In third grade Mathematics, students learn concepts based on the following Strands:
Number Concepts, Theory, Sense
- Read and write numbers through hundred thousands; rename numbers through 9,999 using place value.
- EXT: Investigate other ways of grouping and writing numbers (e.g., Egyptian numbers).
- Order and compare measurements and numbers to 9,999 using the symbols >, <, and =.
- EXT: Order and compare numbers to 999,999 using the symbols >, <, and =.
- Use ordinal numbers to identify position in a sequence.
- Explore estimation strategies (rounding, compatible numbers, and using a referent). Round to the nearest 10 and 100.
- Demonstrate the inverse relationship between multiplication and division by using fact families; explain the relationship between addition and multiplication.
- Recall basic strategies for addition and subtraction facts.
- Develop concept of equal groups and use arrays to represent those groups. State the symbolic multiplication fact for an array. Organize the multiplication facts on a chart recognizing the square numbers and using the commutative property of multiplication.
- Develop and use the strategies to learn the multiplication facts through nine (multiples/skip counting, properties of 0 and 1 as factors, square numbers, doubles, one more set, twice as much as a known fact, patterns, multiples of ten, etc.).
- Illustrate the concept of division in a problem-solving setting by identifying number of equal groups or how many are in each group; record the related division statement using ÷ and .
- Recognize that a fraction represents equal parts of a whole or set; write the fraction when given the model; develop a model for a given fraction.
- EXT: Investigate and model mixed numbers with concrete materials and on a number line.
- Compare fractions less than one (halves, thirds, fourths, fifths, sixths, eighths, tenths) using models.
- EXT: Use models to find equivalent fractions.
- Count, read, write, and compare money amounts to $10.00.
- EXT: Change fractions to decimals for tenths and hundredths and do the reverse.
- Relate "tenths as fractions" to "tenths as decimals" (i.e., 1/10 = 0.1).
- Compare and order decimals through tenths.
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Operations
- Estimate and add three-digit numbers to solve problems, with and without regrouping, including money amounts; extend the process to four-digit numbers. Check addition by using subtraction.
- Estimate and add three or more addends (one- and two-digit numbers).
- Estimate and subtract three-digit numbers to solve problems, with and without regrouping, including subtracting money amounts and subtracting across zeroes; extend the process to include four-digit numbers. Check subtraction by using addition.
- Mentally compute the multiplication facts through the nines.
- Estimate and multiply one-digit numbers by two-digit numbers.
- EXT: Multiply one-digit numbers by three-digit numbers.
- Model division situations with and without reminders.
- Estimate and divide a one- or two-digit number (with and without a remainder) by a one-digit number using the multiplication facts.
- Estimate, add, and subtract fractions with like denominators (halves, thirds, fourths, fifths, sixths, eighths, or tenths) using models.
- EXT: Estimate, add, and subtract mixed numbers with like denominators.
- Find fractional parts of a group of up to 30 objects.
- EXT: Find fractional parts of the day using a 24-hour clock (see Ready, Set, Go, Lesson 5).
- Estimate, add, and subtract decimals to tenths.
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Measurement
- Estimate, measure, and compare (using > or <) lengths to the nearest half inch and centimeter. Select appropriate unit of measure. Know that 12 inches = 1 foot, 3 feet = 1 yard, 36 inches = 1 yard, and 100 centimeters = 1 meter.
- EXT: Estimate, measure, and compare lengths to the nearest quarter inch.
- Find perimeter and area in problem-solving settings.
- Estimate and find the volume of rectangular solid using concrete materials.
- Use a balance to measure weight in ounces, pounds, grams, and kilograms. Select appropriate unit of measure. Know that 16 ounces = 1 pound and 1000 grams = 1 kilogram.
- Measure capacity in nonstandard units; estimate and measure capacity in cups, pints, quarts, gallons, and liters. Select appropriate unit of measure. Know that 2 cups = 1 pint, 2 pints = 1 quart, 4 quarts = 1 gallon.
