# Unit 1, Review Transitioning from Previous Mathematics Instructional Resources: McDougal Littell: Course 1

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1 Unit 1, Review Transitioning from Previous Mathematics Transitioning from previous mathematics to Sixth Grade Mathematics Understand the relationship between decimals, fractions and percents and demonstrate on a number line Interpret percents as part of a hundred Determine the prime factors of all numbers through 50 and write the products of their prime factors by using exponents to show multiples of a factor Add, subtract and perform simple multiplication and division of fractions and decimals California Standards Key Book Course 1 P2 P68 Topic 1: Estimation and Number Sense Topic 2: Numbers and their Factors Topic 3: Fractions and Decimal Factor Prime factor Decimal Percent Product 18

2 Unit 1, Concept 2 Rational Numbers: How to connect Properties and Applications NS 1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line Understand the multiplicative identity property and understand relationships (including equivalence) among decimals, fractions, and percents Compare and order positive and negative fractions Place positive and negative fractions, mixed numbers, and decimals on a number line Convert numbers from one form to an equivalent form (fractions, decimals, mixed numbers, and percents) Use the multiplicative identity property to find equivalent values 1.5 Comparing & Ordering Decimals 2.6 Comparing & Ordering Fractions 2.7 Mixed Numbers & Improper Fractions 2.8 Connecting Decimals & Fractions 4.1 Integers & the Number Line 4.8 Comparing Positive & Negative Numbers Multiplicative identity property Least common denominator Least common multiple Improper fraction Mixed number Number line 19

3 Unit 1, Concept 3 Rational Numbers: How to connect Properties and Applications NS 2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation. NS 2.2 Explain the meaning of multiplication and division of positive fractions and perform the calculations NS 2.4 Determine the least common multiple and the greatest common divisor of whole numbers; use them to solve problems with fractions (e.g., to find a common denominator to add two fractions or to find the reduced form for a fraction). Understand the basic arithmetic operations (+,,x, ) on fractions, and the relationships among these operations Find LCM and GCF of whole numbers Add and subtract positive fractions and mixed numbers with unlike denominators Multiply and divide positive fractions and mixed numbers 2.2 Greatest Common Factor 2.4 Fractions in Simplest Form 2.5 Least Common Multiple 3.1 Adding & Subtracting Fractions 3.2 Using a Least common Denominator 3.3 Adding & Subtracting Mixed Numbers 3.4 Multiplying Fractions & Mixed Numbers 3.5 Dividing Fractions and Mixed Numbers Greatest common factor Prime factorization Composite Simplest form Factor Multiple Divisor 20

4 Unit 2, Concept 1 Algebraic Thinking and Proportional Reasoning NS 2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations. Understand variables and expressions as symbolic representations of numerical values Add, subtract, multiply and divide using integers Evaluate expressions using order of operations and commutative, associative, and distributive properties Write verbal expressions using symbolic representations, and vice versa Translate between verbal expressions and symbolic representations 4.2 Adding Integers on a Number Line 4.3 Adding Integers Using Addition Rules 4.4 Subtracting Integers 4.5 Multiplying Integers 4.6 Dividing Integers Integer Inverse property of addition 26

5 Unit 2, Concept 2 Algebraic Thinking and Proportional Reasoning AF 1.1 Write and solve one-step linear equations in one variable AF 1.2 Write and evaluate an algebraic expression for a given situation, using up to three variables. AF 1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process. AF 1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator. Understand equations Use integers and properties of equality to solve one-step equations 5.2 Writing Equations 5.3 Solving Addition Equations 5.4 Solving Subtraction Equations 5.5 Solving Multiplication Equations 5.6 Solving Division Equations 5.7 Solving Two-Step Equations Expression Equation Subtraction property of equality Division property of equality Multiplication of equality 27

6 Unit 2, Concept 3 Algebraic Thinking and Proportional Reasoning AF 2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity AF2.3 Solve problems involving rates, average speed, distance, and time. NS 1.2 Interpret and use ratios in different contexts to show the relative sizes of two quantities, using appropriate notations NS 1.3 Use proportions to solve problems. Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. NS 1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips. Understand and use ratios, proportions, percents and rates Write ratios in different ways (1to 5, 1/5, 1:5) Calculate unit rates Convert one unit of measurement to another Interpret and use ratios in different contexts Solve percentage problems 3.8 Rates 6.1 Ratios 6.2 Solving Proportions 6.3 Writing Proportions 6.4 Similar Polygons 6.5 Scale Drawings 7.1 Percents, Fractions, and Decimals 7.2 Finding a Percent of a Number 7.3 Large and Small Percents 7.4 Solving Percent Problems 7.6 Simple Interest 7.7 Discounts and Sales Tax Unit rate Ratio Proportion Cross multiplication Similar polygons 28

