Hi crew! I miss you! Below are some optional math activities to keep you occupied for this first week. Please note that these will not be assessed for a grade, and are not expected to be completed upon our return to school. They are simply some ideas if you would like some extra work to do. My wish for you is to prioritize your mental and physical health, as well as your family time. Below are the optional activities for this week, and in the future Mme Samuel and I will be putting some new activities on Google Classroom every Monday morning. So.... please check Google Classroom each Monday morning. FYI - I am breaking up that huge first package I previously sent out, so that you now have five pages per week (roughly one page of math per 'school day'!)
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Recently, our class experimented with a really COOL instructional practice called "The Jigsaw Method." Interestingly, it was invented by social psychologist Elliot Aronson in 1971 in response to the racial turmoil caused by the recent school desegregation in Austin, Texas. Teachers were noticing that students were not interacting with each other, even when in the same classrooms, and pre-existing assumptions were being made about student intelligence. The Jigsaw method was devised to get students interacting with each other, learning from each other, and showcasing their own intellect. In the early 70s, it was hailed as a great equalizer. Now, we just know it to be a very effective teaching strategy. I've never used the Jigsaw Method before, so I was excited to try it. The concept is that students are put into "Home Groups," but then break into "Expert Groups" to learn about a topic. Once they are experts at one aspect of the learning, they go back to their home groups and teach it to their peers. Throughout the whole process, students interact with about ten of their peers - all while asking questions, learning together and teaching each other. Usually, this method lends itself well to science or social studies, but hey... why not math? For this task, students in each Expert Group received a specific manipulative and had to figure out a) how that manipulative can be used to teach about fractions and b) how to teach a simple game to their home group in order to increase our understanding about fractions. WOW - What a success! The expert groups were a place of asking questions, breaking down barriers and exposing pre-existing myths about math. The home groups were a place of confidence, excitement and teaching their peers what they had learned. I can't tell you how much students learned from this one math period. Common understandings about decimals and fractions were solidified, myths were debunked, and so much valuable math dialogue occurred... For instance, this was one conversation in an Expert Group as students were devising a game to teach about fractions using dominos: A: "So player #1 would flip over her domino and player #2 would flip over his domino, and the higher fraction would win - like the game of war. But you have to put the lower number on the top so that the fraction makes sense." B: "No you don't! The fraction would make sense either way! You could put the higher number as the numerator and it would make an improper fraction." A: "Well, if you put the lower number as the numerator it would make a decimal. Like 3/6 is 0.5." B: "It would make a decimal either way. 6/3 is like saying 6 divided by 3... which is 2.0." A: "Is 2.0 a decimal?" B: "Sure, why not? It's like saying two wholes and zero tenths. Or think of a different fraction... like 3/4 would be 0.75 but 4/3 would be 1.33 - still a decimal." A: "Hmmm... so the game would work if the fraction was improper OR proper?" B: "Yes! In fact, you should let the players CHOOSE which way to put the domino. That adds a whole other level to the game!" A: "Ok! Let's do that!" Then both A and B proceed to break off into their home groups and ACE the explanation, therefore leading their peers to a much deeper understanding of fractions. This occurred throughout the class, with students learning how cuisenaire rods, lego, pattern blocks, base ten blocks and dominos can be used to represent both decimals and fractions. Math confidence? #SoaringHigh Students consolidated their learning on the page below: We've also been reviewing converting between decimals and fractions (and percents for Grade 6s), simplifying fractions and creating equivalent fractions. See how much fun fractions are? I love teaching math!
Big Ideas for Number Sense (Fractions/Percents and Rates/Ratios): -A fraction can represent part of a whole, part of a set, division or ratios. -Fractional quantities can be expressed as fractions, decimals and percents; these number forms can represent equivalent quantities (e.g., 1/2, 0.5, 50%). -A fraction is not meaningful without knowing what the whole is. -The size of a fraction can be thought of in terms of the ratio of the numerator to the denominator. -"Renaming fractions" is important to compare them; every fraction can be renamed in an infinite number of ways. -Benchmark numbers (fractions, decimals, percents) can be used to estimate, compare and give meaning to numbers. -A percent is a ratio where the second number is 100 (only Gr 6) Some specific topics that we'll be learning about (and how they 'spiral back' to topics we've already learned): -Relationships between fractions, decimals, percents (SPIRAL to decimals and place value ***spend time reviewing here) -Equivalent fractions (SPIRAL to number sense operations) -Compare & order fractions with like denominators (Gr 5) and unlike denominators (Gr 6) -Proper vs improper fractions -Mixed Numbers (Spiral to whole vs decimal numbers) -Percentages - and percentage benchmarks (Gr 6 only) -Ratios (Gr 6 only) -Rates (unit & other) (Spiral to number sense operations & fractions and SPIRAL to ALGEBRA: equality is an expression of balance ) We began the week with some basic fraction review: Then students took part in "Fraction Stations." Our favourite was the "clothespin fractions" number line, where students had to sort many fractions and decimals in order from least to greatest. This was a fun way to get the dialogue going about ordering fractions: "I don't think 9/10 is the same as 99/100. 9/10 is like 90/100... so it's less." "Hold on, I think 0.2 is the same as 1/5, because 1/5 is equivalent to 2/10, which is 0.2." "How can you tell if 7/15 is bigger than 0.5?" "Well, half of 15 is 7.5, and 7 is less, so it has to be less than 0.5." I loved all the learning from this "Clothespin Fractions" activity - including all the smiles when they finally put them in order! Students also worked on open number lines, and discovered that it's much harder to create a number line that extends past "one" - improper fractions and mixed numbers here we come!
