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Khan Academy has gained popularity over the past few years and includes videos, usually with step-by-step breakdowns of mathematical topics stretching across grade levels. The page linked is helpful for 5th graders who are struggling or need more practice and explanation regarding place value with decimals. A short video provides a visual and auditory explanation and also offers a quiz to practice the skills. This quiz can serve as a type of Exit Ticket to inform instruction.

CCSS CCSS.MATH.CONTENT.5.NBT.A.1, CCSS.MATH.CONTENT.5.NBT.A.2,CCSS.MATH.CONTENT.5.NBT.A.3, CCSS.MATH.CONTENT.5.NBT.A.3.A

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On this portion of the Math Playground site, students build a model and solve for x. It has options for one step problems, two step problems, or even the option to make your own problem which can be helpful if there is a problem within the textbook or homework and students need some additional support in working it out. They are able to manipulate the blocks and once again, are given color coded blocks to create a more powerful visual representation. Students will isolate the x blocks which will ultimately allow them to gain the value for x. Some beneficial features include the ability to instantly check to see if your answer is correct, color coded blocks, automatic counting, etc. For assessment purposes, an Exit Ticket can be provided to students giving them an equation. They can input this equation by clicking on the “Make your own” option and the teacher can instantly see which students will need additional support and focus on where their misunderstandings might be.

CCSS CCSS.MATH.CONTENT.6.EE.A.2, CCSS.MATH.CONTENT.6.EE.B.5, CCSS.MATH.CONTENT.6.EE.B.6, CCSS.MATH.CONTENT.6.EE.B.7

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In seventh grade, students must continue to make use of variables by combining like terms, using positive and negative coefficients, using the distributive property with the variables, etc. The National Council of Teachers of Mathematics offers a tool on their site comprised of algebra tiles. The students are given an algebraic expression that they must build and multiply. They are able to use both positive and negative blocks and will be able to see that some will cancel each other out (a positive and a negative of the same type of tile). They will then combine like terms using this visual representation and be able to solve for the variable. The hands-on approach along with the colored tiles, ability to switch between negative and positive, and instant ability to check your work makes this a nice tool to practice these concepts. As an assessment, “My Favorite No” can be used (Vierstra, 2015). Since the screen instantly turns orange and makes a special sound when the answer input is incorrect, the teacher can take note of those students, and use one of those expressions whole class to initiate discussion of how to work through the problem, what the mistake was, and why.

CCSS CCSS.MATH.CONTENT.7.EE.A.1, CCSS.MATH.CONTENT.7.EE.A.2, CCSS.MATH.CONTENT.7.EE.B.3, CCSS.MATH.CONTENT.7.EE.B.4

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Modes

In Solve and Substitute, vertical lines indicate "is equal to" (=).

In Expand and Factor, the large area is the product of the top and left areas, as in a standard multiplication table.

Adding Tiles

Add tiles to the workspace from the bottom left bank. The value of each tile is indicated. When moved to the workspace, the value will be erased.

Flip turns tiles over, giving the inverse value. For example when a green x is flipped, it becomes a red -x tile. Flipping the red -x tile, gives the inverse green x tile. You can click the button to flip all tiles in the bank or move tiles to the workspace, and then click to flip those tiles over.

Turn rotates the green x and red -x tiles 90°. This is most useful in the Expand and Factor activities.

Other Tools

Tools may be used on single tiles by select them or a group of tiles by selecting several or dragging a rectangle around a group of tiles. The tool may be selected before the tile for a single action or after to allow for a repeated action.

Pointer selects and moves tiles. This is the default tool. When the empty workspace or a tile from the bank is selected, this tool is automatically selected.Note: Depending on the activity, some tiles may not be removed.

Eraser removes tiles from the workspace. Note: Depending on the activity, some tiles may not be removed.

Remove Zero Pairs allows only zero pairs to be removed from the workspace. This is most helpful in solving Solve and Expand problems or anytime in Factor problems to ensure tiles are properly removed. A zero pair is a pair of tiles that sums to 0, such as a yellow 1 tile and a red -1 tile.

Copy copies the currently selected tile(s). Move the tile(s) to see the copy. This is most helpful when a large number of tiles must be placed in the workspace, such as forx ² - 16.

Completing a Problem

All problems must be completed in two steps:

1. Build the model
Place the correct pieces in the workspace. After you build the model of the given problem, Check your answer to move on to the next step. Only tile type, tile quantity, and workspace area are checked, not the way in which tiles are arranged.

If you want to start again, Reset to empty your workspace.

2. Solve the problem
in After you solve the problem, Check your answer. Where applicable, answers must be given in simplified form. Both the entered answer and workspace must be correct. If one or both is incorrect, the incorrect portion will be indicated. Note: Factor mode, all factors must be entered in parentheses. x(x + 1) will be marked wrong. (x)(x + 1) will be accepted.

If you want to start again, Reset to go back to your original model.

3. When you complete your problem or at any other point, you may start a New problem.

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Use tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor.

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Often when people think of algebra, they think of the x and the y and of course, graphing and plotting points. This can be a confusing process and one riddled with self-doubt. However, the hrw.com website can help students with graphing equations. They can enter the equations and a graph will be formed for them. It also allows them to plot points and color coordinates the different equations so that you can view the line created for each. Students can see the ways in which the lines intersect, find the slope, etc. The user friendly aspects of the site including the color coding of each line, easy to use buttons reminiscent of a calculator, and tabs which separate the job you wish to do can help students focus on graphing. In terms of assessment, I would use the Stoplight Method which would allow students to state what they learned about graphing (green), ideas or things they explored on this graphing site (yellow), and anything they might have become stuck or confused on (red) (Vierstra, 2015). The teacher would then be able to display the graphing tool on the board for all to see and a discussion can occur about any misconceptions or students can explain their methods and thinking.

CCSS CCSS.MATH.CONTENT.8.EE.C.8, CCSS.MATH.CONTENT.8.EE.C.8.A, CCSS.MATH.CONTENT.8.EE.C.8.B, CCSS.MATH.CONTENT.8.EE.B.5