MATH MANIPULATIVES
Here are 5 math manipulatives that I find to be very useful. I believe that all students should have access to manipulatives to help them develop strong conceptual understanding in math by connecting the physical to the abstract. Manipulatives encourage the use and integration of all types of intelligences, analytical, practical, and creative (according to Sternberg's Triarchic Theory).
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1. BASE TEN BLOCKS
Base ten blocks are a valuable manipulative for the classroom that provides a visual and tactile approach to help students grasp the concept of working in a base ten system. Base ten blocks are useful for teaching all sorts of math concepts from numeration, addition, subtraction, multiplying, dividing, fractions, decimals, and percents, patterns. Example: Teaching subtraction with regrouping (algorithm) using base ten blocks to illustrate the physical regrouping process. Mark gave Sally has 541 smarties. Sally ate 195 of them right away. How many does she have left for the rest of the day? 524 -195 or 524 -195 1) We cannot take 5 ones away from 4 ones. So one set of the tens needs to regrouped into 10 ones which will be added to the 4 ones to get 14-5=9 ones. 2) We cannot subtract 9 tens from 1 ten, so one set of the hundreds needs to be exchanged (regrouped) into 10 tens so we have 11 (tens) -9 (tens)= 2 tens (or 110-90=20). 3) The last step does not require regrouping because 4 hundreds can be subtracted by 1 hundred. 4 hundreds - 1 hundred = 3 hundreds (400-100=300). Answer: 329 2. GEOBOARDS
Geoboards are a fun tool for students which are by no means limited to learning geometry. Area, perimeter, fractions, decimals, percents, symmetry, spatial sense, and graphing are several other mathematical concepts where geoboards can be a useful manipulative. Example: Quick and Fun Formative Assessment (A good warm-up before a lesson on attributes of quadrilaterals). 1) Instruct students on respectful use of elastic bands 2) Distribute bands and boards 3) Give students a few minutes to create different shapes with the boards. 4) Play the Game: “Make me a....Show me a...” Call out different quadrilaterals for students to create and have students hold up their geoboards for the teacher to see. Call out the following quadrilaterals: square, rectangle, trapezoid, rhombus, parallelogram, kite (convex, concave). 3. FRACTION FACTORY PIECES
Fraction factory pieces is a manipulative that I would want in my future classroom. Fraction pieces can be used to teach patterns and algebra because of their varying colours and sizes. They can also help students with the 4 operations, compering, ordering problem solving and of course equivalent fractions. Example: Explore Fun with Fractions! Use the red rectangle represents one whole. Use it as a base for the other pieces. 1) Open the back of fraction pieces. 2) Group them by colour and size. 3) How many pieces are in each group (whole). (How many of each colour set fit on the red piece?) 4) Use a variety of tiles to cover the red piece. How many of each did you use? 4. POLYDRONS
Polydrons are a fantastic manipulative for teaching geometry especially when comparing properties of polygons to 3D solids. Students will have fun putting into practice their engineering skills and develop a deeper understanding of edges, vertices, faces, and bases as they construct various polygons and solids. Polydrons can also be used for nets, patterns, and area. Example: Exploring 3D solids (prior knowledge of polygons and previous introduction to edge, face, and vertices) 1) Construct a 3D solid of your choice. 2) What polygon shape(s) did you use as building blocks? 3) What is (are) the term(s) used in a 3D solid for these polygons? (face, base) 4) Are their points on your 3D solid? What are these points called? (vertices) 5) What are the lines between each polygon called? How many of them are their on your solid? ( edges) Modification: Question using the terms (edges, vertices, and faces/bases). 5. MIRAS
Miras are excellent manipulatives for students to use when learning mathematical concepts such as properties of polygons and line segments, transformational geometry, and angles. I used miras a lot in my first internship when I taught the geometry unit and the concept of symmetry to grade 5 students. This tool not only points out exact symmetry but can be used to create symmetrical shapes and designs. this can easily integrate art into math, provide a practical and creative experience for the students, and has them thinking on higher levels of the Blooms Taxonomy. Example: Geometry: Tatto Symmetry 1) Think-pair-share : "What is symmetry? 2) Group discussion 3) Show Showing Symmetry with a Mira https://www.youtube.com/watch?v=qakJ_SUFjeU Or have a mini lesson on symmetry, providing plenty of examples. 4) Discuss cultural significance of tattoos and origins 5) Project pictures of symmetrical tattoos. Have students take turns to draw on the smart board the line(s) of symmetry 5) Distribute pencils, paper, and miras. Have students design a symmetrical tattoo by creating one half, and using the mira to draw the second half. 6) Students may colour their tattoo and outline it with a sharpie. |