In Grade 5, students recognized volume as an attribute of solid figures. They measured volume by packing right rectangular prisms with unit cubes and found that determining volume was the same as multiplying the edge lengths of the prism (5.MD.C.3, 5.MD.C.4). Students extend this knowledge to Module 5, Topic C where they continue packing right rectangular prisms with unit cubes; however, this time the right rectangular prism has fractional lengths (6.G.A.2). In Lesson 11, students decompose a one cubic unit prism in order to conceptualize finding the volume of a right rectangular prism with fractional edge lengths using unit cubes. They connect those findings to apply the formula V = lwh and multiply fractional edge lengths (5.NF.B.4). In Lessons 12 and 13, students extend and apply the volume formula to V = The area of the base times height or simply V = bh, where b represents the area of the base. In Lesson 12, students explore the bases of right rectangular prisms and find the area of the base first, then multiply by the height. They determine that two formulas can be used to find the volume of a right rectangular prism. In Lesson 13, students apply both formulas to application problems. Topic C concludes with real-life application of the volume formula where students extend the notion that volume is additive (5.MD.C.5c) and find the volume of composite solid figures. They apply volume formulas and use their previous experience with solving equations (6.EE.B.7) to find missing volumes and missing dimensions.

Content Standard(s):

Mathematics MA2019 (2019) Grade: 6

19. Write and solve an equation in the form of x+p=q or px=q for cases in which p, q, and x are all non-negative rational numbers to solve real-world and mathematical problems.

a. Interpret the solution of an equation in the context of the problem.

Unpacked Content

Evidence Of Student Attainment:

Students: Given contextual or mathematical situations which may be modeled by x + p = q or px = q (p,q, and x are rational and non-negative),

Explain the role of the variable as a place holder where the variable stands for a particular number (y + 7 = 12) or a value in a formula (A = L × W) and where values are substituted for one or more variables another variable assumes different values.

Write and solve equations modeling the situation, solve the resulting equations, and justify the solutions.

Teacher Vocabulary:

Variable

Equation

Non-negative rational numbers

Knowledge:

Students know:

Correct translation between verbally stated situations and mathematical symbols and notation.

How to write and solve a simple equation using non-negative rational numbers to solve mathematical and real-world problems.

Skills:

Students are able to:

Translate fluently between verbally stated situations and algebraic models of the situation.

Use inverse operations and properties of equality to produce solutions to equations of the forms x + p = q or px = q.

Use logical reasoning and properties of equality to justify solutions, reasonableness of solutions, and solution paths.

Understanding:

Students understand that:

Variables may be unknown values that we wish to find.

The solution to the equation is a value for the variable which, when substituted into the original equation, results in a true mathematical statement.

A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.

The structure of mathematics present in the properties of the operations and equality can be used to maintain equality while rearranging equations, as well as justify steps in the solutions of equations.

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.6.19.1: Define equation and variable.
M.6.19.2: Set up an equation to represent the given situation, using correct mathematical operations and variables.
M.6.19.3: Solve the equation represented by the real-world situation.
M.6.19.4: Identify the unknown variable in a given situation.
M.6.19.5: List given information from the problem.
M.6.19.6: Explain the solution in the context of the problem.

Prior Knowledge Skills:

Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Recognize key terms to solve word problems. Examples: times, every, at this rate, each, per, equal/equally, in all, total.

Define simple expression.

Recall simple equations.

Recognize properties of addition and multiplication.

Apply properties of operations as strategies to add and subtract.

Recall properties of operations as strategies to add and subtract.

Represent addition and subtraction with objects, mental images, drawings, expressions, or equations.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.6.19 Match equations and inequalities to real-world situations.

Mathematics MA2019 (2019) Grade: 6

28. Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

a. Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

Unpacked Content

Evidence Of Student Attainment:

Students: Given a right rectangular prism with fractional edge lengths within a real-world or mathematical problem context,

Find and justify the volume of the prism as part or all of the problem's solution by relating a cube filled model to the corresponding multiplication problem(s).

Given cubes with appropriate unit fraction edge lengths,

Create and explain rectangular prism models to show that the volume of a right rectangular prism with fractional edge lengths l, w, and h is represented by the formulas V = l w h and V = b h.

Teacher Vocabulary:

Right rectangular prism

V = b h (Volume of a right rectangular prism = the area of the base x the height)

Knowledge:

Students know:

Measurable attributes of objects, specifically volume.

Units of measurement, specifically unit cubes.

Relationships between unit cubes and corresponding cubes with unit fraction edge lengths.

Strategies for determining volume.

Strategies for finding products of fractions.

Skills:

Students are able to:

Communicate the relationships between rectangular models of volume and multiplication problems.

Model the volume of rectangles using manipulatives.

Accurately measure volume using cubes with unit fraction edge lengths.

Strategically and fluently choose and apply strategies for finding products of fractions.

Accurately compute products of fractions.

Understanding:

Students understand that:

The volume of a solid object is measured by the number of same-size cubes that exactly fill the interior space of the object.

Generalized formulas for determining area and volume of shapes can be applied regardless of the level of accuracy of the shape's measurements (in this case, side lengths).

Diverse Learning Needs:

Essential Skills:

Learning Objectives: M.6.28.1: Define volume, rectangular prism, edge, and formula.
M.6.28.2: Recall how to multiply fractional numbers.
M.6.28.3: Evaluate the volumes of rectangular prisms in the context of solving real-world and mathematical problems.
M.6.28.4: Use models and volume formulas (V=lwh and V=Bh) to find volumes in the context of solving real-world and mathematical problems.
M.6.28.5: Calculate the volume of a rectangular prism using fractional lengths.
M.6.28.6: Test the formula V= lwh and V=Bh with the experimental findings.
M.6.28.7: Experiment with finding the volume using a variety of sizes of rectangular prisms manipulatives.

Prior Knowledge Skills:

Define volume.

Recognize the formula for volume.

Recall the attributes of three-dimensional solids.

Compare the unit size of volume/capacity in the metric system including milliliters and liters.

Measure and estimate liquid volumes.

Describe attributes of three-dimensional figures.

Describe attributes of two-dimensional figures.

Define volume including the formulas V = L × W × h, and V = B × h.

Define solid figures.

Define unit cube.

Recognize that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals).

Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Describe attributes of three-dimensional figures.

Describe attributes of two-dimensional figures.

Compare the unit size of volume/capacity in the metric system including milliliters and liters.

Alabama Alternate Achievement Standards

AAS Standard: M.AAS.6.28 Solve real-world and mathematical problems involving the volume of cubes and rectangular prisms.

Tags:

edge, equations, formula, length, realworld, right Rectangular prism, unit cubes, volume