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COURSE OBJECTIVES
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CONTENT OUTLINE
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1. Students will develop an understanding of numbers, number systems and number relationships.
Pennsylvania Academic Standards for Mathematics
2.1. Numbers, Number Systems and Number Relationships
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1. Numeration to 100,000,000—place value, counting, writing, reading, estimating, rounding, comparing and ordering (100,000,000,000)
Use expanded notation to represent whole numbers up to 9 digits (999,999,999,999)
Use simple concepts of negative numbers (temperature thru -20, number lines, counting)
Use drawings, diagrams, and models to represent the concept of decimals and fractions as part of a whole or set
Compare proper fractions with like and unlike denominators through 16th (improper and proper)
Identify place value of digit from billions through hundredths (thousandths)
Use models and expanded notation to represent and compare decimals to hundredths (thousandths)
Develop and apply number patterns (multiples, factors, primes, and composites) =100 (any)
Apply money concepts in everyday problem solving
Review and use the inverse relationships between addition, subtraction, multiplication, and division fact families
Apply integers in everyday problem situations
Develop number theory concepts to show a number can be stated several ways
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2. Students will apply computation and estimation skills in mathematical operations.
Pennsylvania Academic Standards for Mathematics
2.2. Computation and Estimation
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2. Demonstrate the ability to round numbers thru millions (billions) including decimals thru hundredths (thousandths)
Determine through estimation the reasonableness of answers to problems involving addition, subtraction, multiplication, and division of whole numbers
Use estimation to solve problems involving whole number thru thousands and decimals thru hundreds including time and money
Review and extend multiplication tables through 9 and corresponding division facts with the expectation that most children will master these facts
Add and subtract up to 5 digit numbers with regrouping. Multiply using 2 digit numbers and divide by single divisors (3 digit multiplication, 2 digit divisors)
Add and subtract fractions – like and unlike denominators taking to simplest form through 16th (multiply and divide)
Develop and apply algorithms to solve problems that involve addition, subtraction, multiplication, and division
Add and subtract, multiply decimals (division decimal by decimal)
Select methods of computation and explain why appropriate
Create and solve word problems involving addition, subtraction, multiplication and division of whole numbers, fractions, mixed numerals, and money using concrete materials, paper and pencil, estimation, mental computation and calculators
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3. The students will demonstrate an understanding of true and estimated measurements.
Pennsylvania Academic Standards for Mathematics
2.3. Measurement and Estimation
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3. Select and use appropriate instruments and units for measuring quantities such as length, perimeter, area, volume, weight, time, and temperature.
Solve problems using time without regrouping; use regrouping
Estimate and measure pictorial and concrete objects with standard (e.g. US customary and metric) units—length, width, temperature, capacity, area, perimeter and volume
Add and subtract measurements without regrouping; use regrouping
Convert linear measurements within the same system using conversion chart or hint (mm, cm, m, km, mL, L, g, kg, cup, pint, quart, gallon, in, ft, yd, oz, lb) without any hints, dm, mg, metric ton, fl. oz., ton
Use a ruler measure to nearest 1/8 inch or centimeter (1/16th) inch
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4. The students will communicate their use of mathematical reasoning and problem solving.
Pennsylvania Academic Standards for Mathematics
2.4 Mathematical Reasoning and Connections
2.5 Mathematical Problem Solving and Communication
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4. Determine the operation needed to solve a problem.
Determine whether there is sufficient information to solve a problem and predict solutions
Develop a plan to analyze a problem, identify the information needed to solve the problem, carry out the plan, check whether an answer makes sense and explain orally and in writing how a problem was solved
Develop a variety of strategies to solve problems (e.g. construction graphs, diagrams, drawings and tables, solving a similar or easier problem; guess and check; acting the problem out; work backwards; using objects; writing equations; looking for patterns using logical reasoning
Use precise mathematical language in solution to problem
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5. The students will predict and interpret data they have gathered and organized.
