Department/Grade: Math/Grade 3 Course: 3rd Grade Math Revision Date: April 2008
Required/Elective: Required Course Length: 1 year Pre-requisite: 2nd Grade Math
Course Description:
|
COURSE OBJECTIVES |
CONTENT OUTLINE |
|
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 9,999 (apply place value, counting, writing, reading, estimating, rounding and ordering) Count by 2’s, 3’s, 5’s, 10’s and 25’s to 200 (ongoing) Introduce expanded notation to represent whole numbers up to 999 Use models to represent and compare decimals (tenths) Apply number patterns (Identify even and odd numbers up to 3 digits) and compare values of numbers (>,<,=) (9,999) Count money up to $5.00, compare and make change using penny, nickel, dime, quarter, half dollar and dollar bill and write amounts with cent symbol and dollar/decimal point (change less $2.00) Use the inverse relationship between addition and subtraction (e.g. fact families) Describe the inverse relationships between multiplication and division Use whole numbers and fractions to represent quantities; numerators 1-9, denominators (2-10) (no equivalents or mixed) Use drawings, diagrams and models to show the concept of fractions as part of a whole or set Math a symbolic representation of numbers to appropriate whole numbers (base 10 blocks, 7 hundredths, 4 tens, and 8 ones, etc.)
|
|
2. Students will apply computation and estimation skills in mathematical operations.
Pennsylvania Academic Standards for Mathematics 2.2. Computation and Estimation |
2. Master sums up to 18 and corresponding subtraction facts Add 3 or more single, double, or triple digit numbers with regrouping Solve single and double, digit addition and subtraction problems with and without regrouping in vertical and horizontal form Demonstrate concept of multiplication as repeated addition, arrays and groups of the same number (0-9 times tables) (through 9x5) Demonstrate concept of division as repeated subtraction and as sharing Create, solve and develop-apply algorithms to word problems involving addition, subtraction, multiplication and division of whole numbers (no more than 2 operations) Determine the reasonableness of calculated answers Solve triple digit addition and subtraction problems without regrouping in vertical and horizontal form Estimate sums and differences of quantities Round 2 digit numbers to the nearest 10 and 3 digit numbers to the nearest 100, before computing
|
|
3. The students will demonstrate an understanding of true and estimated measurements.
Pennsylvania Academic Standards for Mathematics 2.3. Measurement and Estimation |
3. Determine and compare elapsed time (5 minutes), temperature, length, weight, capacity, area, perimeter (no volume) Estimate and measure pictorial and concrete objects with non-standard and standard (e.g. US and metric) units, length, temperature, weight, capacity, area and perimeter Demonstrate that a single object has different attributes that can be measured in different ways Determine the appropriate unit of measure (5 in., 5 ft., 5 yds.) Identify measurements from least to most and greatest value Use ruler to ½ inch (no centimeter) Introduce addition and subtraction with measurements Estimate the length of time for completing various tasks (second, minute, hour) Tell time (analog and digital) to the minute Identify time of day as AM and PM
|
|
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. Make, check and verify predictions about the quantity, size and shape of objects and groups of objects. Determine when sufficient information is present to solve a problem and explain orally and in written form how to solve a problem (missing and extra facts) – choose a # sentence that matches a story problem (+,-) Apply problem solving strategies to solve problems using an appropriate method, strategy and materials Use measurements in everyday situations (e.g. determine the geography of the school building)
|
|
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 pictures, tallies, charts, and bar graphs and pictographs. Formulate and answer questions based on data shown on graphs Form and justify an opinion on whether a given statement is reasonable based on a comparison to data Understand the term probability using prediction and simulations Analyze data using the concepts of largest, smallest, most often, least often and middle Sort data using Venn diagrams Design a fair and unfair spinner and determine its fairness
|
|
6. The students will use algebra and functions.
Pennsylvania Academic Standards for Mathematics 2.8. Algebra and Functions |
6. Recognize, describe, extend, create and replicate a variety of patterns including attribute, activity and geometric pattern Demonstrate simple function rules (addition/subtraction/multiplication) (Identify missing symbols (+,-,x, <,>,=) Substitute a missing addend in number sentence Verbally and in written form explain the meaning of solutions and symbols (+,-,x,,=) Analyze simple functions and relationships and locate points on a simple grid Use trial and error to solve number sentences and check if solutions are sensible and accurate Describe and interpret the data gathered and displayed in a table or chart (e.g. guess and check problems) Use concrete objects and symbols to model the concepts of variables, expressions, equations and inequalities Create a story to match a given combination of symbols and numbers (+,-,x,>,<,=) Find a missing number that makes a number sentence true (1 digit or 2 digit numbers up to 18 using +, -, or x through 9x5)
|
|
7. The students will demonstrate knowledge of basic geometric and trigonometry concepts.
Pennsylvania Academic Standards for Mathematics 2.9 Geometry 2.10. Trigonometry |
7. Name and label characteristics of geometric shapes in 2 and 3 dimensions (circle/sphere, square/cube, triangle/pyramid, rectangle/rectangular prism, cone/cylinder, pentagon, hexagon, octagon) Build three dimensional shapes using concrete objects Identify and draw line(s) of symmetry in geometric figures (2 dimensional shapes) Identify congruent geometric figures Find and describe geometric figures, lines of symmetry, and right angles in real life and nature Show relationships between and among figures using reflections (no flip, turn,) Predict how shapes can be changed by combining or dividing them Model right angles and right triangles using concrete objects (no right angles)
|
|
8. The students will demonstrate basic concepts of calculus.
Pennsylvania Academic Standards for Mathematics 2.11. Concepts of Calculus |
8. Categorize rates of change as faster and slower Continue a pattern of numbers or objects that could be extended infinitely Identify least and greatest values represented in bar graphs and pictographs Identify whole number quantities and measurements from least to most and greatest value
|
|
RESOURCE MATERIALS |
ASSESSMENT |
|
· Houghton Mifflin Mathematics Text Gr. 3 · Available Computer Software · Teacher Made Materials · Notetaking Guide · Refer to Standards Booklet · Math Resource Books · Study Island · Computers-portable lab · Calculators · Judy Clocks · Manipulatives · Measuring tools · Calendar |
· Teacher Made Tests · Textbook Tests · Teacher Observation · Student Oral and Written Responses · 4 Sights · Anecdotal records · Performance tasks |