How awesome is this?? 3rd grade at TCE put a hopscotch board in the middle of their hallway so their learners could practice their equivalent fractions. What a great idea to engage our learners in a kinesthetic way!
Math is all about numbers, symbols and Maths formulas. These symbols are required for different operations. These symbols are used in different mathematical fields. From representing the equation to telling the relationship between the two numbers.
Years ago, my district adopted the Bridges Math Program. Thus began an era of teacher angst, quiet and loud rebellion, and desperate determination. I gnashed my teeth along with my colleagues, but I vowed to give it a fair shake. Today, I find myself reflecting on how I've changed as a math teacher. The Bridges Math Program changed how I teach math. I am now a manipulative-based math teacher. I use games consistently, and push myself and my students to see math everywhere. As painful as it was leaving the traditional math program we had had, Bridges did one thing for my pedagogy: It made me reclaim my creativity. You see, I was that student who never had to really work hard in school, unless I was learning math. My mom, a teacher herself, tried to help me, but we were like oil and water together. And so, I would end up at the dining room table with a box of Kleenex and my father, who quickly became the delegated math teacher in the family. It wasn't until I was in college that I realized that I am good at math. I had a lovely professor who valued my outside-the-box thinking. That semester, I learned that I am a creative mathematical thinker. This past week, my principal observed me teaching math for the second time this year. Usually, I'm observed teaching writing or reading for my evaluations. I used to be a literacy coach in our district. It's content with which I am confident. But this year, I requested that she observe my math workshop. I've had one huge goal this year: My students will be able to explain their thinking, especially their mistakes. This breaks down to these three things: My math workshop will be student-centered. My voice is secondary to their voices. I will expect my students to make their thinking visible. My students will view math creatively, and their outside-the-box thinking will be celebrated. I accomplished these things using many traditional methods. But I also tried some untraditional things too! When students made their thinking visible on graffiti boards or in their math notebooks, I copied them and put a clip art frame around them. I hung the "frames" on the wall, as if they were works of art. Students signed their math as they would a painting. When a student said something in math class that "gave us goose-bumps," I wrote it down, as if I were quoting a famous author. I displayed their words on our math wall on fancy sentence strips, as I would a quotation of Einstein's. We tallied up all the different ways we could solve one story problem. Students named their strategies like "Jared's Break Apart Strategy" or "Cassie's Leap Frog Strategy." These strategies were displayed on the wall, and students began trying each other's problem solving routines. I also used thinking routines from Ritchart's Making Thinking Visible. We used these weekly in our math journals, and I often used my visible thinking organizers as comprehension checkups throughout our math units. We also connected mathematical concepts to non-mathematical situations or stories. For example, we described mixed numbers and improper fractions as long lost twin siblings that ran into each other at the airport. Mixed Number dresses in suits and ties while Improper Fraction wears flip-flops and Hawaiian shirts, often sticking French fries up his nose when he eats in public. He is improper, you know! We told stories about the geometry families. My proudest math moment this year, so far, was this past week. My administrator was in observing. She leaned down to ask one of my students about how he thinks decimals relate to fractions. He launched into the long lost twin story, explaining that decimals are actually a triplet sibling that no one knew about until now. "They're siblings because they represent the same amount, Mrs. S." No doubt, Mrs. S. now understands decimals a bit better. Made my heart sing. That's what a non-traditional resource like Bridges has done for me. It's not perfect. Nothing ever is. The traditional resources were far from perfect, as well. However, after 24 years of teaching, I've learned that a resource is JUST that...a resource. It is not curriculum. It is not good teaching. It is not differentiation. It is not thinking made visible. It is not good pedagogy. It is simply a resource. The good stuff starts with us. We're the good stuff. Until next time, teach on, my friends! Tracy @ If you want to learn more about the "good stuff" I use daily, see below!
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I had a goal to have my students write more in math class this year, without making writing such a big deal. When students hear that they are writing in math, their responses range from disbelief to outright indignation. "Why are we writing in math?! This isn't English." So I try to sneak it in their when possible. I did this activity with my students at the end of the year--really the last few weeks of school, after STAAR testing was over. I was pleasantly surprised how engaged they were and I am excited to try it again next year when summer isn't on everyone's mind. In this activity, we start by playing Two Truths and a Lie-- the get to know you game. This can work at anytime of the year as students always like sharing things about themselves. I first share two truths and one lie about myself (this is how I announced my pregnancy to my students last year) so students know what to do. Then, I give each student a post-it and ask them to write Two truths and one lie about themselves then they share with their group and the other students guess what is the lie. I spent about 10 minutes on this part. It gets students talking to each other and excited about class. This way when they go into the activity they are smiling and laughing instead of depressed that they have to writing. Then I explain we are going to do Two Truths and a Lie-- The Math Version. Each group is given a sheet of paper with a graphic or word problem on it. There are 2-3 students per group, so I will have about 12 different papers distributed around the room. The group is then asked to write two truths and one lie about the graphic or word problem. I did model this for my students before I passed out the papers. I asked them to dig deep and come up with something profound--not something like there are two dots on this graph. I was happy that some students voluntarily did computation as their truths and then wrote a sentence about it instead of just stating facts they could see without computation. After all groups had their two truths and a lie written down, I gave each student 4 post-its and asked them to find the lies on 4 other papers. I asked them to write a sentence about why it was a lie instead of just stating "Number 2 is a lie." In the process, students found that some papers had two lies or that there weren't any lies at all--either students didn't follow instructions, or they had made a mistake. Here are some students papers after the activity. This activity can be made easily-- you can take pictures of graphics in textbooks, worksheets, make your own graphics, etc. You can have the whole activity be centered around one concept, or a review of several concepts. I have a FREE sample of what I used in my classroom--it is appropriate for grade levels 6-8. Here is my first completed activity focused on one topic--Geometry. This has 21 pages of graphics that will prompt students to write about triangle properties, area of polygons, and volume of rectangular prisms. There are two versions--one with just the graphics and the other with two truths and a lie already written for students to choose from. Get it HERE. Here is the next completed activity focused on Statistics. This one is editable if you want to change out the truths and lies to focus on specific vocabulary or concepts. Get it HERE.
Chapter-wise NCERT Solutions for Class 8 Maths solved by Expert Teachers as per NCERT (CBSE) Book guidelines. CBSE Class 8 Maths All Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks.
For many people, Mathematics has been an extremely challenging subject. However, these useful Math hacks will guide you! Ready to solve some equations?
Calculus is arguably the most influential mathematical discovery in history, finding uses in physics, economics, engineering, biology, and so much more. Calculus has two branches: Differential…
It's more straightforward than anything you were taught at school.
Math doesn’t always have to be hard and confusing, sometimes it can be fun. These funny math jokes and puns are the perfect way to make math a good time.
