Day 1

Introductions & explore algebra tiles & I Spy paterns (NCTM 3-5 Navigations Through Algebra)

Day 2

What's my rule, looking at patterns

Day 3

Arithmetic and Geometric Sequences

Day 4

Graphs to stories and Stories to Graphs

Day 5

Interpretting graphs
Independent and Dependent variables

Day 6

Building Houses and practice problems from LaunchPad

Gayle has $30,000 salary and 2.4% commission while Helena has a $25,000 salary and 4% commission. Who has the better compensation package?

Day 7

K-2 Navigations: Math Machines, How Does it Grow?, Number Roads, Block Pounds, Balancing Act, and I Spy Patterns.

3-5 Navigations: The Ups & Downs of Patterns, Squares Cubed, Triangle Rule Machine, and Algebra Scales

Day 8

Test 1

Day 9

Review Test 1 and begin geometry. Finding central, interior, and exterior angles of regular polygons.

Day 10

Geometry terms and finding missing angles

Day 11

Venn Diagrams of quadrilaterals and triangles

Day 12

Polyhedra: Faces, Vertices, and Edges of Relational Geo-solids. Are they related?

Day 13

Isometric dot paper and perspective drawings

Day 14

Nets to make polyhedra

Day 15

Tetrominoes spinner & cover up board

Day 16

Alphabet Symmetry

Day 17

Box Puzzle and tessellations

Day 18

Tangrams -- make the seven squares

Reflections of Images & Using Scale Factors (NCTM - Navigations Through Geometry 6-8)

Day 19

Isometric Explorations & Isodot Paper

More Tangrams -- looking at side length and area of the seven squares

Day 20

Review for Test 2

Day 21

Test 2

Day 22

Euclidean constructions

Day 23

Proving the Euclidean constructions worked!

Day 24

Geometric topics

Day 25

Reflection of Image and Scale Factor (NCTM Navigations Through Geometry 6-8)

Day 26

Translations, Rotations, and Reflections

Day 27

Measurement with non-standard units

Day 28

Finding lengths and area on Geoboard
Pick’s Theorem -- Area, Border pegs, and Interior pegs

Day 29

Compare volume of prism and pyramid – arrange geo-solids by volume

Day 30

Calculate surface area and volumes of geo-solids

Day 31

Metric and standard measurements – metric time?

Day 32

Building formulas – A = b h and V = 1/3 B h

Day 33

Using formulas on a test.  Tennis ball problem (missing area/volume)

Day 34

Test 3

Day 35

Introducing probability as a number between zero and one

Day 36

Tree diagrams, area model, list, and tables to represent probability

Day 37

Dr. Todd presenting at NCTM

Day 38

With replacement or without replacement

Day 39

Solving similar triangles

Day 40

Euclidean constructions

Day 41

Translations and rotations

Day 42

Topological equivalency

Day 43

Test 5

Day 44

Review for Final exam

Department of Mathematics and Computer Science

8710.3200 Teachers of Elementary Education K-6

In this syllabus you will find the word TEACH. This will mean to:

1. Launch:  This is where the teacher sets the context of the problem or activity being worked on this day.  This involves making sure the students clearly understand the mathematical context and the mathematical challenge of the day’s activities.
2. Explore:  This is the time where the students get to work in pairs, individually, or as a class to solve problems presented by the lesson.
3. Share: This occurs when most of the students have made sufficient progress toward solving the problem presented with today’s lesson.  It is during this phase that the students learn how others approached the problem and possible solution routes.  Helps students deepen their understanding of the mathematical ideas presented in the day’s lesson.
4. Summarize/Apply:  During this phase the teacher concludes the lesson by clearly stating what the main idea was in the lesson, being sure to clear up any confusion that may arise during the “share” segment.  Helps students focus their understanding of the mathematical ideas presented in the lesson.

Standard

K/A

Activity

Assessment

H. A teacher of children in kindergarten through grade 6 must demonstrate knowledge of fundamental concepts of mathematics and the connections between them. The teacher must know and apply;

(2) concepts and techniques of discrete mathematics and how to use them to solve problems from areas including graph theory, combinatorics, and recursion and know how to:

(a) help students investigate situations that involve counting finite sets, calculating probabilities,

KA

Chapter 11
HW 11.1, 11.2

Students will demonstrate their ability to count finite sets with the counting principle, table diagram, or tree diagram as they build sample space models for events on homework, in-class work, and on questions on Test 3.

Students will demonstrate their ability to calculate probabilities for simple and compound events on homework, in-class work, and on questions on Test 3.

tracing paths in network graphs,

KA

Euler circuits and paths

Students will demonstrate the understanding of  tracing of network graphs by classifying the graphs as Euler circuits, Euler paths, or neither on homework, in-class work, and on questions on Test 5.

and analyzing iterative procedures; and

KA

Arithmetic and geometric sequences

Students will use iterative procedures to find elements of arithmetic, geometric, and other sequences on homework, in-class work, and on questions on Test 1.
Students will analyze arithmetic, geometric, and other sequences to generate iterative procedures or rules for the sequences on homework, in-class work, and on questions on Test 1.

