Chapter -"Number Theory and Systems"-Understand numeration, number theory, and number systems.
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| 1 |
Read & Write Numbers-Use numeric digits and words to read and write numbers including the trillions. Using the signs <, >, and =, order and compare numbers including the trillions.
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6632 6633 6634
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| 2 |
Round Numbers-Round to the nearest thousand; nearest ten thousand; nearest hundred thousand; nearest million.
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6635 6636
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| 3 |
Divisibility Rules-Apply the divisibility rules of 2, 3, 4, 5, 6, 8, 9, and 10 to various numbers.
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67113
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| 4 |
Prime Factorization-Use prime factorization to determine the prime factors of a number.
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67114
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| 5 |
Greatest Common Factor-Find the greatest common factor among 2 or more numbers.
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67115 67156
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| 14 |
Square Numbers-Identify square numbers.
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6B003
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| 6 |
Powers of 10-Identify powers of 10 through the 6th power.
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6643 6644 67258 6B005
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| 7 |
Scientific Notation-Write numbers in scientific notation. Convert scientific notation to standard form.
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6645 6646 67116
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| 8 |
Compare Scientific Notation-Using the signs <, >, and = compare rational numbers in scientific notation.
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67121 67158
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| 15 |
Negative Numbers-Understand the concept of negative numbers using number line representations.
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6B004
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| 9 |
Number Line-Identify and represent integers and rational numbers on a number line.
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6710 6711 67147
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| 10 |
Inequality Symbols-Using the symbols <, >, and =, compare integers.
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6714 6715 67148
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| 11 |
Absolute Value-Define absolute value and its opposite.
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67149 67157
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| 16 |
Pi-An introduction to pi.
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6B014
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| 12 |
Skills & Strategies-Analyze and solve problems using number-sense skills and strategies.
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6647 6648
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| 13 |
Everyday Math-Identify mathematical concepts and apply them to everyday experiences.
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6649 6650
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Chapter -"Meanings of Operations"-Understand the meanings of operations and how they relate to one another.
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| 1 |
Properties-Describe and apply the Commutative, Associative, and Distributive Properties.
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6651 67122
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| 2 |
Exponential Expressions-Evaluate exponential expressions. Explore relationships of exponents and roots.
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6637 6638 6639 6640 67123
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| 3 |
Order of Operations-Apply the order of operations including exponents and roots.
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67124 67194
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| 4 |
Add & Subtract Numbers-Add and subtract using five-digit numbers, including subtracting across zeros.
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6652
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| 5 |
Estimate Sums & Differences-Estimate sums and differences.
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6653
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| 6 |
Whole Numbers (x and ÷)-Multiply and divide whole numbers.
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6654 6655 67153
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| 12 |
Inverse Operations-Understand that addition and subtraction are inverse operations. Understand that multiplication and division are inverse operations.
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6B001 6B002
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| 7 |
Estimate Products & Quotients-Estimate products and quotients using a variety of estimating techniques including front-end, compatible numbers, and rounding.
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6656 6657 67154
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| 8 |
Mental Math-Demonstrate mental computation strategies for multiplication and division by powers of 10.
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6658 6659
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| 9 |
Division & Decimal Remainders-Solve division problems by writing the remainders as a decimal.
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67155 67195
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| 10 |
Use a Calculator-Using a calculator, add, subtract, multiply, and divide up to five-digit numbers.
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6662 6663
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| 11 |
Strategies to Add & Subtract-Use a variety of problem-solving strategies to analyze and solve problems involving addition and subtraction.
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6660 6661 6664 6665
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Chapter -"Fractions and Decimals"-Understand relationships among numbers and ways of representing fractional and decimal numbers.
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| 1 |
Least Common Multiple-Find the least common multiple of 2 or more numbers.
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67117
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| 2 |
Least Common Denominator-Determine the least common denominator of fractions with unlike denominators.
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67118
|
| 15 |
Locating Fractions on a Number Line-Locate proper and improper fractions and mixed numbers on a number line.
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6B006
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| 3 |
Add and Subtract Mixed Numbers-Convert between mixed numbers and improper fractions. Add and subtract mixed numbers and fractions having like and unlike denominators with regrouping.
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67119 67120
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| 4 |
Fraction Inequalities-Using the signs <, >, and =, compare mixed numbers and fractions having like and unlike denominators.
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6666 6667
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| 5 |
Add & Subtract Fractions-Add and subtract mixed numbers and fractions having like and unlike denominators.
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6668 6669
|
| 16 |
Add and Subtract Fractions and Whole Numbers-Add and subtract mixed numbers, whole numbers, proper and improper fractions having like and unlike denominators.
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6B007
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| 6 |
Multiply Mixed Numbers-Multiply mixed numbers by whole numbers and fractions.
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6670 6671 67150
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| 7 |
Divide Fractions-Divide whole numbers by fractions. Divide fractions by fractions. Divide mixed numbers by whole numbers and fractions.
