Math: Grade 4

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 extend their understanding of number and place value to include decimals to thousandths.

1.1 read, write, order, compare, and round numbers from .001 to over 1,000,000

1.2 choose an appropriate order of magnitude and decide whether an exact or approximate solution is called for in situations involving quantity

2. Students demonstrate an understanding of negative integers and their relationship to positive integers.

2.1 interpret negative integers (to -20) as temperatures below zero, below sea level, distances to the left of zero on an integer number line, or solutions to problems where a larger number is subtracted from a smaller number

2.2 model the concept that a whole number and its opposite add to be zero

3. Students identify, represent, interpret, and use fractions.

3.1 demonstrate understanding that the value of a fraction is not changed when the numerator and denominator are multiplied by the same number and use this fact to simplify and compute with fractions

3.2 compare the numerical value of fractions having denominators of 12 or less (e.g., 3/5 > 3/7) and mixed numbers where the fractional parts have denominators of 12 or less (e.g., 4 5/6 < 5 2/3 or 3 5/8 > 3 1/2 ) and find their approximate location on a number line

4. Students estimate, calculate, and model situations involving sums and differences.

4.1 estimate and compute the sum or difference of whole numbers and positive decimals (to thousandths), judge the reasonableness of an answer, and explain the methods used

4.2 add, subtract, and use drawings or objects to model these operations with fractions having like and unlike denominators of 12 or less

5. Students demonstrate understanding of multiplication and division and compute accurately with these operations.

5.1 model and recall multiplication facts through 12x12 and describe methods of modeling multiplication of two digit numbers

5.2 estimate and find the quotient of two whole numbers (two-digit divisor and two- or three- digit dividend), or decimals (dividend expressed as a decimal through thousandths and single-digit divisor) and explain the methods used

5.3 find multiples and factors of numbers to 400, identify, and explain the meaning of square numbers and cube numbers (use calculators to determine larger square and cube numbers)

Task/Assignment

Identify a whole number which lies between two non-consecutive whole numbers and a decimal number which lies between two consecutive whole numbers.

Show that 4/8, 1/2, and .5 all represent the same part of a whole.

Show (using symbols, drawings, or groups of objects) a variety of ways to find the product of 12 and 24 such as 12 x 24 is 10 24's plus 2 24's; 12 x 24 is twice (12 x 12); 12 x 24 = 10 x 20 + 10 x 2 + 2 x 20 + 2 x 2.

Symbols and Algebra

1. Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.

1.1 model, describe, and use the distributive property

1.2 write and simplify numerical expressions involving addition, subtraction, multiplication, division, and parentheses (e.g., m = 3x(2 - 7) - 8) including various indicators of multiplication (x,·, parentheses, juxtaposition) and division (÷, /, long division box)

1.3 develop, interpret, and use formulas (e.g., A = bh, ) to answer questions about quantities and their relationships

1.4 solve verbal problems of up to three­steps and interpret the solution in light of the context of the problem

Task/Assignment

If Josh reads 5 times as many books in a year as Ellen reads, 5 could represent that number of books when Ellen reads books.

Measurement and Geometry

1. Students read and use scales in maps, drawings, and on coordinate graphs.

1.1 use and interpret scales on maps and drawings

1.2 use simple two-dimensional coordinate systems to find locations on a map (e.g., A4) and to represent points and simple figures on a coordinate grid

2. Students demonstrate understanding of the relationship between area and length and use appropriate units to measure each.

2.1 estimate and measure area, recognize and use appropriate units in both the metric and customary system (square centimeter (cm2), square meter (m^2), square kilometer (km^2), square inches (in^2), square yard (yd^2), square mile (mi^2))

2.2 determine and use formulas to find the perimeter of a polygon, the area of a square, rectangle, and triangle

2.3 demonstrate understanding that a given area can be enclosed by several different perimeter lengths and that a given perimeter can encase figures of different areas (e.g., Given 12 square tiles, make all the rectangles you can that use all the tiles. Find the perimeter of each rectangle.)

3. Students measure and draw line segments, measure, draw, identify, and classify angles.

3.1 identify, name, and draw points, line segments, rays and lines that appear to be parallel, perpendicular or intersecting

3.2 estimate, draw, measure, and classify right, acute, or obtuse angles and associate an angle with an amount of turning (1/4 turn with 90°, 1/2 turn with 180°)

4. Students draw, analyze, and classify plane and solid geometric objects based on position and size of sides, faces, and angles.

4.1 identify whether the sides of a plane figure or the edges or faces of a solid object are the same size, parallel, or perpendicular

4.2 identify and classify quadrilaterals as squares, rectangles, rhombuses, parallelograms, or trapezoids

4.3 demonstrate and explain relationships (e.g., same size/shape/orientation, congruent, similar) among figures (includes using slides, reflections, rotations, and size changes to arrive at the answer)

4.4 construct new 3-dimensional objects by combining or taking apart other 3-dimensional objects

Functions

1. Students use information given verbally, in tables, and on graphs to create and interpret other representations of the same information.

1.1 complete a table from given information, read, and interpret tables within the context of a given situation

1.2 identify verbal, numerical, and graphical representations which convey the same information

1.3 describe and explain the effect one quantity varying has on the variation of a second quantity (e.g., Every two days the bean plant grows 1.8 cm)

2. Students create and interpret simple coordinate graphs.

2.1 graph and name integer points on a four-quadrant coordinate grid

2.2 read and interpret scales on axes

Statistics, Data Analysis, and Probability

1. Students collect, record, graph, and interpret data and communicate their findings clearly.

1.1 formulate questions of interest and select ways of systematically collecting data to answer them

1.2 display data in a tally, table, bar graph, or line graph, identify and explain what they show and how they show it

2. Students determine the possible outcomes of an event and the simple probability that it will occur.

2.1 determine (using concrete materials or lists) all possible outcomes of an event involving four or fewer items (e.g., the number of ways Jose, Mary, and Flo can finish 1st, 2nd, and 3rd in a race) and explain a process for ascertaining that there have been no omissions or duplications

2.2 determine and explain how likely an event is (e.g., If I have a bag with 4 red marbles and 5 blue marbles then I have 5 chances out of 9 of choosing a blue marble) and interpret this as the probability that the event will occur

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