Math: Grade 5

Draft Standards From The State of California Academic Standards Commission

Source

State of California Academic Standards Commission

Contents

Forums

Related Articles

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, place value, and computation to very large and very small numbers.

1.1 estimate, determine, and interpret the meaning of very large numbers (e.g., What day was it 1,000,000 seconds ago?, How many pieces of paper would you need to write your name 500,000 times?, How many miles would 1,000,000,000 pieces of paper stretch if they were laid side by side in a row?)

1.2 read, write, and interpret whole number powers of 10 (e.g., 104 = 10,000)

1.3 round, add, subtract, multiply, and divide with whole numbers and positive decimals from .0001 to over 1,000,000 using an appropriate method of calculation (pencil and paper, estimation, mental computation, and calculator) and judge the reasonableness of the results

2. Students model, explain, and compute with positive and negative integers.

2.1 model, explain, and determine the value of the sum of a positive and a negative integer or two negative integers

2.2 identify and represent integers on a number line

2.3 separate sets of integers into subsets (e.g., odd/even, positive/negative, prime/composite, multiple/divisor, square number/not-square number)

2.4 determine the least common multiple and greatest common divisor of two or three whole numbers, explain the process used, and use them to solve problems

3. Students demonstrate their understanding of decimals and fractions and compute with them.

3.1 write terminating decimals as fractions and explain why they represent the same value

3.2 explain how the relationship between multiplication/division of whole numbers extends to fractions, multiply simple fractions, and reduce to lowest terms

3.3 arrange fractions, mixed numbers, and decimals in order, represent them on a number line, and explain the process used

3.4 add and subtract fractions and mixed numbers with denominators 20 or less and express answers in simplest form

Task/Assignment

An elevator goes down 3 floors then goes up 7 floors; describe its position relative to the floor on which it started.

An elevator goes down 3 floors then goes down 4 more floors; describe its position relative to the floor on which it started.

If red markers indicate positive and blue markers indicate negative, then a group with 8 red and 12 blue markers represents a value of negative 4.

Demonstrate that adding a negative number is the same as subtracting a positive number and that subtracting a negative number is the same as adding a positive number.

Demonstrate taking a fractional part of a fractional part (e.g., 1/2 x 3/4 = 3/8 because dividing each "fourth" into two pieces gives and equivalent portion, 6/8, and taking half of these six­eighths yields 3/8).

18 ÷ 3 = 6 because 3 x 6 = 18 so 18 ÷ 1/3  = 54 because 1/3 x 54 = 18.

Identify at least two fractions, or two decimals which lie between consecutive whole numbers.

Symbols and Algebra

1. Students describe and use variables to express a verbal, numeric, geometric, or graphical relationship.

1.1 use information taken from a graph or equation to answer questions about a problem situation or create a "story"

2. Students model and solve algebraic equations in one variable.

2.1 use concrete materials to model and solve an equation

2.2 solve one-step linear equations in one variable involving whole number coefficients and rational solutions

Task/Assignment

Find the length of the side of a square if its perimeter is 54", if its perimeter is 20w units long and explain how you came to this conclusion.

Measurement and Geometry

1. Students measure and compare weights, times, and temperatures using appropriate units and tools.

1.1 use a balance, a reference object, and a scale to measure and compare weights

1.2 determine the duration of a time interval (e.g., 11:00 a.m. to 3:30 p.m. the next day)

2. Students use cubic units to measure volume, identify, and differentiate between one-, two-, and three-dimensional parts of a plane or solid object.

2.1 differentiate between perimeter, area, and volume and determine which of these is appropriate to use in a given problem

2.2 find one dimension of a rectangle given its other dimension and either its area or its perimeter

2.3 estimate pi, the circumference, and the area of a circle and use the corresponding formulas

2.4 model and compute the volume of geometric solids (rectangular solids, prisms, and cylinders), selecting and using appropriate units in both metric and customary systems (cubic centimeter (cm^3), cubic meter (m^3), cubic inches (in^3), cubic yard (yd^3))

2.5 identify and determine a method to calculate the surface area of a cube and a rectangular solid

3. Students identify and draw one-, two-, and three-dimensional geometric objects and use their properties.

3.1 estimate, measure, identify, and draw perpendicular and parallel lines, angles, midpoints, and bisectors (perpendicular and angle) using appropriate tools (e.g., straight edge, ruler, compass, protractor, and drawing software)

3.2 state and use properties of squares and rectangles (e.g., identify the angles of a square or rectangle as right angles,)

3.3 associate 3/4 turn with 270° and a full turn with 360°

3.4 identify, describe, and classify triangles by their angles (acute, right, obtuse) or sides (equilateral, isosceles, scalene) and use appropriate tools to draw various types of triangles

3.5 recognize and describe bilateral and rotational symmetry in two- and three-dimensional figures

3.6 Students visualize, represent, and interpret two-dimensional views of three-dimensional objects which are made from rectangular solids

Task/Assignment

Demonstrate that the volume of a rectangular container can be determined by finding the area of its base (counting the cubes that cover the bottom of the container) and finding the height (the number of layers needed to fill the container).

ABCD is a rectangle, how many degrees are in angle x?

draw the solid that remains when the two shaded cubes are removed and determine how many cubes remain.

Functions

1. Students investigate, describe, and extend numerical and geometric patterns.

1.1 identify and describe triangular, square, and cubic numbers, investigate and extend patterns involving them using drawings and concrete materials as needed

1.2 create, describe, and extend patterns formed by powers and arithmetic sequences

Statistics, Data Analysis, and Probability

1. Students use and analyze data generated by themselves and others to ask and answer relevant questions.

1.1 formulate questions, carry out a survey or experiment, accurately record data, and clearly communicate the results

1.2 create and interpret circle graphs and display information in alternative graphical formats (e.g., show information in a bar graph as a circle graph)

1.3 draw conclusions, note trends, and make a recommendation based on data analysis

2. Students select and use a method for determining the likelihood of a simple event.

2.1 use experiments with concrete materials (e.g., dice, spinners, cards) to determine a relative frequency for an event and compare that with the expected probability derived from a tree diagram, sample space, or area comparison

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