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Course Objectives

These are the course objectives from the textbook (A Problem Solving Approach to Mathematics for Elementary School Teachers by Billstein, Libeskind, and Lott). There are additional objections not from the book, such as problem solving objectives and mental math objectives. (Note for Spring 2016: Objectives are being adjusted to match the 12th Edition of the textbook.)

All objectives will appear on homework, homework quizzes, and potentially* on exams (*to keep exams reasonable in length, there may be some objectives which will not appear on exams). SBA (Standards Based Assessment) Objectives will also appear on SBA quizzes.

Objectives from Chapter 3

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 3-2 S.1 Models for AdditionDemonstrate* addition using the

  • (a1) join sets model (using manipulatives) and
  • (a2)  number-line model

(Additional objectives involving addition follow.)

 A.1 Closure Property of Addition (and of Multiplication) –  Determine if a set is closed under addition and under multiplication.
 3-3 S.2 Models  Subtraction – Demonstrate subtraction using the

  • (s1) take-away model (using manipulatives),
  • (s2) comparison model (using manipulatives), and
  • (s3) number-line model.

S.3 Addition and Subtraction Algorithms with Units – Perform addition and subtraction with units, when regrouping may be required.

S.4 Model the Standard Algorithms for Base-Ten Addition and Subtraction – Demonstrate (using base-ten blocks) addition (using the join sets model*) and subtraction (using the take-away model*). *On the quizzes you need to know to join and take-away.)


A.2 Problem Solving – Apply concepts of addition and subtraction to solve problems.A.3 Addition and Subtraction Algorithms – Use the standard algorithms for addition and subtraction and use the equal-additions algorithms for subtraction.
 3-4 S.5 Properties of Addition and Multiplication – Given a sentence, identify the property illustrated.

S.6 Model Base-Ten Multiplication – Demonstrate (using base-ten blocks) 2-digit multiplication.

A.4 Fundamental Counting Principle – Apply the  fundamental counting principle to problems.  A.5 Distributive Property – Apply the distributive property. A.6 Solve Equations – Solve linear equations.

A.7 Standard Multiplication Algorithm – Apply the standard multiplication algorithm to multiply numbers.

A.8 Properties of Exponents – Simplify expressions with exponents.

 3-5 S.7 Fact Family for Multiplication and Division – Given one member of a multiplication-division fact family, state all members of the family. A.9 Long Division Algorithm– Apply the long division algorithm to find quotients

  • with a remainder,
  • as a mixed number,
  • as a decimal.

A.10 Short Division Algorithm – Apply the short division algorithm to find quotients. (#HO4)

A.11 Problem Solving – Apply concepts of multiplication and division to solve problems.

*Generally, ‘demonstrate’ means to be able to do it with physical manipulatives or make a diagram of the manipulatives.

Objectives from Chapter 4

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 4-1  S.8 Divisibility Tests – Apply the divisibility tests for 2, 3, 4, 5, 6, 8, 9, and 10 to (a.) Fill in a missing digit of a number to make it divisible by a given number and (b) List all the divisors of a number.  A.12 Divisibility Tests – Apply the divisibility tests for 2, 3, 4, 5, 6, 8, 9, and 10 to determine if a given number is divisible by a given number. (#A3, B3)A.13 Divisibility Problem Solving – Apply concepts of divisibility to solve problems. 4-1 (#A2, B2) & 4-2 (#A7, 19; B7, 19; Connections 6)A.14 Reasoning about Divisibility– Use the concepts of divisibility (terms: divisor, divisible, factor, multiple) and divisibility notation (the vertical var: |) to answer true-false questions and provide counterexamples. (#A1, 8, B1, 8)
 4-2  S.9 Prime Factorization and Number of Factors – Find the prime factorization of a number and use it to determine the number of factors the number has. A.15 Primes and Composites – Determine if a number is prime or composite. (#A2, B2)A.16 Prime Factorization – Find the prime factorization of a number that is already partially factored. (#A6, 17, 20; B6, 17, 20)A.17 List Factors – List all the factors (divisors) of a number. (#HO1)
 4-3 S.10 Greatest Common Factor – Find the GCF using prime factorization and find GCF using the Euclidean Algorithm.S.11 Least Common Multiple – Find the LCM using prime factorization and find the LCM using the relationship between LCM and GCF. (Calculator allowed on standard 11.) A.18 Greatest Common Factor – Find the GCF using the listing factors, ladder, and relationship to the LCM methods. (#A1, B1, #HO2)A.19 Least Common Multiple – Find the LCM using the listing multiples and ladder methods. (#A1, B1, #HO2)A.20 Problem Solving with GCD and LCM – Apply GCD and LCM to solve problems. (#A6-13; B6-13)