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6672 6673 6674 6675 67151 67152
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| 8 |
Read & Write Decimals-Read, write, and order decimals to the nearest hundred thousandth.
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6676 6677
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| 9 |
Decimals in Expanded Form-Write decimals (up to the hundred thousandths) in expanded form.
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6678 6679
|
| 10 |
Calculating Decimals-Round decimals to the nearest hundredth; to the nearest thousandth; to the nearest ten thousandth. Estimate decimal sums and differences through the nearest hundred thousandth. Add and subtract decimals through the hundred thousandths.
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6680 6681 6682 6683 6684
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| 11 |
Multiply Decimals-Multiply decimals. Round decimals to the nearest hundredth, thousandth, and ten thousandth.
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6686 6687 67174
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| 12 |
Divide Decimals-Divide decimals by whole numbers. Divide decimals by other decimals.
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6688 6689 6690 6691 67175 67181
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| 17 |
Estimate Products and Quotients of Decimals-Estimate products and quotients of decimals.
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6B009 6B010 6B011
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| 13 |
Fractions and Decimals-Convert between fractions and decimals.
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6692 6693 67187
|
| 14 |
Repeating Decimals-Define and identify terminating and repeating decimals.
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67188 67189 6B008
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Chapter -"Percents and Ratios"-Understand relationships among numbers and ways of representing percents and ratios.
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| 1 |
Convert between Numbers-Convert between fractions, decimals, and percentages.
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6694 6695 67162
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| 2 |
Calculate the Percent -Calculate the percent of a number. (What is 25% of 100?)
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6696 6697 67163
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| 3 |
Use Percent to Find a Number-Find an unknown number when a percentage of the number is known.
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6698 6699
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| 4 |
Percents Greater than 100-Solve problems involving percentages greater than 100. (match with diagrams)
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6702 6703 67164
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| 5 |
Percent Increase & Decrease-Solve problems involving percent increase and decrease such as sales tax and discounts.
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6700 6701 67165
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| 12 |
Estimate Percent-Estimate percents.
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6B012
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| 6 |
Simple Interest-Solve problems using simple interest.
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67166
67191 |
| 7 |
Ratios-Define and write ratios and express decimals and percents as ratios.
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67182
|
| 8 |
Compare Variables & Ratios-Compare two values or variables as ratios, using appropriate notations such as a/b, a to b, and a:b.
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6704
|
| 9 |
Proportions-Solve proportions including problems involving proportions with one unknown through cross products.
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6706 6707 67183
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| 10 |
Rates-Solve problems involving rates.
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67192 67196
|
| 11 |
Skills & Strategies-Analyze and solve word problems using fraction, decimal, ratio, and percentage skills and strategies.
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6708 6709
|
Chapter -"Patterns-Relations-Functions"-The learner will understand patterns, relations, and functions.
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| 1 |
Identify Pattern Rules-Identify and apply pattern rules using diagrams, charts, lists, and tables. Identify and extend figurate number patterns. (triangular, square, etc.)
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6801 6802 67200
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| 2 |
Function Rules-Express function rules using algebraic symbols. (e.g. add 2 expressed as n + 2)
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6803 6804 67201
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| 3 |
Function Tables-Identify functional relationships and complete function tables. Identify algebraically the rule used to generate a group of ordered pairs.
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6805 67202 67207
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| 4 |
Using Patterns & Functions-Solve problems and model real-world situations using patterns and functions.
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6806 6807
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Chapter -"Algebra"-The learner will represent and analyze mathematical situations and structures using algebraic symbols.
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| 1 |
Add & Subtract Integers-Add and subtract integers. Define the Additive Inverse, Identity Element of Addition, and the Equality Property.
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6716 6717 67203
|
| 2 |
Multiply & Divide Integers-Multiply and divide integers. Define the Multiplicative Inverse, Zero Property, Identity Element of Multiplication, and the Equality Property.
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67204
|
| 3 |
Integers Everyday-Use integers in real-life situations.
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6718 6719
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| 4 |
Simplify Expressions-Simplify algebraic expressions.
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6809 6810 67205 67211
|
| 5 |
Solve One-Step Equations -Solve one-step algebraic equations with a variable and express the solution on a number line.
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67212
|
| 6 |
Solve Two-Step Equations-Solve two-step algebraic equations with a variable and express the solution on a number line.
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6811 6812 67213
|
| 7 |
Simple Linear Word Problems-Write and solve simple linear equations for word problems, and explain reasoning orally or in writing.
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6813 6814
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| 8 |
Inequalities-Solve algebraic inequalities with a varible. Graph the solution set of an algebraic inequality on a number line.
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67214 67215
|
Chapter -"Geometry"-Analyze characteristics and properties of two- and three-dimensional shapes.
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| 1 |
Points-Segments-Rays-Lines-Identify and draw points, line segments, angles, rays, planes, parts of a circle, and horizontal, vertical, perpendicular, parallel, and intersecting lines.