- EXT: Estimate and measure capacity in milliliters. Know that 1000 milliliters = 1 liter.
- Read Fahrenheit and Celsius temperature on a thermometer.
- Find equivalent amounts of money to $10.00. Make change for amounts to $5.00.
- EXT: Use outside resources to explore foreign currencies (e.g., money from China, Greece, or Egypt).
- Read time to the nearest five minutes using both analog and digital clocks. Extend reading time to the nearest minute.
- EXT: Subtract or count on in minutes to determine time intervals within an hour.
- Know time equivalencies such as month/year, day/week, minute/hour, and hour/day.
- Develop strategies for estimating large quantities of objects.
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Geometry
- Identify and draw representations of points, lines, line segments, angles, horizontal lines, and vertical lines using the appropriate tools; recognize right angles.
- EXT: Recognize and describe angles greater than 90š as obtuse and angles less than 90š as acute angles.
- Identify and describe lines of symmetry.
- EXT: Make a book illustrating symmetry using real-world contexts.
- Identify a figure as open or closed; identify open figures as polygons or nonpolygons; identify circles, triangles, rectangles, squares, and other polygons.
- EXT: Investigate and classify quadrilaterals; explain the classification criteria.
- Explore and identify congruent figures by manipulating shapes.
- Investigate moving figures using lids and/or flips.
- EXT: Investigate moving figures by rotating.
- Recognize, sort, and compare solid shapes and explore faces, edges, and vertices (corners) of cubes, rectangular prisms, and cylinders.
- Investigate the use of a grid (axis from 0-5) and ordered pairs to locate points.
- EXT: Play the game "Battleship" and similar computer games.
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Data Analysis/Statistics/Probability
- Collect data from a variety of sources, including content from other disciplines; represent data with tally marks and on charts/tables, pictographs, and bar graphs. Explain findings. EXT: Use a data base (e.g., ClarisWorks) to record, organize, and present information.
- Interpret pictographs, charts/tables, and bar graphs.
- EXT: Investigate line graphs as a way to represent certain kinds of data.
- Determine if an event is equally likely (50% chance of occurring) or not equally likely to occur; make predictions based on results of simple experiments about the outcome of an event; organize in charts.
- EXT: Record probability of an outcome as a ratio.
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Patterns/Functions/Algebra
- Recognize, describe, predict, extend, and create patterns of objects, pictures, charts of numbers, and simple number patterns.
- EXT: Locate patterns in Native American and African art. Create a similar pattern.
- Write simple equalities by finding missing addends and factors.
- Multiply by multiples of ten (6x10, 6x20) using patterns.
- EXT: Use a calculator to investigate number patterns by multiplying by 100 and multiples of 100 (6x100, 6x200...); extend to 1000 and multiples of 1000 (6x1000, 6x2000...).
- Find the function rule (pattern) that completes a chart of factors or products.
- Recognize, explain, and use the properties of addition including associative, commutative, and zero.
- Recognize, explain, and use the properties of multiplication including commutative, zero, and one.
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Problem Solving/Application
- Identify and/or pose problems from everyday life and mathematical situations including problems to fit a given equation.
- Solve problems using a logical procedure (a plan).
- Identify information that is available but not needed. Identify additional information needed to solve a problem.
- Solve problems using appropriate materials and tools (e.g., grid paper, collectibles, measurement tools, manipulatives, calculators).
- Develop and apply operations and strategies (e.g., act it out, build a model, draw a picture or diagram, guess and check, make a chart or table, make a list, make a graph, use a pattern, work backward) to solve a wide variety of routine and nonroutine problems. EXT: Find alternative ways to solve problems.
- Solve problems by working collaboratively with peers; entertain others' points of view.
- EXT: Recognize similarities and differences among solution paths.
- Share and explain (verbalize/record/demonstrate) thinking during and after solving a problem.
- EXT: Recognize when a solution does or does not make sense. Explain why.
- Acquire confidence in using mathematics meaningfully to solve problems.
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