Best Standards-Based Technology Integration Practices

for 21st Century Classrooms in Harrison County Schools

Janet Benincosa, Harrison County Technology Integration Specialist

 

MOUNTAINEER MIDDLE:  SIXTH GRADE MATH

Team Members:

          Cristy Buffington

          Renee McLean

          John Rogers

          Lisa Pritts

 

21st CENTURY

SIXTH GRADE MATH

CONTENT STANDARDS AND OBJECTIVES FOR WEST VIRGINIA SCHOOLS  (2520.2)

 

The West Virginia Standards for 21st Century Learning include the following components:

21st Century Content Standards and Objectives and 21st Century Learning Skills and Technology Tools. 

 

All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives. 

 

Sixth Grade Math

M.O.6.1.1

demonstrate an understanding of large numbers by converting and comparing numbers in scientific notation and standard notation (with and without technology).

Use a Calculator to do the actual exponent and multiplication for a number in scientific notation.  Record numbers in a table, then search for a pattern.

 

M.O.6.1.2

determine the greatest common factor and least common multiple using multiple strategies to solve real-world problems; find prime factorization of a number.

Using the National Library of Virtual Manipulatives and a whiteboard (http://nlvm.usu.edu/en/nav/vlibrary.html).  Use “Factor Tree” applet to introduce prime factorization using factor trees.

M.O.6.1.3

compare and order integers using multiple strategies (e.g., symbols, manipulatives, number line).

In a word processing document, have each student “create” an integer in large type, then print.  On a “human” number line have the students sort and order themselves holding their integer.

 

M.O.6.1.4

analyze and solve real-world problems involving addition, subtraction , multiplication and division of

·              whole numbers,

·              fractions, mixed numbers,

·              decimals,

·              integers, and

justify the reasonableness by estimation.

Implement Odyssey Lessons below using either the “Smartboard” or individual computers.

 

6668, 6669 – Addition and Subtraction of fractions.

6670, 6671 – Multiplication of fractions and mixed numbers

 

M.O.6.1.5

apply the distributive, commutative, associative and identity properties to numeric expressions and use to prove equivalency.

Introduction to the commutative, associative, and distributive properties with this site. http://home.europa.com/~paulg/mathmodels/commutative.html

 

Practice:  www.algebrahelp.com/worksheets/view/simplifying/distributionquiz

 

Check work: (Expression Calculator) www.algebrahelp.com/calculators/expressionloops/

 

M.O.6.1.6

convert between fractions/ratios, mixed numbers, decimals and percents in appropriate real-world problems.

Implement Odyssey Lessons below using either the “Smartboard” or individual computers.

 

67162, 6694, 6695 and Quiz

 

M.O.6.1.7

compute the percent of a number to solve application problems and justify the reasonableness by estimation.

Choose from any of the following online stores: champssports.com, oldnavy.com, walmart.com, target.com.  Each store is having a ___% off sale.  Have the students estimate the price sale price of 5 to 10 items then have them calculate the sale prices.

 

M.O.6.1.8

demonstrate an understanding of the effect of multiplying and dividing, whole numbers, fractions and decimals by numbers  including 0, 1 and values between 0 and 1 .

Using a table and calculator, have teams multiply and divide 5 whole numbers, 5 fractions, and 5 decimals by 0, 1, 0.5, ½, 0.75, ¾, 0.25, and ¼.  For each problem, make observations and record.

 

M.O.6.1.9

develop and test hypotheses to derive the rules for addition, subtraction, multiplication and division of integers, justify by using real-world examples and use them to solve problems. 

http://illuminations.nctm.org/lessondetail.aspx ID=l285

 

Illuminations – Multiplying integers using videotape

Students discuss and explore multiplication of integers using video.

M.O.6.2.1

simplify numerical expressions and evaluate algebraic expressions using order of operations.

After you have taught Orders of Operation, use

 

www.quia.com/rr/116044.html

Multiple Choice, game format – solve and get money

 

M.O.6.2.2

use inductive reasoning to extend patterns to predict the nth term (e.g., powers and  triangular numbers).

Implement Odyssey Lessons below using either the “Smartboard” or individual computers.

 

67123, 6637, 6638, 6639, 6640, and quiz

 

 

M.O.6.2.3

create algebraic expressions that correspond to real-world situations; use the expressions to solve problems.

http://illuminations.nctm.org  – Go to lessons and find the following lesson

 

Building Bridges (6-8 Math Lessons – Algebra)

 

Students will solve expressions using an Algebra Balance from NLVM (National Library of Virtual Manipulatives)

http://nlvm.usu.edu/en/nav/vlibrary.html

M.O.6.2.4

determine the rule, output or input; given an input/output model using one operation, write an algebraic expression for the rule and use to identify other input/output values.

Using NLVM (http://nlvm.usu.edu/en/nav/vlibrary.html ) and whiteboard, use “Function Machine” applet to observe a “machine” to determine the function rule or pattern.

 

 

 

M.O.6.2.5

solve real-world proportion problems involving rates, probability and measurements using multiple strategies, justify selection of strategies.

Tremendous Trees www.thesolutionsite.com/lesson/14151/treeslp.html

 

Photograph a tree/building etc. with you and then compare your actual height (compare ratios) to figure trees actual height.