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6720 6721 66948 67257
|
| 12 |
Open and Closed Figures-Identify whether figures are open or closed.
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6B013
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| 2 |
Geometric Shapes-Classify, describe, and compare two-dimensional geometric figures. Define and identify attributes of three-dimensional figures.
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6722 6723 6728 6729 67159
|
| 3 |
Construct Parallelograms-Using a ruler and compass, construct parallelograms.
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6730 6731
|
| 4 |
Circles-Investigate and determine the relationship between the diameter and circumference of a circle and the value of pi.
|
67160 67161
|
| 5 |
Angle Measures-Using a protractor, measure and classify acute, right, obtuse, and straight angles.
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6734 6735 6736 6737 67216
|
| 6 |
Bisectors-Define and identify altitudes, midpoints, diagonals, angle bisectors, and perpendicular bisectors.
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6732 6733 6738 6739 67217
|
| 7 |
Angle Relationships-Define and identify adjacent, vertical, interior, exterior, complementary, and supplementary angles. Define and identify alternate interior, alternate exterior, corresponding, and vertical angles.
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67218 67219
|
| 8 |
Construct Triangles-Use a compass and straightedge to construct equilateral, right, and isosceles triangles.
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6740 6741
|
| 9 |
Right Triangles-Use the Pythagorean theorem to find the hypotenuse of a right triangle.
|
67252
|
| 10 |
Properties of Triangles-Find the measure of the third angle of triangles when given the measure of two angles.
|
6742 6743 67253
|
| 11 |
Similar Triangles-Use proportions to find the length of a missing side when given the length of two sides of similar triangles.
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6744 6745 67254
|
Chapter -"Coordinate Geometry"-The learner will specify locations and descibe spatial relationships using coordinate geometry
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| 1 |
Plotting Points-Plot points on a four quadrant coordinate plane by determining and using ordered pairs of positive and negative whole numbers.
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6724 6725 67255
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| 2 |
Distance-Find the distance between two points on a vertical or horizontal line.
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67245
|
| 3 |
Transformations -Locate, give the coordinates of, and graph plane figures which are the results of translations or refelctions in the first quadrant.
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67256
|
Chapter -"Transformational Geometry"-The learner will apply transformations and use symmetry to analyze mathematical situations.
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| 1 |
Congruence & Similarity-Explore congruence and similarity of objects using transformations.
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67249
|
| 2 |
Symmetry-Explore line and rotational symmetry of objects using transformations.
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67250
|
| 3 |
Similar, Congruent & Symmetric-Identify and distinguish among similar, congruent, and symmetric figures. Name corresponding parts.
|
67251
|
Chapter -"Spatial Reasoning"-The learner will use visualization, spatial reasoning, and geometric modeling to solve problems.
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| 1 |
Cross Sections-Identify and classify cross sections of three-dimensional figures.
|
67236
|
| 2 |
Surface Area-Explore surface area of three-dimensional figures.
|
67237
|
| 3 |
Geometric Models-Use geometric models to solve problems using two-dimensional attributes of three-dimensional figures.
|
67238
|
| 4 |
Scale Drawings-Use grids to make scale drawings to relate scale to ratio.
|
67241
|
| 5 |
Distances on Maps-Use proportional reasoning to determine distances on a map.
|
6795 6796 67242
|
| 6 |
Geometry Everyday-Identify and use geometric concepts in areas other than mathematics, such as science, architecture, art, and everyday life.
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6758
|
Chapter -"Time"-The learner will understand the attributes of time and apply appropriate techniques, tools, and formulas to determine measurements.
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| 1 |
Units of Time-Identify varied units of time including seconds, minutes, hours, days, weeks, months, years, decades, centuries, and milleniums. Relate time by using fractions of an hour or a year.
|
6791 6792 67197
|
| 2 |
Elapsed Time-Use schedules, calendars, and elapsed time to solve real-world problems. Interpret and create time schedules. Solve problems involving time zones.
|
6793 6794 67198
|
| 3 |
Rates-Solve problems involving rates, average speed, distance, and time.
|
67199 67206
|
Chapter -"Measurement Systems"-The learner will understand the attributes of length and weight and apply appropriate techniques, tools, and formulas to determine measurements.
|
| 1 |
Estimate Measurements-Estimate the length, weight/mass, and capacity/volume of an object, and compare the estimate with an actual measurement.
|
6785 6786
|
| 2 |
Customary System-Estimate and measure length, weight, and capacity in customary units.
|
67171
|
| 3 |
Converting Customary Units-Choose the proper tool/unit for measurement. Convert between units in the customary system.
|
67172
|
| 4 |
Indirect Customary Measurement-Determine lengths, weights, and capacities using proportional reasoning and indirect measurement.
|
67173 67180
|
| 5 |
Metric System-Estimate and measure length, mass, and capacity in metric units.
|
67176
|
| 6 |
Converting Metric Units-Choose the proper tool/unit for measurement. Convert between units in the metric system.
|
6787 6788 67177
|
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