We're having so much fun learning geometry here at KHPS. I love seeing the excitement on kids' faces once they understand something or create something amazing. I'm CERTAIN that all kids truly want to succeed - and it's really incredible to get a first row seat on their learning journey. Here are some photos about what we've been doing: In Gr 5, we reviewed symmetry in terms of world flags.... boy does this crew know a LOT about the history of flags!!! In Gr 6, we also began to tackle rotational symmetry.
Don't forget about our math extensions... I work hard to ensure that we always have fun and subject-specific extensions available in our classroom for kids to challenge themselves with. Students are especially loving our new problem solving bags (they won't leave for recess). There are also several geometry extension sheets/projects as well as a geometry extension menu (order up the challenge that appeals most to you!)
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For the next month, our focus will be on exploring geometry, while 'spiralling' (ie, coming back to) multiplication and decimals. PLEASE buy your child a protractor! I have a few at school, but just like pencils, they seem to grow legs and disappear... Some expectations include: Gr 5: -classify all polygons (2D shapes) and prisms/pyramids (3D) -Lines of symmetry -measure and construct angles up to 90 using a protractor -identify and classify acute, right, obtuse and straight angles -identify triangles based on side length and angles (Alert! New math terminology here...) -construct triangles when given side lengths and angles ("Use a protractor and ruler to make a scalene triangle with a 30 degree angle and a side measuring 12.5cm") -translations (ie, slides - translate this rhombus up 2 and to the right 3) -reflections (ie, flips across x and y axis) Gr 6: -classifying quadrilaterals (this is a specific Gr 6 focus, although they would have already been introduced to this in Gr 5) -symmetry (including rotational symmetry - a brand new concept) -construct any polygons when given angle and side measurements ("Use a protractor and a ruler to make a trapezoid with a 45 degree angle and a side measuring 11.5cm") -isometric sketches (NEW! This involves building 3D models from isometric sketches and drawing isometric sketches of 3D models, including views from the top, side and front. This is quite difficult!) -coordinate grid system on a Cartesian plane (only first quadrant) -rotations of 90 and 180 both clockwise and counterclockwise -translations and reflections -also ALL Gr 5 expectations in preparation for EQAO (ex. Gr 6s will review triangle classification again b/c they've probably forgotten it... and it's on our standardized tests in May...) Do math jokes make anyone else super happy?!!? We've been learning a lot about what patterning and algebra looks like in the junior grades. Here are some photos to review with your child in preparation for a quiz early next week. The daily math problems below show the difference between simple patterns (ex. start at 4 and add 4 each time... in the first photo) and composite patterns (Ex. Term number x4+6... in the second photo). Composite patterns allow us to solve for higher numbers (ex. How many feet will there be in week 34? Students can just do 34 x 4 + 6 to get their answer). What a perfect time to review multiplication without a calculator... Each day we work in our daily math books... many students are working very hard to extend their learning during this time. I learn a lot from student observation too! We sometimes also take a look at how students organize their math work. I hide their names and project an image of their work on the projector. Analyzing student work gives us feedback about how to organize our answers for readability (ex. final answers are circled/written in a sentence, labels help a lot, etc). We take a look at the difference between organized/non-organized work and it's very easy to see the difference. Aren't the student samples below well organized and easy to read??? Gr 5s have been introduced to variables for the first time, and Gr 6s are building up more knowledge about them. We have worked on solving for variables in simple (4 + F = 12) and more complex (145 - 56 = B + 47) equations. We've also been writing equations to go along with story problems. Below are quite a few examples - it would be worth reviewing these with your child! We've spent quite a bit of time finding relationships and writing equations... And finally, the Grade 6s attempted a question on "Who Wants to Be a Millionaire." This poor contestant lost $15,000 due to math - but we didn't! Way to go Grade 6s! The Gr 6s also wrote variable equations using tables of values. Wow!
This week, students made their own composite pattern and wrote their pattern rule down (on a flipped cue card). Then they did a "Visit and Record" where they visited the patterns of their friends and tried to figure out their pattern rules (and then they could check by flipping over their friend's cue card). Below are some examples... Students loved these! It's a great kinesthetic, hands-on way to do patterns! We are, of course, still doing Daily Math Talks and learning lots from our peers: Look what I got for Christmas!!! Sending some positive messages along via my new lightbox. So proud of the hard work and perseverance that our students are doing - we're seeing such growth and improvement, and having fun while we're at it :-)
There will be a short quiz on finding the area and perimeter of composite shapes next week. Gr 5 - only using rectangles Gr 6 - using rectangles, triangles and parallelograms Students need to use formulas and units :-) What is the most common mistake I see? When finding the total perimeter of a composite shape, some students are still finding each individual shape's perimeter and adding them together - you don't need to do this, and in fact, it will give you an incorrect answer! To find the total perimeter of a composite shape, simple add up all the outside edges. Below is some Gr 6 work. We've had time to really delve into some problem solving with area and perimeter now that we have a firm foundation on it. The Gr 6s are flying through 2D measurement! They have latched on quickly and easily to the area of a parallelogram and triangle (and the area of a trapezoid as an extension). It takes a lot to challenge this crew - but the Bansho question below worked to stump them for a good 30 minutes. Success! I love getting their problem solving and critical thinking gears going... you should see how excited they were when they made a breakthrough. Below are some more pics of our Gr 6 work this week:
The Grade 5s have been rotating through math centers to practise their area and perimeter finding skills! Not only do they need to be able to use formulas this year, but they also need to find the area and perimeter of composite shapes (ie, shapes joined together). For the complete overall math expectations read the previous post! Gr 5s have also been doing lots of daily math (more problem-solving based) and have even attempted their first Bansho question (open-ended problem solving in groups)
