20804214Math for Elementary Education 2
Course Information
Description
A second course in mathematics needed for teaching K-8. Emphasis will be on the student communication how and why standard and alternative algorithms work. Content will focus on problem solving strategies and word problems involving geometry, measurement, algebra, statistics, and probability. The courses in this sequence can be taken in any order.
Total Credits
3
Course Competencies
  1. Apply Algebraic strategies to a variety of problems.
    Assessment Strategies
    Test
    Criteria
    Formulate and evaluate numerical expressions efficiently.
    Evaluate algebraic expressions at given values for variables.
    Write expressions for quantities and explain why they are formulated the way they are.
    Formulate equations arising from scenarios using rectangular designs, strip diagrams, or tables.
    Solve equations by reasoning about numbers, operations, and expressions.
    Explain different ways to reason to solve one-step equations.
    Solve equations algebraically, and describe the method of solving.
    Give examples of equations in one variable that have no solutions.
    Give examples of equations in one variable that have infinitely many solutions.

  2. Solve problems involving sequences.
    Assessment Strategies
    Test
    Criteria
    Solve problems about growing sequences using algebra and by reasoning.
    Given an arithmetic sequence, find an expression for the Nth entry, and explain why this expression is valid.
    Given a geometric sequence, find an expression for the Nth entry, and explain why this expression is valid.
    Given an arithmetic sequence, describe the associated function, make a table and graph for the function, find an equation for the function, and explain why the equation is valid.

  3. Use Functions to describe real-life situations.
    Assessment Strategies
    Test
    Criteria
    Determine if a proposed function is or is not a function.
    Use words to describe a function for a given context.
    Given a description of a function in words, draw a graph of the function. Explain how the graph fits with the description of the function.
    Given the graph of a function, describe aspects or features of the function. Explain how the graph informs you about those sections or features.
    Given an equation of a function, use reasoning to determine information about the function.
    Given two quantities in a proportional relationship, describe an associated function, make a table and graph for the function, and find an equation for the function.
    Given information about a function, determine if the function is linear or not.
    Describe a linear function in words, with a table, with a graph, and with an equation, and explain why the equation is valid.
    Contrast patterns of change in linear and other types of functions.

  4. Discuss and solve problems about angles.
    Assessment Strategies
    Test
    Criteria
    Explain why the angles opposite each other, which are formed when two lines meet, are equal.
    Show informally that the sum of the angles in a triangle is 180 degrees.
    Use the Parallel Postulate to prove that the sum of the angles in every triangle is 180 degrees.
    Apply facts about angles produced by configurations of lines to find angles.

  5. Discuss and solve problems about triangles, Quadrilaterals, and other Polygons.
    Assessment Strategies
    Test
    Criteria
    Give definitions of special quadrilaterals and triangles.
    Describe how categories of quadrilaterals are related to each other.
    Use a compass to construct triangles of specified side lengths (including equilateral and isosceles triangles), and use the definition of circle to explain why the construction must produce the required triangle.
    Use a compass to construct rhombuses, and use the definition of circle to explain why the construction must produce a rhombus.
    Fold and cut paper to produce various triangles and quadrilaterals.
    Describe how to make shapes by walking and turning along routes.

  6. Discuss and solve problems involving measurements.
    Assessment Strategies
    Test
    Criteria
    Discuss units and how a measurement is a comparison with a unit.
    Use proper notation for units of length, area, and volume.
    State the meaning of common metric prefixes.
    Describe how capacity, weight (mass), and volume are linked in the metric system.
    Compare objects with respect to one-dimensional, two-dimensional, and three-dimensional attributes.
    Describe how one object can be larger than another object with respect to one attribute, but smaller with respect to a different attribute.
    Explain how a reported measurement conveys how precisely the measurement is known.
    Use multiplication or division or both to convert a measurement from one unit to another. Explain why multiplication or division is the correct operation to use (without using dimensional analysis).
    Use dimensional analysis to convert from one measurement to another, explaining the method.

  7. Discuss and solve problems involving areas of shapes.
    Assessment Strategies
    Test
    Criteria
    Explain why it is valid to multiply the length and the width of a rectangle to determine its area.
    Explain and use the area formula for rectangles in the case of fractions, mixed numbers, and decimals being careful with the units of length and area.
    Use the moving and additivity principles to determine areas of shapes, including cases where ultimately subtraction is used to determine the area of a shape of interest.
    Determine the area of a triangle in various ways.
    Use the moving and additivity principles to explain why the area formula for triangles is valid for all triangles.
    Use the area formula for triangles to determine areas and to solve problems.
    Use the moving and additivity principles to explain why the area formula for parallelograms is valid.
    Use the area formula for parallelograms to determine areas and to solve problems.
    Determine areas of various polygons.
    Use the definition of  and the fact that the diameter of a circle is twice its radius to explain the  formula for the circumference of a circle of radius r.
    Explain why the  formula for the area A square units of a circle of radius r units is plausible by subdividing a circle and rearranging pieces.
    Use the formulas for circumference and area of a circle to determine lengths and areas and to solve problems.
    Explain why and how to calculate perimeters of polygons. Discuss misconceptions with perimeter calculations.
    Given a fixed perimeter, determine the areas of all rectangles of that perimeter and determine the areas of all shapes of that perimeter.
    State and prove the Pythagorean Theorem. Use the Pythagorean Theorem to determine lengths and distances.

