Base ten blocks have a medium level of abstraction. While students must assume a value for a block, one rod is 10, even though it is just one block , unlike the Cuisenaire rods, base ten blocks provide centimeter marks on the each block so students can easily double check their values for each block.
Pattern Blocks Pattern blocks are a basic necessity for every classroom. Among the shapes within each set are a hexagon, trapezoid, triangle, parallelogram, square and rhombus. Most pieces have relationships to one another.
For example, assuming the triangle has a value of 1, the parallelogram then holds a value of 2, the trapezoid a value of 3 and the hexagon a value of 6.
The square and the rhombus values do not translate as easily but make for excellent investigations. Pattern blocks are a very versatile manipulative. Use for symmetry, counting, money values, geometry, angles, fractions what if the hexagon was the whole? These blocks can facilitate a very high level of abstraction, as students are required to associate a value with a block shape. One yellow hexagon can have a value of 6 even though it's just one block.
If students are not yet demonstrating the ability to make that leap, you need to have them work with a less complicated manipulative to solve their task. Pentablocks These lightweight Pentablocks with opaque washed surfaces are a wonderful extension to pattern block activities. They do NOT share the same measurements as the pattern blocks, yet they offer brilliant extensions to tasks learned with the pattern blocks, using an entirely new set of acute and obtuse angles to measure, as well as new symmetry design challenges.
Cuisenaire Rods These wooden Cuisenaire rods are graduated in length and based on a single centimeter cube as a unit of measure. They are one of the oldest manipulatives around, developed decades ago, and also one of the most versatile tools in a classroom.
Cuisenaire rods can be used for counting just counting rods without attaching a value , addition, subtraction, multiplication multiples and factors , division, area, perimeter, volume, geometry and algebra. These rods are complex in nature and thus have a very high level of abstraction, meaning that, for ideal use, students must be able to assign values to different sized single blocks.
One blue block has a value of nine units even though it's just one block. Remember, if students are having difficulty illustrating their work with these Cuisenaire blocks, have them use unifix cubes instead. The level of abstraction for that manipulative is lower, and students will be able to prove and illustrate their work more easily using them.
Geoblocks These wooden Geoblocks come in a set filled with a myriad of geometric shapes. They are certainly used with young children for building and vocabulary development always use rich mathematical vocabulary with your students , but more frequently they are used with geometry projects. Students decide upon a square unit of measure and then work to find the volume and surface area for these regular and irregular shapes.
They construct surface area nets or jackets for the individual shapes as well as combine several blocks to make the learning task more complex. Fraction Tiles Every classroom should have a few sets of fraction tiles.
These make for possibly the best way to finally understand adding, subtracting, multiplying and dividing fractions! Each set comes with 16ths, 12ths, 8ths, 6ths, 4ths, 3rds, halfs, and a whole. Of course, it's more challenging and fun to create projects that change the value of the "whole," thus changing the value of the other pieces! This is an outstanding manipulative to use in your classroom.
Fractional Pattern Blocks These small tiles are sized to work with pattern blocks. They are an outstanding addition to any pattern block set as they let you turn a hexagon into fourths and twelfths. These make a great extension piece for fraction work. Fractional Pattern Blocks These pink and black wooden blocks measure exactly the same as pattern blocks. They are designed to offer students extensions with pattern block fractions.
Basically, by assigning values to these pieces what if one black piece had a value of one? While they are convenient, students can do the same extensions with the standard pattern blocks. Cuisenaire Rod Counting Track These plastic counting tracks come in 24 inch and 36 inch lengths. They fit Cuisenaire rods and any other centimeter size cubes and have numbers and centimeter marks along the side.
By placing blocks in the track, students can figure out the sum of a multi-digit equation or use the track to double check their answer for an algorithm they are learning. These are wonderful tools for students who can build complex equations but do not yet have the algorithm skills to solve the corresponding numeric equation. Base Six Blocks These plastic blocks mirror the base ten set with cubic centimeter units and rods, flats and cubes, except only six units form a rod.
The flat, therefore, is equal to six rods 36 units , and the cube can be formed using six flats units. Of course using multi-base blocks is a terrific extension for students needing to solidify their understanding of place value trading.
Surprisingly, this manipulative is also great for younger students who are just learning to count and trade. Base ten might be too many objects to work with so teach the trading process using smaller bases. Other base block sets available are base 5, base 4, base 3 and base 2. Be aware, the smaller the base the more frequent the trades Try base 2 yourself for a fun challenge!
Base Five Blocks These plastic blocks mirror the base ten set with cubic centimeter units and rods, flats and cubes, except only five units form a rod. The flat, therefore, is only five rods in width 25 units and the cube is five flats tall units. Of course using multi-base blocks is a terrific extension for students needing to solidify their understanding of place value. Base ten counting might involve too many objects to work with so teach the trading process using smaller bases.
Other base block sets available are base 6, base 4, base 3 and base 2. The discrepancy may arise partly because the students know that their small-group colleagues will not accept inexact or unclear oral explanations, whereas a written letter provides no immediate feedback. This lack must be addressed, however, because the development of students' communication skills is an important goal of reform.
Task design considerations: This is an excellent task to illustrate the importance of the precise wording of questions. It is tempting to say "using two colors" instead of "when you had two colors available to work with.
There's certainly nothing wrong with the task of determining the number of towers that use exactly two colors, but it is not the same as the task of finding the number of towers that use no more than two colors. The essential point here is that small changes in the wording of questions can have significant and often unintended consequences. Ordinarily, it is not the aim of the task to have children make these subtle distinctions, so it is important.
The instructions deliberately say "Please send a letter to a student …. For the same reason there are no lines on which to write — just blank space that the student can use as he or she wants to.
Other kinds of colored cubes are often used in elementary school classrooms, but one should be aware that certain brands of cubes can snap together on their sides, so that L-shaped towers can be built. As a result, these cubes are not appropriate for this task unless the students understand that only three-in-a-row towers are to be counted.
Variants and extensions: This task lends itself well to simple alterations of the numbers: One can change the height of the towers or the number of different colors that are available. Moreover, one can vary the difficulty of the task by changing the rules that determine what towers are allowable. For example, how many towers five blocks high can be made from red or blue blocks if no pair of blue blocks can touch each other?
One can vary the whole context as well, using something other than towers of blocks. Care must be taken to ensure that the mathematics of the situation is still what is intended. Consider, for instance, the problem of creating rows of plants in a garden. Blue-flowered plants and red-flowered plants are available. How many different rows of three plants are possible? This is not the same as the towers problem because a garden row can be viewed from either side; R-R-B is the same as B-R-R.
The high response shows recognition of the need for a systematic scheme to keep track of "all possibilities" in a way that supports a conclusion that there could not be any other towers of height three. The student reasoning does not rely on the argument that "I cannot think of any others," but instead presents some reasonable scheme that is potentially exhaustive.
Proof by cases. There is only one tower that has zero blues. There are three towers with exactly one blue in the bottom, middle, or top positions in the tower. There are three towers with exactly two blues there is usually some weakness in the argument at this point.
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Dice Dice are fun way to practice math concepts. Modeling addition combinations with Unifix Cubes. We used both snap cubes and linking cubes for this 3-D to 2-D activity. Maria Arana Hi, I am Maria, a mom to three wonderful kiddos. Previous Post Tips for Taking Notes. Next Post How to Study Effectively. Leave a Reply Cancel reply Enter your comment here Fill in your details below or click an icon to log in:. Email required Address never made public.
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