Math: Grade 3

Draft Standards From The State of California Academic Standards Commission

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State of California Academic Standards Commission

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Mathematics is a language we use every day, often without knowing it. It builds and draws on conceptual understanding and skills, and helps us make decisions and solve problems. In this draft document we have tried to connect the notion of problem solving to conceptual understanding and skill development by embedding it within the content strands at every grade. Given here are only some of the ways you will see this exemplified. Students are asked to:

• ask relevant questions about problem situations
  
  
• decide between relevant and extraneous information
  
  
• choose appropriate operations tools and approaches to problem situations
  
  
• decide whether an exact or approximate answer is called for
  
  
• apply specific techniques in new situations
  
  
• explain, check, justify, prove, and judge the reasonableness of results
  
  
• create new approaches and connect knowledge and understanding in new ways
  
  

Number Sense

1. Students describe and compare exact and approximate quantities using whole numbers to 100,000.

1.1 count, read, write, order, and compare whole numbers to 100,000 and identify the place value for each digit

1.2 describe the relative size of large numbers using models or numbers derived from computed quantities (e.g., How many days (hours, minutes) old are you?)

1.3 round a whole number and estimate to the nearest ten, hundred, thousand, and ten thousand

1.4 use and interpret negative numbers in simple contexts (temperature, "owing," number line)

2. Students demonstrate an understanding of decimals and simple fractions.

2.1 associate a fraction and decimal with a part of a whole or a part of a set (halves, thirds, fourths, eighths, tenths), write the corresponding fraction, and recognize that when all fractional parts are included (2 halves, 3 thirds, 10 tenths, etc.) the result is equal to a whole and to 1

2.2 identify the part of a set or region that represents the sum or difference of two fractional parts of the set or region

2.3 demonstrate understanding that a mixed number is a whole number plus a fraction

2.4 read, write, represent, interpret, add, and subtract decimals through hundredths, multiply a decimal by a whole number and explain what happens to the place value of the answer

2.5 order money amounts written as decimals, count, compare and make change using a collection of coins and bills for amounts up to $20.00

3. Students estimate and demonstrate facility with calculating sums and differences.

3.1 estimate and find the sum or difference of two whole numbers, each 10,000 or less using such terms as closer to, between, and a little more than

3.2 solve simple subtraction problems when differences are in the range -10 to -1 and recognize the addition of a negative number as the subtraction of a positive number

4. Students understand the mutual relationship between multiplication and division and how these operations extend to two-digit numbers.

4.1 estimate and find the product of two whole numbers in which one factor has two digits or less and the other factor has three digits or less

4.2 estimate and find the quotient of two whole numbers given one-digit divisors and three-digit dividends including those with remainders

4.3 give multiples and factors of a number and identify square numbers to 100

Task/Assignment

Find the answer and explain how you solved this problem: How much more money does Sara need to buy a book which costs $8.95 if she already has $6.45?

Symbols and Algebra

1. Students demonstrate an understanding of and use of and properties governing variables and symbols used in simple number sentences

1.1 use variables as place holders for numbers in sentences involving addition, subtraction, or multiplication (m + w = 6; 3 x K = 12)

1.2 express simple unit conversions in symbolic form (e.g., #inches = #feet X 12)

1.3 identify and describe the commutative and associative properties of multiplication and the special properties of 0 and 1

2. Students represent operations and express relationships using words, tables, and graphs.

2.1 select appropriate information and operations to express and solve word problems

2.2 write one or more number sentences to represent a word problem, solve, and interpret the arithmetic answer(s) in the context of the problem

2.3 identify and use the inverse relationships between multiplication and division (e.g., 3 x 7 = 21, so 21 ÷ 3 = ___) to compute and check results

2.4 use and define the meaning of such mathematical terms as divisor, dividend, product, quotient, multiple, and factor

Measurement and Geometry

1. Students make reasonable estimates and accurately measure distance, area, volume, weight, and time

1.1 estimate and measure length, liquid volume, weight/mass and express the results in terms of a reference object, metric units, or standard units

1.2 find and distinguish between the perimeter and the area of a polygonal shape, identify, and describe situations representing their use

1.3 carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes)

2. Students analyze plane and solid geometric objects including the number of end points, shape of faces, and number of edges and corners

2.1 identify attributes of triangles and quadrilaterals; draw and describe the elements that distinguish those figures (e.g., equal sides, square corners, perpendicular sides)

2.2 identify the radius, diameter, circumference, and area of a circle and draw circles with various radii

2.3 identify, name, describe, and classify polygons including pentagons, hexagons, and octagons

2.4 name and describe (e.g., symmetry, number/shape of faces, straight/curved edges) common three-dimensional geometric objects (cube, rectangular solid, sphere, prism, pyramid, cone, cylinder)

Functions

1. Students represent and interpret a quantitative relationship in a formula, table or graph.

1.1 use a function rule to solve simple problems (e.g., the function rule is "adding 7" so 1-->8, 3-->10, 12-->19, etc.) and graph the resulting ordered pairs of whole numbers on a grid
1.2 recognize, describe, and extend geometric (e.g., ), simple numeric (e.g., odd/even, multiples of 5, factors) and linear patterns (e.g., the number of legs on a given number of horses can be calculated by counting by 4's)

1.3 determine a total cost or amount as a function of the number of units and the unit cost or value

Statistics, Data Analysis, and Probability

1. Students collect, record, graph, and interpret the results of surveys and data on the frequency of events and communicate their findings clearly.

1.1 ask and answer relevant questions from data presented in charts, tables, and graphs

1.2 predict probable outcomes from a collection of organized data

1.3 identify possible outcomes (e.g., with a spinner or die) and predict how likely they are to occur

1.4 find possible combinations and arrangements involving a limited number of variables (e.g., How many ways can you line up a blue block, a red block, and a green block?)

Credits

The Draft Standards were prepared by:

The State of California Academic Standards Commission
The Commission for the Establishment of Academic Content and Performance Standards Comments may be addressed to The Commission