  8. Discuss and solve problems involving the volume and surface area of solid shapes.
    Assessment Strategies
    Test
    Criteria
    Describe prisms, cylinders, pyramids, and cones and distinguish them from two-dimensional shapes.
    Determine the number of vertices, edges, and faces of a given type of prism or pyramid, and explain why the numbers are correct.
    Explain, based on angles, why putting too many faces together at a vertex results in a nonconvex shape.
    Describe what shape a pattern will make.
    Make patterns for prisms, cylinders, pyramids, and cones of specified dimensions.
    Determine the surface area of prisms, cylinders, pyramids, and cones.
    Determine the volume of a solid shape.
    Use the moving and additivity principles for volume.
    Explain why the volume formula for prisms and cylinders is valid.
    Explain why the 1/3 in the volume formula for pyramids and cones is plausible.
    Use the volume formulas for prisms, cylinders, pyramids, cones, and spheres to determine volumes and to solve problems.
    Discuss the distinction between the volume, the surface area, and the height of a solid shape.

  9. Discuss and solve problems involving the Geometry of Motion and Change.
    Assessment Strategies
    Test
    Criteria
    Determine the location of a shape after a translation, a reflection, a rotation of 90 degrees clockwise or counterclockwise, or a 180 degree rotation is applied.
    Given the location of a shape before and after a transformation,, determine the transformation.
    Given a shape or design, determine its symmetries.
    Create designs that have specified symmetries.
    Explain what congruence means.
    Show that some pieces of information specify a unique triangle, whereas others do not.
    Describe and use the SSS, ASA, SAS criteria for congruence.
    Relate the structural stability of triangles to the SSS congruence criterion.
    Contrast the structural stability of triangles with the lack of stability for quadrilaterals.
    Given a line segment, construct the perpendicular bisector by using a compass and straightedge. Describe the associated rhombus, and relate the construction to a special property of rhombuses: In a rhombus, the diagonals are perpendicular and bisect each other.
    Use a compass and straightedge to bisect a given angle. Describe the associated rhombus, and relate the construction to a special property of rhombuses: In a rhombus, the diagonals bisect the angles in the rhombus.
    Describe what it means for shapes or objects to be similar.
    Use the scale factor and internal factor methods to solve problems about similar shapes, explain the rationale for each method and relate them to proportions.
    Explain why triangles are similar by showing that corresponding angles must have the same size (the angle-angle-angle criterion). When the Parallel Postulate applies, use it so show that corresponding angles are produced by a line crossing two parallel lines and are therefore of the same size.
    Use similar triangles to determine heights and distances.
    Use similar shapes or objects to solve problems.
    Use patterns, models, and formulas to explain how areas and volumes of similar objects are related.
    Apply the way that areas and volumes scale in similar objects to solve problems.

  10. Discuss and solve statistical problems.
    Assessment Strategies
    Test
    Criteria
    Describe why some samples may not be representative of a whole population, but that large enough random samples generally are.
    Use random samples to make predictions about a full population with the aid of proportions.
    Make data displays to help convey information about data.
    For a given data display, formulate and answer questions at the three levels of graph reading.
    Recognize erroneous or misleading data displays.
    Describe how to view the mean as leveling out, and explain why this way of viewing the mean agrees with the way we calculate the mean (by adding and then dividing).
    Use the leveling out view of the mean to solve problems about the mean. Also use the standard way of calculating the man to solve problems about the mean.
    Describe how to view the mean as a balance point and describe why this point of view is especially appropriate for data displayed in histograms and dot plots.
    Create data sets with different means and medians.
    Discuss errors that students commonly make with the mean and the median.
    Indicate the shape a data distribution is likely to take, expecially in the case of random samples.
    Given a data set, determine the median, the first and third quartiles, and the interquartile range. Use medians and interquartile ranges to discuss and compare data sets.
    Make box plots and use box plots to discuss and compare data sets.
    Discuss the difference between percentiles and percent correct.
    Given a data set, determine the mean and the man absolute deviation (MAD). Use means and MADs to discuss and compare data sets.

  11. Discuss and solve probability problems.
    Assessment Strategies
    Test
    Criteria
    Use principles of probability to determine probabilities in simple cases.
    Recognize that an empirical probability is likely to be close to the theoretical probability when a chance process has occurred many times.
    Apply empirical probability to make estimates.
    Apply multiplication to count the total number of outcomes in various situations, including those of multistage experiments and cases where the outcome at one stage depends on the outcome oat pervious stages.
    Calculate an expected amount of earnings when probabilities are involved.
    Explain why certain probabilities can be calculated by the multiplication of fractions.
    Use fraction arithmetic to determine certain probabilities, and explain why the method of calculation makes sense.