This week, we practised solving several algebra equations with variables (as a large group, in partners and independently). We also learned how simple and composite pattern rules can be linked to story problems. Students enjoyed our Visit & Record activity, where they first created their own algebra and patterning questions (so creative!), and then they walked around and solved their friend's questions. Each question required students to either represent the story in an equation, or create a table of values. A fun snow day activity: can you figure out the composite patterns of our math robots?? This week started with a bang when students participated in an exciting escape room. As well as applying their patterning skills, students had to problem solve, collaborate and persevere to 'escape.' Fun was had by all, and *most* teams solved the final code!
Student enjoyed some problem-solving pattern fun this week. One favourite activity was a Visit & Record, where students created their own composite patterns, hid their pattern rule, and then visited their friends' patterns to try and solve them. Some students took this to a new level and even tried patterns with exponents! Fun!
Big Ideas for Patterning/Algebra: -Every pattern involves repetition (numbers or objects that repeat in predictable ways). -There is no way to know how a pattern continues without a pattern rule. -Patterns can be used to recognize relationships (ex. multiplication, doubling) and be extended to make generalizations/predictions. -Equality is an expression of balance (equal sign = balance). -An equation can describe many real world situations. Specific Goals for Patterning & Algebra -Create and extend numeric and geometric patterns -Create tables of values for growing and shrinking patterns -Term numbers (when given pattern rule, find 19th term) -Distinction between regular pattern rules vs term number pattern rules -Represent geometric patterns numerically -Variables vs constants -Solve equations with one variable (Gr 5) or 2-3 variables (Gr 6) It's important to note where we've come from and where we are going with patterning. By Gr 5 and 6, we're stepping away from 'primary' patterns (ex. add two each time, multiply by 3 each time) to more complex patterns, and representing them in a table of values. Our task in Gr 5 and 6 is to fully develop a concept of "tables of values", and then generating coordinates from those tables. Why? Well, in later grades, students will be graphing those coordinates and combining this with more complex algebraic concepts.....
It is VERY important to note that students who know their multiplication tables WELL and can "see" which multiplication table a group of numbers belong to do much better in patterning (and fractions - coming up in March). Perfect... now is a GREAT time to help your child develop some fact fluency with multiplication tables. PARENTS: YOU HAVE HOMEWORK! Please click on the button below to discover some ideas of how to help your child memorize their times tables. Ideas go from general to more specific/complex. Please take a few minutes to read the whole document - if there is ONE thing you help your child with this year, this is IT!
Hi all! There will be a math assessment next week on transformational geometry (coordinate grids, translations, reflections and rotations). Your child's folder went home to help with studying, but please be aware that we do lots of paperless activities in class. It's important to take a look at past blog posts while studying in order to see the learning that's happening in class... which might not be represented on paper in your child's math folder!
See some photos of this week's activities below. We'll also continue to investigate these transformations more next week.
For the month of January, we will be learning about 2D geometry. Read below for an overview! Big Ideas for Geometry (Location & Movement) -Transformational geometry can be used to understand and represent locations/directions. -A transformation is a ‘motion’ (translation - slide, reflections - flip, rotations - turn). -Transformations of 2D shapes can result in figures that are similar or congruent to the original figure. -Congruent shapes have identical side lengths, angles, perimeters and areas. -Transformations are often observable in our everyday natural world. Geometry (Location & Movement) -Plot points in 1st quadrant of Cartesian plane -Rotations of 90 and 180, clockwise and counter-clockwise, with center of rotation inside and outside of shape *A focus for Gr 6s (they will be doing this in more depth) -Reflections (flips) and translations (slides) -Identify translations that map congruent shapes onto each other A lot of this 'spirals' back to our geometry learning about triangles and quadrilaterals, so we'll be reinforcing those concepts too as we move forward. Students enjoyed finding the co-ordinates of our Canadian Prime Ministers ("St Laurent was a PRIME MINISTER? I thought it was just a SHOPPING MALL!" #LoveThis). See photos below! Students also created a scalene, obtuse triangle on a geoboard, hid it from their partner, and gave the coordinates of each vertice. Then they checked that they had congruent polygons. This was a great activity to use a lot of math vocabulary! Students enjoyed a battleship type game where they 'hid treasure' - and of course, found it using coordinates. A note about extensions: below are photos of math extensions, designed to be a) on topic with what we are currently learning and b) take your child further in math. Some are fun/easier and others are fun/much harder. The expectation is that if students are done their math work early, they work on a math extension. Up Next: transformations, including translations, reflections and rotations.
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Mrs JorgensenI'm a math nerd and think math jokes are funny. Not all of them though - just sum. Archives
March 2020
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