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CCSS.MATH.CONTENT.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

CCSS.MATH.CONTENT.6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems

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Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects.

We can stack them and make different sized rectangular prisms to find volume, or you can only look at one side of them and calculate surface area.

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6.RP.A. Understand ratio concepts and use ratio reasoning to solve problems.

Students can use these to illustrate ratios through using different colors to represent parts of a ratio.

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CCSS.MATH.CONTENT.6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

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Basically spinners add randomness to the generation of numbers, colours or shapes. Spinners may be substituted for dice and vice versa to generate numbers. Spinners may be used as part of a game scenario in much the same way that dice help to generate moves.

CCSS.MATH.CONTENT.7.SP.C.7.A
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

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CCSS.MATH.CONTENT.6.RP.A.3.DUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantiti

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Cuisenaire blocks/rods                                                          different shapes (triangle, circle, stick etc., made of wood.                

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Cuisenaire blocks/rods                                                          different shapes (triangle, circle, stick etc., made of wood.                

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Students can see what numbers they want to manipulate and solve while multiplying or dividing the quantities using the rods.

They are really good when doing fractions/ counting as well.

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CCSS.MATH.CONTENT.7.RP.A.1
Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

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CCSS.MATH.CONTENT.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates

CCSS.MATH.CONTENT.6.NS.C.7.A
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.

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CCSS.MATH.CONTENT.7.RP.A.2
Recognize and represent proportional relationships between quantities.

Students can use the cubes to represent relationships between fractions. They can use the cubes to represent simplify fractions and represent the equivalency of fractions.

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CCSS.MATH.CONTENT.7.SP.C.7.A
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

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These blocks come in stacks of 1's, 10's, and 100's (typically). These blocks are usually used in elementary schools to help with addition and subtraction, however they can also be used in middle school:

CCSS.MATH.CONTENT.6.NS.B.2
fluently divide multi digit numbers. Students should be able to compute fluently with multi-digit numbers and find common factors and multiples.

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The abacus is used as a counting tool, for whole numbers, decimals, fractions. Also can be used for Addition, Subtraction, Multiplication and division.
CCSS.MATH.CONTENT.6.RP.A.3.D would work best with the abacus in 6th grade

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Find high-quality images, photos, and animated GIFS with Bing Images

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ccss.math.content.6.ns.a.1
apply and extend previous understandings to divide fractions by fractions.

By the time they hit middle school, the students have already had a lot of experience with fractions. They learn how divide them in 6th grade and then move onto ratios and proportions throughout the rest of middle school.

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Math.Content.6.NS.B.4
Find the greatest common factor within numbers up to 100 and the lowest common multiple of numbers
-Roll two dice and try and find the least common multiple between them
-Roll two dice, write down that two digit number, then roll it again and write down that number, then find the greatest common factor between them

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They are used in 6th, 7th and 8th grade math. An example is with equations and expressions, each grade has a standard that includes using graphs under equations & expressions.
Example:
CCSS.MATH.CONTENT.6.EE.C.9: Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
CCSS.MATH.CONTENT.7.EE.B.4.B: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
CCSS.MATH.CONTENT.8.EE.C.8.A: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

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You can use these chips when working with ratios because most of them are different colors or two colors on one.

CCSS.MATH.CONTENT.6.RP.A.1
Understand concept of ratio using ratio language to describe relationship

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) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation)

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CCSS.MATH.CONTENT.7.G.A.1
Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
CCSS.MATH.CONTENT.7.G.A.2
Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

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http://www.corestandards.org/Math/Content/6/G/A/3/   Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.

Students can use these to recognize geometric math in everyday life to solve problems

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Typically used in elementary school, but can be related to proportional reasoning in middle school.

CCSS.MATH.CONTENT.6.RP.A.2
Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."

CCSS.MATH.CONTENT.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

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AngLegs are adjustable, easy-to-manipulate strips that snap together to create different shapes such as triangles, squares, polygons, and rectangles.

CCSS.MATH.CONTENT.6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Students can use the AngLegs, create a geometric shape, and use that to help them solve a given problem. (especially helpful with geometry)