Department/Grade: Math/Grade 4 Course: 4th Grade Math Revision Date: April 2008
Required/Elective: Required Course Length: 1 year Pre-requisite: 3rd Grade Math
Course Description:
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COURSE OBJECTIVES |
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 |
1. Numeration to (100,000) (apply place value, counting, writing, reading, estimating, rounding, comparing and ordering) Use expanded notation to represent whole numbers up to six digits Write numbers in word form through 6 digits and through the tenths place Review and use the inverse relationship between addition, subtraction, multiplication and division (e.g. fact families) Develop and apply number patterns (multiples and factors) thru 10 of any number Count, compare, make change using penny, nickel, dime, quarter, half dollar and dollar bill and write amounts with cent symbol and dollar/decimal point Use drawings, diagrams, and models to show the concept of fractions as part of a whole or set Use simple concepts of negative numbers (temperatures) Use models to represent and compare decimals to tenths and hundredths
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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 |
2. Demonstrate the ability to round numbers through 100,000 through 6 digits Determine through estimations the reasonableness of answers to problems involving addition, subtraction, multiplication and division of whole numbers Review and extend multiplication tables through 10 and corresponding division facts Add and subtract up to five digit numbers with regrouping, multiply by one and two digit multipliers and divide by one digit divisor Develop and apply algorithms to solve problems that involve addition, subtraction, multiplication and division Introduce equivalent fractions, simplest form, addition and subtraction of like and unlike denominators and fractional parts of a whole Create and solve word problems involving addition and subtraction, multiplication and division of whole numbers, using concrete materials, paper and pencil, estimation, mental computation and calculators Round amounts of money to the nearest dollar Solve addition or subtraction problems with decimals through hundredths Locate/identify fractions or decimals on a number line thru tenths
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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 |
3. Select and use appropriate instruments and units for measuring quantities such as length, perimeter, area, volume, weight, time and temperature to the nearest ¼ inch or cm Tell time to the minute Match analog time to digital Calculate elapsed time to the minute Determine beginning or ending time, given elapsed time Solve problems using time Estimate and measure pictorial and concrete objects with standard (e.g. US and metric) units, length, width, temperature, weight, capacity, perimeter, area and volume Add and subtract measurements
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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 |
4. Determine the operation needed to solve a problem Determine whether there is sufficient information to solve a problem 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 written form how a problem was solved Develop a variety of strategies to solve problems (e.g. drawings, table, lists, solving a similar problem, guess and check logical reasoning, working backwards, acting them out and diagrams)
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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 |
5. Gather, organize, and display data using pictographs, tallies, tables charts and graphs. Translate data from one type of display to another Formulate and answer questions based on data shown on graphs Sort data using Venn diagrams Predict the likely number of times a condition will occur based on trials with concrete objects Form and justify an opinion on whether a given statement is reasonable based on a comparison to data Determine the fairness of the design of a spinner and perform simulations to predict the chance of an event occurring Understand the probability of a simple event Express probability as fractions Solve problems by finding and analyzing patterns Understand terms (mean, median, mode, range)
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6. The students will use algebra and functions.
Pennsylvania Academic Standards for Mathematics 2.8. Algebra and Functions |
6. Locate and identify points on a coordinate system. Recognize, describe, extend, create and reproduce a variety of patterns (+,- or x) (3 repetitions) whole numbers or money and geometric patterns Create a story to match a given combination of symbols and numbers 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 and explain verbally and in writing the method of solution Estimation, guess and check, etc. Determine the missing elements in a function table (+,-,x) (whole numbers and money) Determine rules for function given a table Identify the missing symbols (+,-,x, division) also (=,<,>) that makes a number sentence true
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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 |
7. Identify, classify and/or compare geometric shapes in two and three dimensions (circle/sphere, square/cube, triangle/pyramid, and rectangle/prism) Construct two and three dimensional shapes and figures using concrete objects and relate to geometric figures in real life Identify the basic properties of squares, pyramids, parallelograms, quadrilaterals, polygons, rectangles, circles, triangles, cubes, prisms, spheres and cylinders Define and construct right angles and right triangles using concrete objects (i.e. Geoboards) and relate to the environment Identify and measure circles, their diameter and radii Represent and use the concepts of line, line segments, point, planes, rays and angles Identify properties of geometric figures (i.e. parallel, perpendicular, similar, congruent, one, two or no lines of symmetry or symmetrical Introduce the concepts of perimeter and area in squares and rectangles Estimate and compute area and volume using tiles and cubes Match or plot the ordered pair with the appropriate point (or object) on a simple grid |
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8. The students will demonstrate basic concepts of calculus.
Pennsylvania Academic Standards for Mathematics 2.11. Concepts of Calculus |
8. Identify least and greatest values on graphs and charts Describe the relationship between the rates of change and time Introduce maximum and minimum
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RESOURCE MATERIALS |
ASSESSMENT |
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Houghton Mifflin Mathematics Text Mathematics Resource Packet Available Computer Software Teacher Made Materials Investigations Curriculum Calculators Manipulatives Measuring Tools Calendar Geoboards Fraction Strips
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· Textbook Tests · Teacher Made Tests · Teacher Observation · Student Oral and Written Responses · Student Demonstration
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