 Objectives from Chapter 6

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 6-1  † *E.1 Fundamental Law of Fractions – For any fraction \frac{a}{b} and any number c \neq0\frac{a}{b}=\frac{ac}{bc}E.2 Cross Multiplication for a Proportion – If \frac{a}{b}=\frac{c}{d}, with b,d \neq 0, then ad=bc.A.21 Model Fractions – State the fraction for a given diagram. (#A2-6; B2; Connections 7)A.22 Convert Units and Use a Scale – Solve problems involving scales and units. (#A21, B21)A.23 Problem Solving with Fractions – Apply fraction concepts to solve problems. (#A25, B14, 23; Connections TIMSS and NAEP items)
 6-2  † E.3 Adding Fractions – Explain why a common denominator is required for addition and subtraction of fractions?A.24 Problem Solving with Fractions – Apply fraction concepts to solve problems. (#A13, B11, 13)A.25 Benchmark Fractions – Approximate situations with benchmark fractions. (#A4, 6, 7; B8)
 6-3  † E.4 Multiplying Fractions – Explain why it is legal to simplify (‘cancel’) when multiplying fractions.E.5 Dividing Fractions – Explain why, when dividing fractions, we invert and multiply.E.6 Zero Exponent – Explain why x^0=1 (for all x\neq 0).A.26 Modeling Fraction Multiplication – Use grid paper to model multiplication of fractions. (HO1, A1, 2A.27 Problem Solving with Fractions – Apply fraction concepts to solve problems. (#A12-16, B12-16; Connections NAEP item)A.28 Solve Fractional and Exponential Equations – Solve equations involving fractions and exponents. (#A6, 20; B6, 20) & 6-4 (A2, B2)A.29 Properties of Exponents – Simplify expressions with exponents. (#A17, 18; B17,18)A.30 Division of Fractions Word Problems – Analyze a word problem involving division of fractions by

  • Stating the meaning (of division),
  • Drawing a diagram to model the operation and meaning,
  • Writing a number sentence,
  • Stating the answer to the question. (#HO4-12)
 6-4  †  A.31 Problem Solving with Proportional Reasoning – Apply proportional reasoning to solve problems. (#A4-11, 14, 16-20; B4-9, 14-18; Connections 3 Brothers TIMSS item, NAEP item)

*E objectives are “Explanation” Objectives. These will be on a quiz late in the semester. For each objective, typically, you will be asked to explain:

  1. Why we do it
  2. Why it is legal

†For Chapters 6 and 7 we will not have PBA Quizzes, but instead will have Mastery Quizzes.  There are 16 objectives on fractions, decimals, and percents.  This are here.

Fraction-Decimal-Percent Objectives (from Chapter 6 and 7)

The student should be able to (by hand, without using a calculator):

1. Put a fraction into lowest terms.
2. Put a fraction into higher terms.
3. Rewrite an improper fraction as a mixed number.
4. Rewrite a mixed number as an improper fraction.
5. Add and subtract fractions (and mixed numbers).
6. Add and subtract decimals
7. Read a decimal number properly. (2.03 is “two and three hundredths”)
8. Convert fractions (and mixed numbers) to decimals and to percents.
9. Convert decimals to fractions (or mixed numbers) and to percents.
10. Convert percents to decimals and to fractions (or mixed numbers).
11. Multiply fractions (and mixed numbers).
12. Multiply decimals.
13. Divide fractions (and mixed numbers).
14. Divide decimals.
15. Solve percent problems of the form ___% of ___ is ___, where two of the three blanks are known and one of the blanks is unknown.
16. In a percent change situation, find the percent change, the amount of change, or the original amount.