Students have all received back their latest graphing math assessment. Haven't seen it? Ask your child to bring home his/her math folder to show you! Next up, we will be learning about 2D measurement. That being said, I'm a huge believer in "spiraling" the math curriculum, meaning that I try not to teach math concepts abstractly. While we will be starting measurement, we will also spiral our number sense learning back into this new learning. This allows children a chance to practice core math concepts (especially multiplication, decimals, fractions, etc) in different contexts. It also helps to really reinforce number sense concepts in different ways as we never really "stop" learning them! Grade 5 "Big Ideas" for 2D Measurement: -estimation vs precise measurement -elapsed time to the nearest minute (ex. Took train from 11:35 to 3:42pm... how much time elapsed?) -length, perimeter and area of various polygons, especially the area of rectangles with a proper formula and units -metric units to measure length and distance (mm to km) -conversion between metric units (ex. converting from meters to centimeters... this ties in nicely with reviewing "multiplying decimal numbers by 10, 100, 1000 and 10,000 and dividing numbers by 10 and 100" in our number sense strand) -construct 2D shapes with the same perimeter or area (Ex. How many triangles can you create with a perimeter of 14 units?) -area and perimeter of composite shapes using different rectangles Grade 6 "Big Ideas" for 2D Measurement: -estimation vs precise measurement -metric units to measure length and distance (mm to km) -conversion between metric units (ex. converting from meters to centimeters... this ties in nicely with reviewing "multiplying and dividing decimal numbers by 10, 100, 1000 and 10,000" in our number sense strand) -converting between squared metric units -creating a variety of polygons given the area and/or perimeter (ex. create two different triangles with an area of 12 units) -area of rectangles, parallelograms, triangles with proper formulas and units -area and perimeter of composite shapes (including rectangles, parallelograms and triangles) You might want to "front load" some vocabulary by reviewing the two charts below with your child. Don't panic if they don't know this already. We will be learning these... but sometimes families like to review vocabulary regularly. Converting back and forth between units is difficult for most students. We will be practising this next chart lots over the next few weeks, including numbers with decimals: Please note: sometimes I'll throw in an imperial measuring unit.... because in reality, we're so close to the USA and still see imperial units everywhere. We even measure height in feet/inches, use fahrenheit for oven temperature, bake with cups/ounces... it's everywhere! While we won't be necessarily converting between metric and imperial, I want students to at least recognize some of the units they will see in everyday life.
Over the past few weeks, we have been learning about broken line and continuous line graphs, as well as stem and leaf plots (Gr 6). We've been interpreting data from different kinds of graphs and making conclusions about what they tell us (and what they don't!). There will be a math assessment next week on graphing - please review your child's math folder! We often do daily math in class... for the above photo we talked about what we DO know from the graph and what we DON'T know for sure from the graph... which led us to understand the importance of descriptive titles (so we made a new, more descriptive title together!) We've also been learning about the STAR strategy, an acronym to help students problem solve difficult questions. I'm encouraging students to use this method a) for any complicated math problem and b) if they don't know how to even begin a math problem. To practice the STAR strategy, I had to give them a really hard problem (else they don't need it!) Many students went above and beyond and even accounted for leap years... which lead us into leap year learning.... how many days in a year? Ask your child how many days are in a year (hopefully they'll answer 365.24 to be exact!). We are also continuing to play around with fractions and decimals, including adding, subtracting and arranging them in order. We sure are putting lots of new tools into our math skills toolbox! I love, love, love teaching math. Today the students brainstormed the differences and similarities between improper fractions and mixed numbers (see venn diagrams below), and then taught the class what they knew. As I walked around checking in with different groups, I heard so much 'math terminology' being spoken, and so much math understanding on display. They came up with so many UNIQUE similarities/differences that I didn't even think of. For stance...
"Both improper fractions and mixed numbers have a line between the numerator and the denominator. It's actually a dividing line. It means division. That means that when you look at a fraction, you can make a division sentence. For instance, 17/5 actually means '17 divided by 5' which equals 3 and 2/5. On a calculator, the 2/5 part will actually look like a decimal. So a similarity between the two types of fractions, is that they BOTH can make an equation and they BOTH have an answer." WOW WOW WOW! They understand. They REALLY do. They debate, and discover, and learn. They are beginning to take risks. They are beginning to not fear making a mistake. They are beginning to see how in math, you can debate things in different ways in order to reach a deeper understanding of something... Student A: "In an improper fraction, the numerator is always bigger than the denominator - example 17/5. In a mixed number, the numerator is always smaller than the denominator. - example 3 and 2/5" Student B: "I respectfully disagree." Class: WHAT?!?!?! Student B: "In a mixed fraction, the numerator is not 'always' smaller than the denominator. What if you didn't 'pull out' all three wholes? What if you only pulled out two wholes? Than 17/5 would be 2 and 7/5. In this case, the numerator of a mixed number is BIGGER than the denominator, just like the improper fraction." Class: Silence Me: "Is that allowed? Can you do that?" Class: Healthy debate ensues on whether you can do that, whether you should do that, and why on earth you would do that. Throughout this all, they are using math language and really displaying their understanding. Mission: accomplished. Quiz your child - these guys know fractions and decimals well now! OPTIONAL HOMEWORK: Click here for math homework on improper and proper fractions. This is optional. Most kids will fly through this... if you know your child is doing well, feel free to also just 'show' your child and ask them to do a few of each type of question. |
Mrs. JorgensenThis page is written by Mrs. Jorgensen, who loves all things math :-) Helpful Math Sites: |