8 8
by 2. Type 3: Denominator of 1st fraction is numerator of next fraction-
1 2 3 4 5 6 7 , , 4 , 5 , 6 , 7 , 8 . On adding, 2 3
numerator remains same and denominator increases by 2. 3 4 5 6 7 , , , , . Addition shows interesting results. Here, numerator 2 3 4 5 8 increases by 4 and denominator by 2. Type 4: Improper fractions:
13 Anjali’s presentation was one of the first we had in class and was a bit more disorganized than the other presentations following. I thought she did a good job of explaining how we add or subtract fractions. The only think I would do differently would be to have the students be more involved with practising rather than just standing at the front of the class writing on the board. It’s important to get students involved in their learning to have them engaged with the lesson.
Improper Fractions and Mixed Numbers Amberly Morris Grade: 5 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 ← Numerator 4 ← Denominator New Terminolgy: Watch: “Improper Fractions and Mixed Numbers” video at https://www.youtube.com/watch? v=ggYdPef3Nuk 1/5 6/3 2 1/ 2 ☼ 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
14 fraction to mixed number calculator (http://calculator.tutorvista.com/math/1/improper-to- mixed-fractionscalculator.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? Use the space below for your rough notes and problem solving! Amberly did a phenomenal job of incorporating technology within the classroom by using a funny YouTube video to explain how to create improper fractions and proper fractions. She made a very interesting point that we can’t show videos all the time because they lose their novelty and don’t catch student’s attention as much. She also gave us a handout to practice our fractions and ordering improper/proper fractions from greatest value to least. I thought her handout was very informative and her way of getting us to differ our usual groups was very interesting. She put smiley faces on all of handouts and based on the color that was our new group. This simple step allows for differentiation where she can group children based on needs, learning styles and more. Overall, I thought her presentation was one of the best yet!
2. Geometry and Spatial Sense Using technology to teach Geometry:! Victoria Medeiros November 27, 2015 Grades 4-8 (Grade 5) 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
15 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 threedimensional 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/ This activity is great to assess students learning in a fun and interactive way. I’ve seen this used in a couple classrooms and students always look forward to the activity. I think it’s a great activity to see how well students understand the material and where you may need to re-focus your lessons to ensure overall learning for your student needs.
Reflections - Geometry and Spatial Sense Marissa Di Camillo November 6, 2015 Grade 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)
16 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
Marissa’s presentation was a great use of visuals to get students to understand flipped images. I thought she did a great job with her activity having us flip an object on many different lines to improve our understanding. We didn’t really get a chance to use a mira and I think next time I would want to incorporate that into my lesson so students can see before hand what they are expected to draw.
3D Geometry: Representing Shapes Nicole Horlings November 6, 2015 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.
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17 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.
Nicoles activity for creating 3D shapes was very hands on and a great use of manipulatives. However, I would make sure there are enough supplies for the entire class to create their cube. Some of us were not able to participate because there were not enough toothpicks or marshmellows.
3. Data Management and Probability Mean, Median and Mode Jeff Heartwell November 20, 2015 Grade 6 & 7 Overall Expectations:
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18 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
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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: Jeff’s activity was very organized and I liked how he related mean, median and mode to real life situations. He taught us the importance of what we were learning and why we needed to have an understanding of what he was teaching us. Overall, he did a great job and I’m excited to use this activity in my future classroom.
Bar Graphs Asma Malik November 20, 2015 Grade 4/5
20 Activity: 19.4 (modified), page 527 of Making Math Meaningful to Canadian Student, K-8 textbook 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.
21 # of Rolls 1 2 3 4 5 6 7 8 9 10
Student 1
Student 2
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). Asma’s activity was great to get students to think how they would organize a bar graph. We got to work in pairs and I thought it made the activity more interesting. What I found a bit difficult was actually how we were supposed to do the layout of our bar graph and I think I would explain to my class how to set up the graph to ensure no confusion among students.
4. Measurement Grade 4 Math Problem: Estimating and Measuring Length Tim D’ana November 13, 2015
22 Grade 4 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 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.
23 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?
Tim got students to guess the height of volunteers standing at the front from shortest to tallest. He explained how it would be more difficult for us to estimate height if they were arranged randomly rather than in order. We were forced to use cm instead of inches and feet, which was also a good way of converting measurement. I think it is a great introduction to estimation of length and is a fun activity for students. 3.
Patterning and Algebra Patterning
Kelsey Potts November 20, 2015 Grade 4
24 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 ie. color, shape, size etc.
attribute 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
Algebra Brett John November 6, 2015 Grade 5/6 Overall Expectations - Recognize and represent algebraic relationships between a group of numbers
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25 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…
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Looking at this as a pattern we see the pattern as being adding 3 to each value
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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 1 2 3 6 12
Output 4 5 10 3 5
Relationship
Equation
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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…