# Apply mathematical problem solving to machining operations.

## Definition

Application should include using arithmetic, geometric, algebraic, and trigonometric operations when- selecting and sequencing operations
- holding the work
- producing surfaces
- locating surfaces and center lines
- analyzing operations and sequences
- troubleshooting a machine tool or cutting tool
- calculating speeds and feeds
- calculating operation times
- calculating dimensions from a blueprint
- factoring statistics required by control charts
- identifying the impact of a change of speed or feed
- calculating the volume of material stored
- using trade formulas to prepare a process plan
- performing benchwork and layout operations
- operating machine tools
- performing inspection and control functions
- solving for unknowns in right triangles
- analyzing parts for plane perpendicularity, Cartesian coordinates, concentricity, parallelism, straightness, flatness, circularity, and symmetry, with an accuracy required by the blueprint and industry standard.

## Process/Skill Questions

- What tools are available to assist machinists in their calculations?
- What is a common machining task or problem that would require the machinist to apply principles of trigonometry?
- How are tolerances applied to dimensions?

## Related Standards of Learning

## Mathematics

### A.1

The student will

- represent verbal quantitative situations algebraically; and
- evaluate algebraic expressions for given replacement values of the variables.

### A.4

The student will solve

- multistep linear and quadratic equations in one variables algebraically;
- quadratic equations in one variables algebraically;
- literal equations for a specified variable;
- systems of two linear equations in two variables algebraically and graphically; and
- practical problems involving equations and systems of equations.

### G.13

The student will use surface area and volume of three-dimensional objects to solve practical problems.

### G.14

The student will apply the concepts of similarity to two- or three-dimensional geometric figures. This will include

- comparing ratios between lengths, perimeters, areas, and volumes of similar figures;
- determining how changes in one or more dimensions of a figure affect area and/or volume of the figure;
- determining how changes in area and/or volume of a figure affect one or more dimensions of the figure; and
- solving problems, including practical problems, about similar geometric figures.

## Science

### PH.2

The student will investigate and understand how to analyze and interpret data. Key concepts include

- a description of a physical problem is translated into a mathematical statement in order to find a solution;
- relationships between physical quantities are determined using the shape of a curve passing through experimentally obtained data;
- the slope of a linear relationship is calculated and includes appropriate units;
- interpolated, extrapolated, and analyzed trends are used to make predictions; and
- situations with vector quantities are analyzed utilizing trigonometric or graphical methods.

## Other Related Standards

## Common Career Technical Core

### MN-MIR4

Investigate and employ techniques to maximize manufacturing equipment performance.