 Objectives from Chapter 7

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 7-1  †  A.32 Reading Decimals – Be able to read a decimal correctly. (#A4, B4)A.33 Expanded Place Value Form – Write a decimal in expanded place value form. (#A1, 2; B1, 2)A.34 Order Decimals – Put decimals in order (for example, from largest to smallest). (#A10, B10)
 7-2  †  E.7 Adding and Subtracting Decimals – Explain why, when adding or subtracting decimals, we need to line up the decimals.E.8 Multiplying Decimals – Explain why, when multiplying decimals, we do not need to line up the decimals, but we count the number of decimals places to the right of the decimal points.E.9 Dividing Decimals – Explain why, you can, and should, move the decimal point in the divisor and the dividend to make the divisor a whole number.A.35 Problem Solving with Decimals – Apply concepts to solve problems involving decimals. (#A1-8; B1-8)
 7-3  †  A.36 Repeating Decimals – Convert a repeating decimal into a fraction. (#A2, B2)
 7-4  †  A.37 Problem Solving with Percents – Apply concepts to solve problems involving percents, including simple interest and percent change (Note: There are 6 different percent change problems). (#A6-14; B6-14)

 Objectives from Chapter 8

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 7-5 S.12 Identify Real Number Subsets Given a number, determine to which sets it belongs (Natural, Integer, Rational, Real, Irrational).  A.38 Pythagorean Theorem – apply the Pythagorean Theorem. A.39 Real Number Subsets Answer questions (including true-false and intersection and union questions about the subsets of the real numbers (Natural, Whole, Integer, Rational, Real, Irrational).
 Solve-An-Equation P.S. Strategy  S.13 Solve Word Problems Apply the Solve-An-Equation Problem-Solving Strategy to solve word problems.
Spotting Numbers & Visual Patterns   S.14 Geometric Patterns Given a geometric pattern, which produces a numeric pattern, find numbers in the sequence and the algebraic expression for the nth number in the sequence.
8-4   S.15 Multi-step Equations Solve multi-step equations.  A.40 Systems of Equations Solve a system of equations using substitution or elimination.A.41 Word Problems Resulting in a Systems of Equations Solve word problems involving systems of equations (using substitution or elimination).

“S.14” has been removed.

 Objectives from Chapter 11

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 11-1  S.16 Intersections and Unions Find the intersection and union of points, lines, planes, segments, and rays.S.17 Relationship of Lines Determine if two given lines are skew, parallel, intersecting, or the same line. A.42 Basic Notions Answer questions about the relationships of points, lines, planes, segments, and rays.A.43 Relationship of Planes Determine if two given planes are parallel, intersecting, or the same plane.A.44 Drawing Geometric Figures Draw geometric figures (a specific list will be provided in class).
 11-2  S.18 Symmetry Determine if a figure has (i) Reflection symmetry, (ii) Rotation symmetry,  or (iii) Point symmetry.  A.45 Diagonals of a Polygon Determine the number of diagonals of an n-gon.A.46 Categorize Triangles Categorize triangles.A.47 Categorize Quadrilaterals Categorize quadrilaterals.
 11-3  S.19 Angles in a Polygon Solve problems involving the angles in an n-gon (which may, or may not, be regular).   A.48 Angles Formed by Parallels Apply relationships of angles formed by parallel lines and transversals (to find angles or determine if the lines are parallel).E.10 180° in a Triangle – Show why there are 180° in a triangle, three different ways.
11-4  S.20 Find the number of vertices, edges, and faces Given a description or picture of a pyramid, prism, or Platonic solid, determine the number of vertices, edges, and faces.

 Objectives from Chapter 13 (formerly chapter 14)

The student will be able to:

 Section  SBA Objectives  Additional Objectives & Explanation Objectives
 13-1  S.21 Convert Units Convert units.  A.49 Estimate Lengths Estimate lengths (and distances) in inches, feet, mm, cm, and m.A.50 Perimeter and Circumference Answer questions involving perimeter and circumference.A.51 Triangle Inequality Apply the Triangle Inequality.
 13-2  S.22 Areas on a Geoboard Find areas on a geoboard. E.11 Derive Area Formulas – Derive the area formulas for a ●triangle, ●parallelogram, ●trapezoid.A.52 Find Areas Solve area problems involving polygons and circles.
13-3 S.23 Graph a Circle Given the equation, graph the circle.  A.53 Pythagorean Theorem Apply the Pythagorean Theorem.A.54 Distances in the Plane Find the distance between points in the coordinate plane.
Conic Sections  will not not appear on an SBA Quiz  A.55 Given an equation, determine which conic section it is.  A.56 Graph a conic section.
14-4 will not not appear on an SBA Quiz  A.57 Find the Surface Area of 3-dimensional solids.
14-5 will not not appear on an SBA Quiz   A.58 Find the Volume of 3-dimensional solids.