Gresham/Barlow School District

Mathematics Curriculum Map {Grade: 5 }

2005/2006

COMMON GOALS

STANDARD /FOUNDATIONS/

OSAT ELIGIBLE CONTENT AND CLASSROOM ONLY CONTENT

(Words in bold text are for Classroom only. Words italicized are Eligible Content for creation of items on the OSAT.

*TIME

FRAME

*UNIT

*TOPICS

*ASSESSMENT

**Vocabulary

Mathematical Problem Solving (current language but under revision)

 

Select, apply, and translate among mathematical representations to solve problems.

 

Apply and adapt a variety of appropriate strategies to solve problems.

 

Monitor and reflect on the process of mathematical problem solving.

 

Communicate mathematical thinking coherently and clearly; use the language of mathematics to express mathematical ideas  precisely.

 

Accurately solve problems that arise in mathematics and other contexts.

CONCEPTUAL UNDERSTANDING

Interpret the concepts of a problem-solving task and  translate them into mathematics.

PROCESSES AND STRATEGIES

Choose strategies that can work and then carry out the strategies chosen.

VERIFICATION

Produce identifiable evidence of a second look at the concepts/strategies/calculations to defend a solution.

COMMUNICATION

Use pictures, symbols, and/or vocabulary to convey the path to the             identified solution.

ACCURACY

Accurately solve problems using mathematics.

September-June

Problem Solving

Problem Solving Strategy Focus: Work Backwards and Make it Simpler

 

Problem Solving Journals: 2-3 times per week. The problems are set up so that they cycle through all mathematics strands continuously through the year.

 

Classroom Resources:

 

(I.)[1] 10 Minute Math Activities and throughout the tasks

 

(S.F.)[2] Problem Solving Transparencies

 

Problem Solving Literature Connections

Sample open-ended prompts that could be scored as work samples are available online at www.octm.org

 

 

All Standards

September-June

Skill Practice and Review

Math Journals: 2-3 times per week. The problems are set up so that they cycle through all mathematics strands continuously through the year.

 

Classroom Resources:

(S.F.) Spiral Review

(S.F.) Assessment Sourcebook: Diagnosing Readiness for Grade 5 pg. 43-46.

 

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

 

Compute fluently and make reasonable estimates.

 

Identify classes of numbers (e.g., primes, composites,  

 even, odd, multiples) in a 1-to-100 number chart and describe numeric                                patterns related to them.

 

Recognize characteristics of odd, even, prime, and

composite numbers.

 

Determine the order of operations for multiple-step

calculations involving addition, subtraction,

multiplication, and division.

 

Divide by two-digit numbers.

 

Determine the meaning of a remainder expressed

as a whole number, fraction, or decimal in a

problem situation involving division.

 

Sept

( 4 weeks)

 

Base Ten Number Systems, factors and multiples of 100, 1000, and 10,000, 100,000 and 1,000,000.

 

Numbers to 1,000, 000

Concepts of odd, even, primes, factors, multiples, and composites

 

Estimations using all operations

 

Factors and multiples through 100

 

Strategies for 2-digit multiplication and division

Calculators to check divisibility

 

September Calendar:<>  [3]

       Odd & Even Pattern

       Decimal Grid color in .01 daily

       Class Bank:  1 + 2 + 3 add to total daily

       Arrays (2 digit by 2 digit multiplication pictures)

       Word for the Day: What is fraction of vowels compared to consonants in todays word? . . . (words are selected from the grade level vocabulary bank)

 

Math Stations:

 [4]

Students participate in games and activities that reinforce multi-digit reading, writing, comparing and decomposing numbers.

 

 

 Classroom Resources:

 (I.) Mathematical Thinking at Grade 5, Building on Numbers You Know

 

(S.F.) Ch. 1 & 2

 

Number and Place Value Literature Connections

Basic Facts Tests

 

(I.) Assmt. Masters: 1-4

 

(S.F.) Ch. 1 & 2 Tests

Composite Number

Digit

Expanded form

(expanded notation)

Factors

Integers

Inverse operations (inverse)

Least common multiple

Multiple

Prime factorization

Prime number (primes)

Remainder

 

Apply appropriate techniques, tools, and formulas to determine measurements.           

 

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.              

 

Use visualization, spatial reasoning, and geometric modeling to solve problems.

 

Apply transformations and use symmetry to analyze mathematical situations

 

                 

 

Develop strategies to measure the perimeter of

simple polygons and everyday objects.

 

Analyze the effects on area and perimeter by

combining two simple geometric figures (e.g., two

right triangles and a rectangle).

 

Compare and contrast the formulas for area of

rectangles, related triangles, and parallelograms.

 

Develop and use formulas for determining the perimeter and

area of rectangles, and related triangles and parallelograms.

 

Identify, describe, compare and classify triangles by

their sides and angles.

 

Use properties of triangles to determine the lengths of

their sides and perimeters.

 

Develop, understand, and apply the property that the

sum of the angle measures in a triangle is 180 degrees.

 

Draw conclusions about the measures of

corresponding sides and angles of two congruent

and similar triangles.

 

Accurately draw and label triangles, angles, and

line segments using measurement tools.

 

Identify and build three-dimensional objects from two-

dimensional representations.

 

Identify and describe line and rotational symmetry

in two-dimensional shapes and designs.

 

Identify and describe a motion or series of motions that will show two triangles are congruent

 

Estimate and measure volume of a rectangular

solid using unit cubes.

 

Use referents for metric measurements to make

estimates of length, weight, and volume and evaluate

the reasonableness of the estimate (e.g., height of

teacher estimated in height of student lengths).

 

Make and use coordinate systems to specify location                                             and describe paths.

 

Find the distance between points along the horizontal

and vertical lines of a coordinate system.

 

Oct/Nov

(6 Weeks)

Geometry

 

Angles up to 180 degrees using protractor

 

Attributes of shape including polygons (of 8 sides or less) circles, ovals, simple irregular shapes and 3-D figures (sphere, cube, prism, cone, cylinder, pyramid)

 

Points, line segments, rays, angles (acute,

right, obtuse), circles (radius, diameter)

 

Classification of triangles according to properties of sides and angles

 

Line and rotational symmetry in 2-D shapes and designs

 

Rotations, reflections and translations

 

Sum of angles in a triangle

 

Congruent and similar shapes

 

Coordinate Grids

 

Measures of length, area, perimeter and volume

 

Use of appropriate units and tools for measuring

 

Construction of 3-D objects from  2-D representations

 

Area formula (l X w)

 

Volume formula ( l X w X h)

 

October Calendar:

       Decimal Grid color in .01 daily

       Class Bank:  1 + 2 + 3 add to total daily

       Patterns of polygons

       Fraction for # of  Days Left in the calendar year

       Word for the Day: What is fraction of vowels compared to consonants in todays word? . . . (words are selected from the grade level vocabulary bank)

 

Math Stations:

Students participate in games and activities that reinforce geometry concepts