 

M.O.6.2.6

write and solve one-step equations using number sense, properties of operations and the idea of maintaining equality to represent and solve real-world problems.

Implement Odyssey Lessons below using either the “Smartboard” or individual computers.

 

67212, and quiz

 

 

M.O.6.3.1

analyze characteristics using defining properties of

·              lines, / angles, / polygons,  / triangles, and / compare these geometric figures.

www.thesolutionsite.com/lesson/17061/lesson1.html

 

“Everyday Polygons” lesson – Use overhead projector to examine shapes and determine if they are polygons.

 

 

M.O.6.3.2

use inductive reasoning with the measures of interior angles in polygons and derive the formula to determine the sum of the measures of the interior angles.

Implement Odyssey Lessons below using either the “Smartboard” or individual computers.

 

67253, 6742, 6743, and quiz

 

 

M.O.6.3.3

apply the concepts of parallel, perpendicular, intersecting, and skew lines to real-world situations (i.e. roads and routes).

On the whiteboard, pull up www.mapquest.com and enter a random address.  Use the map to introduce parallel, perpendicular, intersecting, and skew lines.

 

 

 

M.O.6.3.4

create designs using line and rotational symmetry.

On the whiteboard, pull up www.schools.ash.org.au/

 

“Symmetry at the Beach”

 

Also Google line symmetry for other good resources.

 

 

M.O.6.3.5

predict, describe, and perform transformations on two-dimensional shapes

·              translations / rotations  / reflections

After predicting and exploring with actual manipulatives, use the NLVM (http://nlvm.usu.edu/en/nav/vlibrary.html ) to perform all 3 transformations (“Transformation” applets)

 

Best done individually with a lab sheet.

 

M.O.6.3.6

use geometric representations to solve real-world problems.

Implement Odyssey Lessons below using either the “Smartboard” or individual computers.

 

6758 and quiz - Geometry all around you

 

 

M.O.6.3.7

plot polygons on coordinate grids, determine lengths and areas from the graph.

On whiteboard, use NLVM http://nlvm.usu.edu/en/nav/vlibrary.html

Click on virtual coordinate geoboard and students can plot polygons and determine lengths and areas.

 

M.O.6.4.1

determine an approximation for pi using actual measurements.

In the computer lab, students create circles using appropriate word processing program (or another program).  When finished have them print and measure the circumference and diameter.  Record both measurements in a chart, then divide c/d and record using calculators.

 

M.O.6.4.2

develop and test hypotheses to determine formulas for

·        perimeter of polygons, including composite figures

·        area of parallelograms

·        area of triangles

·        area of composite figures made of parallelograms and triangles

·        circumference of a circle

·        area of a circle

·        volume of a rectangular prism

Using a whiteboard or overhead and graph paper background, draw a series of parallelograms, triangles, etc. and have the students examine the number of “squares” inside the figure.  Begin to develop ideas about possible formulas

M.O.6.4.3

investigate, model and describe surface area of rectangular prisms and cylinders; develop strategies to determine the surface area of rectangular prisms

Implement Odyssey Lesson 67237 and quiz using either the “Smartboard” or individual computers.

 

Using wrapping paper, students could wrap boxes and attempt to figure out exact surface area (amount of wrapping paper).

 

 

M.O.6.4.4

develop strategies to determine volume of cylinders; solve real-world problems involving volume of cylinders, justify the results.

www.mathguide.com/lessons/     Click surface area – Cylinders lesson and quiz

 

Experiment with Volume – Lesson Plan – www.math.rice.edu/~lanius/geom./cyls.html 

 

 

M.O.6.4.5

given a two-dimensional polygon, construct a scale drawing given the scale factor.

www.illuminations.nctm.org/lessondetail.aspx?1d=l259

 

Lesson – Blue Squares and Beyond

 

Lessons that follow in unit will also address other CSO’s.

 

M.O.6.5.1

collect, organize, display, read, interpret and analyze real-world data using appropriate graphs and tables (with and without technology).

“Tinkerplots” software – as a whole class or individually, students can enter collected data and organize it to create pie charts, histograms, scatter plots, or created graphs.

 

www.illuminations.nctm.org  – Look for BUNGEE BARBIE Lesson

 

 

M.O.6.5.2

collect and interpret real-world data, formulate questions using mean, median, mode, and range and determine the effect of outliers on the data (with and without technology).

http://standards.nctm.org/document/eexamples/chap6/6.6/index.htm

 

Display above link on a whiteboard and have student’s complete tasks and answer questions.

 

After use – use your discussion and reflection techniques.

 

 

M.O.6.5.3

perform simple probability events using manipulatives; predict the outcome given events using experimental and theoretical probability; express experimental and theoretical probability as a ratio, decimal or percent.

Using TI-73 calculator in Probability Simulation Mode, you can perform simple events with “virtual” manipulatives (coins, dice, marbles, spinners).  Then the results could be recorded in a graph or table.

 

 

 

M.O.6.5.4

determine combinations and permutations of given real-world situations by multiple strategies, including creating lists.

Introduce vocabulary for combination and permutation using www.mathisfun.com  and search combinations and permutations.

 

Then, Implement Odyssey Lesson 76290 and quiz using either the “Smartboard” or individual computers.