Standards of
Expected Student Achievement
Third Grade
Content Standards
Mathematics
Standards
1999-2000
By the end of THIRD GRADE
Number Sense
Students will:
•Count, read, and write whole numbers to 10,000
-What is the smallest whole number you can make using the digits 4, 3, 9, and 1? Use each digit exactly once
•Compare and order whole numbers to 10,000
•Identify the place value for each digit in numbers to 10,000
•Round off numbers to 10,000 to the nearest ten, hundred, and thousand
•Use expanded notation to represent number (e.g., 3,206 = 3,000 + 200 + 6)
-True or false? 3,105 x 3 = 9,000 + 300 + 15
•Find the sum or difference of two whole numbers between 0 and 10,000
-True or false?
1. 591 + 87 = ?
2. 1,283 + 6,074 = ?
3. 3,215 - 2,876 = ?
-To prepare for recycling on Monday, Michael collected all the bottles in the house. He found 5 dark green ones, 8 clear ones with liquid still in them, 11 brown ones that used to hold root beer, 2 still with the cap on from his parents' cooking needs, and 4 more that were oversized. How many bottles did Michael collect?
•Memorize to automaticity the multiplication table for numbers between 1 and 10
•Use the inverse relationship of multiplication and division to compute and check results
•Solve simple problems involving multiplication of multi-digit numbers by one-digit numbers
(3,671 x 3 =__)
-A price list in a store states: pen sets, $3; magnets, $4; sticker sets, $6. How much would
it cost to buy 5 pen sets, 7 magnets, and 8 sticker sets?
•Solve division problems in which a multi-digit number is evenly divided by a one-digit number
(135 ÷ 5 = __)
•Understand the special properties of 0 and 1 in multiplication and division
-True or false?
1. 24 x 0 = 24; 19 ÷ 1 = 19
2. 63 x 1 = 63
•Determine the unit cost when given the total cost and number of units
•Solve problems that require two or more of the skills mentioned above
-A tree was planted 54 years before 1961. How old is the tree in 1998?
-A class of 73 students go on a field trip. The school hires vans, each of which can seat a maximum of 10 students. The school policy is to pile as many students as possible into a van before using the next one. How many vans are needed?
•Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., 1/2 of a pizza is the same amount as 2/4 of another pizza that is the same size; show that 3/8 is larger than 1/4)
-Which is longer, 1/3 of a foot or 5 inches? 2/3 of a foot or 9 inches?
•Add and subtract simple fractions (e.g., determine that 1/8 + 3/8 is the same as 1/2)
-Solve: 1/2 + 3/4 = ? 1/2 - 1/8 = ?
•Solve problems involving addition, subtraction, multiplication, and division of money amounts in decimal notation and multiply and divide money amount in decimal notation by using whole-number multipliers and divisors
-Pedro bought 5 pens, 2 erasers, and 2 boxes of crayons. The pens cost 65 cents each, the eraser 25 cents each, and a box of crayons cost $1.10. The prices include tax, and Pedro paid with a ten-dollar bill. How much change did he get back?
•Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is ½ of a dollar, 75 cents is 3/4 of a dollar)
Students will:
•Represent relationships of quantities in the form of mathematical expressions, equations, or inequalities
•Solve problems involving numeric equations or inequalities
•Select appropriate operational and relational symbols to make an expression true (e.g., if 4 __ 3 = 12, what operational symbol goes in the blank?)
•Express simple unit conversions in symbolic form (e.g., __ inches = __ feet x 12)
-If number of feet = number of yards x 3, and number of inches = number of feet x 12, how many inches are there in 4 yards?
•Recognize and use the commutative and associative properties of multiplication (e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?)
-When temperature is measured in both Celsius (C) and Fahrenheit (F), it is known that they are related by the following formula: 9 x C = (F - 32) x 5. What is 50 degrees Fahrenheit in Celsius?
•Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items give the cost per unit)
- John wants to buy a dozen pencils. One store offers pencils at 6 for $1. Another offers them at 4 for 65 cents. Yet another sells pencils at 15 cents each Where should John purchase his pencils in order to save the most money?
•Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4's or by multiplying the number of horses by 4)
-Here is the beginning of a pattern of tiles. Assuming that the pattern is the simplest possible, how many tiles will be in the sixth figure? (modeled after TIMSS gr. 4, K-6)
•Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects
•Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them
-Which rectangle is NOT divided into four equal parts? (modeled after TIMSS gr. 4, K-8)
-Make an outline of your hand with your fingers together on a piece of grid paper. Assuming that each grid is 1 cm2, what is roughly the area of your hand?
•Find the perimeter of a polygon with integer sides.
•Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes)
•Identify, describe, and classify polygons (including pentagons, hexagons, and octagons)
•Identify attributes of triangles (e.g., two equal sides for the isosceles triangle, three equal sides for the equilateral triangle, right angle for the right triangle)
•Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, right angles for the rectangle, equal sides and right angles for the square)
•Identify right angles in geometric figures of in appropriate objects and determine whether other angles are greater or less than a right angle
-Which of the following triangles include an angle that is greater than a right angle?
•Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder)
•Identify common solid objects that are the components needed to make a more complex solid object
Students will:
•Identify whether common events are certain, likely, unlikely, or improbable
-Is any of the following certain, likely, unlikely, or impossible?
1. Take two cubes each with the number 1, 2, 3, 4, 5, 6 written on its six faces. Throw them at random, and the sum of the numbers on the top faces is 12
2. It snows on New Year's day
3. A baseball game is played somewhere in this country on any Sunday in July
4. It is sunny in June
5. Pick any two one-digit numbers, and their sum is 17
•Record the possible outcomes for a simple event (e.g., tossing a coin) and systematically keep track of the outcomes when the event is repeated many times
•Summarize and display the results of probability experiments in a clear and organized way (e.g., use a bar graph or a line plot)
•Use the results of probability experiments to predict future events (e.g., use a line plot to predict the temperature forecast for the next day)
Students will:
•Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns
•Determine when and how to break a problem into simple parts
•Use estimation to verify the reasonableness of calculated results
- Prove or disprove a classmate's claim that 49 is more than 21 because 9 is more than 1
•Apply strategies and results from simpler problems to more complex problems.
•Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning
•Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support with evidence in both verbal and symbolic work
•Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy
•Make precise calculations and check the validity of the results from the context of the problem
•Evaluate the reasonableness of the solution in the context of the original situation
•Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems
•Develop generalizations of the results obtained and apply them in other circumstances