Pennsylvania Academic Standards for Mathematics
2.6 Statistics and Data Analysis
2.7 Probability and Predictions
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5. Organize display, and interpret data using pictures, tallies, charts, bar graphs, tables, line graphs using correct title labels and scale (histograms, double bar graph, double line graph, stem and leaf plot, circle graphs)
Form and justify simple conclusions based on data
Sort data using Venn diagrams
Determine data using the terms mean, median, range and mode
Predict the likely number of times a condition will occur based on trials using concrete objects
Calculate the probability of a simple event and compare predictions and results with theoretical probability
Express probability as fractions and decimals
Determine the fairness of a design of a spinner and perform simulations with concrete devices (dice, spinners, etc.) to predict the likelihood of an event’s occurrence
Solve problems by finding and analyzing patterns
Develop a tree diagram
Find all possible combinations or arrangements
Determine probability of event using “and” “or” “not”
Determine why some outcomes are certain, more likely, less likely, equally likely or impossible
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6. The students will use algebra and functions.
Pennsylvania Academic Standards for Mathematics
2.8. Algebra and Functions
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6. Locate and identify points on a coordinate system
Recognize, reproduce, extend, create, and describe a variety of patterns (3 repetitions)
Create a story or realistic situation that matches a given symbol and numbers (variables stand alone)
Use concrete objects and combinations of symbols and numbers to model mathematical situations
Use tables, graphs, and other data to generate and analyze simple functions and relationships
Select and use appropriate strategies to solve number sentences involving a blank, question mark or variable and explain verbally and in writing the method of solution
Explain the use of combinations of symbols and numbers in expressions, equations, and inequalities and apply a realistic situation to given equations and inequalities
Form rules based on patterns or illustrate patterns based on a rule. Must show 3 repetitions
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7. The students will demonstrate knowledge of basic geometric and
Trigonometry concepts.
Pennsylvania Academic Standards for Mathematics
2.9 Geometry
2.10 Trigonometry
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7. Identify and construct geometric shapes in 2 and 3 dimensions
Construct 2 and 3 dimensional shapes and figures using concrete objects and relate to geometric figures in real life and describe in words
Define the basic properties of squares, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, triangles, cubes, rectangular pyramids, prisms, spheres and cylinders
Define properties of geometric figures using faces, vertices and edges
Define and measure angles (acute, obtuse, and right)
Use a geoboard and other concrete objects to construct geometric shapes and describe these shapes in words
Use a geoboard to create right triangles
Identify and measure circles, their diameter and radii and circumference
Represent and use the concepts of line, point, planes, line segment rays, and angles
Identify properties of geometric figures (i.e. parallel, perpendicular, similar, congruent, symmetrical)
Extend concepts of perimeter and area in triangles, quadrilaterals, and circles. Whole numbers and same units use fractions and decimals-various units
Classify and compare triangles and quadrilaterals according to their size and angles
Identify and compare parts of right triangles (legs, hypotenuses, right angle, acute angles)
Create an original tessellation
Estimate and compute area and volume using tiles and cubes
Estimate and compute volume of cubes and rectangular prisms
Identify and draw simple transformations of geometric figures (translation, reflection, rotation)
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8. The students will demonstrate basic concepts of calculus.
Pennsylvania Academic Standards for Mathematics
2.11. Concepts of Calculus
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8. Identify least and greatest values on bar graphs and circle graphs. Identify terms maximum and minimum.
Describe the relationship between the rates of change and time.
Estimate areas and volumes as the sums of areas of tiles and volumes of cubes
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RESOURCE MATERIALS
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ASSESSMENT
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- Houghton Mifflin Mathematics Text Grade 5
- Mathematics Resource Packet
- Available Computer Software
- Teacher-Made Materials
- PSSA Test Prep
- Calculators
- Manipulatives
- Measuring Tools
- Calendar
- Geoboards
- StudyIsland.com
- Textbook Tests
- Teacher Made Tests
- Teacher Observations
- Student Oral and Written Responses
- Student Demonstrations
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