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PRE-ALGEBRA RATIO FORMULA
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Grade Six Mathematics

The sixth grade objectives place continued emphasis on the study of whole numbers, decimals, and fractions. However, students need opportunities to apply their computation skills to real life applications. Calculators and computers may be used to solve problems. Decreased attention should be given to tedious paper and pencil computations. Sixth graders will continue to use manipulatives whenever new material is introduced or whenever it is needed to review previously taught material. The areas of probability, statistics, geometry, and pre-algebra will be stressed. Students will use ratios to compare data sets, make geometric constructions of three-dimensional figures, explore thoroughly the algebra strand, and solve problems involving circles, volume, and surface area.

Number Theory and Number Sense
6.1 (7,8) Read, write, and identify the place value from billions through millionths using standard and expanded form
6.2 (7,8) Compare and order the value of whole numbers, fractions, and decimals from billions through ten-thousandths and write and model equivalences
6.3
(7) Identify prime and composite numbers up to 100 using hundred chart, manipulatives, and calculators
6.4 Identify and represent integers on a number line 6.5 Identify and use the divisibility rules of 2,3,5, and 10
6.6 (7,8) Identify pictorial representations of fractions and decimals
6.7 (5) Identify least common multiple or greatest common factor of two numbers

Computation and Estimation
6.8 (3,4,5,7,8) Use estimation to solve problems with whole numbers (rounding, compatible numbers, clustering, front-end estimation with adjustment) and decimals, including money
6.9 (5,7,8) Continue to reinforce whole number computation skills, applying them to problem- solving situations using estimation, mental math, calculators, and paper and pencil
6.10 (5,7,8) Solve problems in context that involve addition, subtraction, multiplication, and division of fractions and mixed numbers with and without regrouping, including like and unlike denominators, expressing answers in simplest form using estimation, mental math, calculators, and paper and pencil
6.11 (5,7,8) Solve problems in context that involve addition, subtraction, and multiplication of decimals through the ten-thousandths and division of decimals by decimal divisors using estimation, mental math, calculators, and paper and pencil
6.12 (7,8) Use concrete materials, estimation, mental math, calculators, and paper and pencil to find the percent of a number
6.13 Use order of operations to solve multi-step problems
6.14 Identify a number that is 1,000 more or 1,000 less than a given number


 

Patterns, Functions, and Algebra
6.15 Identify missing elements in numeric and geometric patterns and explore a variety of patterns, including perfect squares, square roots, exponents, and scientific notation
6.16 (5,7,8) Use input/output models for functions (number machines).
6.17 Solve equations using the identity property of addition (8+n=8) and the identity property of multiplication (8*n=8)
6.18 Write the cross product of a proportion and solve the resulting equation.
6.19 Represent and solve real world-problems by choosing the appropriate strategy, such as guess and check, make a table, write a proportion, find a pattern, work backwards, use a formula, write an equation, or make a scale drawing
6.20 Write algebraic expressions for word expressions and evaluate them by replacing the variable with a given value
6.21 (5,7) Solve equations with addition, subtraction, multiplication, and division of whole numbers, fractions, decimals, and integers using inverse operations, guess and check, and/or physical models
6.22 Solve inequalities by using a number line
6.23 Graph one-step linear equations in one variable in the first quadrant

Probability and Statistics
6.24 (5,7,8) Collect, organize, display, and interpret data using line graphs, circle graphs, bar graphs, histograms, stem-and-leaf plots, tables, and charts 6.25 (5,7,8) Create and solve problems involving the mean, median, mode, and range of a set of data 6.26 model practical problem- solving situations by constructing a sample space to determine probability
6.27 Determine the probability of a given event and express that probability as a ratio, decimal, or percent
6.28 Test the expected probability of an event against the actual outcome by carrying out an experiment using technology whenever appropriate
6.29 (5,7,8) Determine combinations and permutations (tree diagrams, probability experiments with and without replacement)

Geometry
6.30 (7,8) Classify lines as parallel, intersecting, perpendicular, or skew

 

6.31 Draw, compare, and contrast the following quadrilaterals: parallelogram, rectangle, square, rhombus, and trapezoid along with the following polygons: pentagon, hexagon, octagon, decagon, and dodecagon
6.32 (4,5,7) Classify and compare line segments, angles, and polygons
6.33 Describe, identify, and build models of three dimensional figures, including prisms, pyramids, cylinders, and cones; locate, count, and record the faces, edges, and vertices of the prisms and pyramids
6.34 Bisect a line segment and construct congruent angles using a compass and straightedge 6.35 (7,8) Identify the ordered pair for a point and locate the point in all four quadrants of the coordinate plane
6.36 Recognize line symmetry and rotational symmetry
6.37 Demonstrate flips, slides, and turns using congruent geometric figures
6.38 (7,8) Identify the radius and diameter of a circle

Measurement
6.39
Use concrete materials to derive approximation for pi from actual measurements of circumference and diameter of a circle
6.40 (7) Create and solve problems by finding the circumference and area of a circle when given the radius or diameter
6.41 (7,8) Measure real objects in order to develop the formulas for perimeter and area; determine the perimeter and area of a triangle, square, rectangle, parallelogram, and irregular figures given the appropriate measures
6.42 Investigate and solve problems involving the volume and surface area of rectangular prisms using real objects and practical situations
6.43 (7,8) Use prior knowledge of customary and metric measures of length, mass/weight, and capacity/volume to solve problems
6.44 (2,3,4,5,7,8) Solve application problems using measurement including elapsed time
6.45 (5,7,8) Convert between units within the same system
6.46 (2,3,4,5) Select appropriate units to determine length, weight, temperature, or volume using customary and metric units
6.47 (7,8) Determine measurements indirectly from scale drawings