 (b) apply these ideas and methods in settings as diverse as the mathematics of finance, population dynamics, and optimal planning;

KA

Finance – compound interest
Geometric growth of populations
Snowplow routes, delivery routes, traveling salesman – nearest neighbor

Students will apply iterative procedures in diverse settings of mathematics such as finance, to calculate compound interest, population dynamics to find populations from one generation to the next, or in optimal planning for snowplow routes, delivery routes, and guided tours on homework, in-class work, or on questions on Test 1 and 5.

(3) concepts of numerical literacy:

(d) understand the relationships of integers and their properties that can be explored and generalized to other mathematical domains;

KA

Operations and properties of integers. Evens/Odds in probability.
Regular polygon investigation.

Students will demonstrate that they understand the relationships of integers and their properties that can be explored and generalized to other mathematical domains such as probability, graph theory, and geometry on homework and in-class work.

(4) concepts of space and shape:

(a) understand the properties and relationships of geometric figures;

KA

Chapter 12
Van Hiele levels
Venn diagram triangles, quadrilaterals
Regular polygon investigation

Students will demonstrate  and understanding of the relationships of geometric figures when they construct a Venn diagram for seven classifications of triangles or a Venn diagram for nine classifications of quadrilaterals.

(b) understand geometry and measurement from both abstract and concrete perspectives and identify real world applications; and

KA

Chapter 13
Perimeter, area, and volume
calculate for given figures

Students will design an original abstract measurement system and be able to list positive aspects of their system.
Students will construct a table for eight measurement concepts, English units, and System International, metric, units.
Students will be able to give examples of where the different units for measurement concepts are used in real world applications.
Students will use the relationship between volume, capacity, and mass in the SI (metric) system in homework and in-class discussions and on test 4.

(c) know how to use geometric learning tools such as geoboards, compass and straight edge, ruler and protractor, patty paper, reflection tools, spheres, and platonic solids;

KA

Chapter 9,13
Geoboards – perimeter, area, ratios, Venn diagrams
Chapter 14
Constructions – compass and straight edge, patty paper, MIRA
Surface area and volume of hemi-spheres and spheres
Tiling, regular polygons, platonic solids

Students will demonstrate how to use geoboards to illustrate perimeter, area, ratios and Venn diagrams.
Students will be able to perform standard constructions such as angle bisector, segment bisector, and perpendicular bisector using straight edge and compass, MIRA, and patty paper on homework and in-class work or on Test 5.
Students will find the surface area and volume of a sphere, cylinder, cone, prism, and pyramid on homework, in-class work, or on questions on Test 4.
Students will identify regular and semi-regular tilings of a plane and the platonic solids formed from regular polygons on homework, in-class work or on Test 3.

(5) data investigations:

(a) use a variety of conceptual and procedural tools for collecting, organizing, and reasoning about data;

KA

Chapter 10
Tally marks, stem and leaf plot, box and whisker plot, conclusions
Raisin Activity

Students will collect data on the heights of individuals in cm, organize the data using tally marks and stem and leaf diagrams, and box plots. Students will draw at least one conclusion from the constructed box plot and give it orally when asked in class.

(b) apply numerical and graphical techniques for representing and summarizing data;

KA

Central Tendency: Mean, median, mode
Max, min, range, IQR, quartiles, outlier
Dispersion: range, standard deviation
Bar charts, histograms, pie charts, line graphs, pictographs

For a given set of data, students will organize it and display the data using stem and leaf plots, histograms, pie charts, or appropriate graphical techniques. The students will find the measures of center, mean, median, mode, measures of dispersion and variation maximum, minimum, range, inter-quartile range (IQR), quartiles and outliers for given data sets on homework, in-class work, and on questions on Test 2.

(c) interpret and draw inferences from data and make decisions in a wide range of applied problem situations; and

KA

Use measures of dispersion to identify typical and atypical data

Students will interpret and draw inferences from data and make decisions in a wide range of applied problem situations on homework, in-class work, or on questions on Test 2.

 (d) help students understand quantitative and qualitative approaches to answering questions and

KA

Analysis of qualitative and quantitative data

Students will choose quantitative or qualitative approaches to answer data questions posed in class.

develop students’ abilities to communicate mathematically;

KA

Students will receive feedback on their notation and mathematical symbolism as they communicate between themselves or to the teacher on homework, in-class work, and on questions on all tests.

(6) concepts of randomness and uncertainty:

(a) probability as a way of describing chance in simple and compound events; and

KA

Define probability of events and calculate probability of simple and compound events

Students will model sample spaces for simple and compound events and will calculate the desired probabilities from these sample spaces on homework, in-class work, and on questions on Test 2.

(b) the role of randomness and sampling in experimental studies;

KA

Sampling as a representation of a population

Students will be able to describe how to gather data from a large population to answer questions in experimental studies on homework and in-class work.

(7) mathematical processes:

(b) understand the connections among mathematical concepts and procedures, as well as their application to the real world;

KA

Chapter 12
n-gons and tiling

Students will construct a table to investigate the connections between mathematical concepts procedures of regular polygons in order to answer questions relating to regular, semi-regular, and non-regular tiling of planar surfaces on homework and in-class work.

(c) understand the relationship between mathematics and other fields;

Data and probability

Students will describe how to use data and probability to answer questions of interest in other academic areas and applied areas in real life in class discussion.