7 Unit 3, Concept 1 Statistics Data and Probability SDAP 2.1 Compare different samples of a population with the data from the entire population and identify a situation in which it makes sense to use a sample. SDAP 2.2 Identify different ways of selecting a sample and which method makes a sample more representative for a population. SDAP 2.4 Identify data that represent sampling errors and explain why the sample might be biased. Understand and use methods for selecting a representative sample of a population Describe, identify and implement sampling methods Represent data in multiple ways 10.7 Samples and Populations 10.8 Interpreting Surveys Population Sample Biased sample Random 40

8 Unit 3, Concept 2 Statistics Data and Probability SDAP 1.1 Compute the range, mean, median, and mode of data sets. SDAP 1.3 Understand how the inclusion or exclusion of outliers affects measures of central tendency. SDAP 1.4 Know why a specific measure of central tendency (mean, median, mode) provides the most useful information in a given context SDAP 2.3 Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached. SDAP 2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims. Understand the factors that influence the validity and interpretation of data Calculate range, mean, median, and mode Recognize outliers and their effect on measures of central tendency Discuss the factors affecting the validity of claims 1.6 Rounding Decimals 4.6 (Already Covered in Unit Two) 7.5 Circle Graphs 10.1 Measures of Central Tendency Histograms 10.3 Box-and-Whisker Plots 10.4 The Coordinate Plane and Scatter Plots 10.5 Using Appropriate Graphs 10.6 Interpreting Graphs 10.8 (Already Covered in Unit 3) Measure of central tendency Median Mode Histogram Box-and whisker plot Range Coordinate plane Scatter plot 41

9 Unit 3, Concept 3 Statistics Data and Probability SDAP 3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, 1 P is the probability of an event not occurring. Understand that the probability of an event is between 0 and 1 Calculate theoretical and experimental probabilities Represent probabilities as ratios, decimals, and percents Calculate the probability of an event not occurring Use probability to make predictions Probability 11.1 Organizing Possible Outcomes 11.5 Probability of an Event Not Occurring Event Probability of an event Independent events Dependent events Tree diagram 42

10 Unit 3, Concept 4 Statistics Data and Probability Instructional Resources: McDougalLittell: Course 1 SDAP 3.1 Represent all possible outcomes for compound events in an organized way and express the theoretical probability of each outcome. SDAP 3.5 Understand the difference between independent and dependent events. Understand the difference between dependent and independent events Represent all outcomes for a compound event in multiple ways Identify events as dependent and independent Calculate probability for independent events 11.1 (Already Covered in Unit 3) 11.2 Disjoint Events and Independent Events 11.4 Probability of Disjoint Events Disjoint events Tree diagram 43

11 Unit 4, Concept 1 Plane and Solid Shapes MG 1.1 Understand the concept of a constant such as Π; know the formulas for the circumference and area of a circle. MG 1.2 Know the common estimates of Π and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements. Understand that the ratio of the circumference to the diameter is the same for any circle (i.e. the constant π) Know the common estimates of π Use formulas to calculate the circumference and area of a circle 8.7 Circumference of a Circle 8.8 Area of a Circle 9.6 Surface Area of a Cylinder Circle Radius Diameter Circumference 50

12 Unit 4, Concept 2 Plane and Solid Shapes MG 2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms. MG 2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. AF 3.1 Use variables in expressions describing geometric quantities. AF3.2 Express in symbolic form simple relationships arising from geometry Understand the properties of twodimensional figures Identify special angle pairs Solve problems using the properties of special angle pairs and the sum of the angles of a triangle Classify triangles and quadrilaterals Calculate area and perimeter Solve problems using the properties of special angles 8.1 Intersecting Lines and Angle Measures 8.2 Angles of a Triangle 8.4 Area of a Triangle 8.6 Area of a Parallelogram 8.7 (Already done in Unit Four) 8.8 (Already done in Unit Four) Vertical angles Complementary angles Supplementary angles Adjacent angles Right angle Acute angle Obtuse angle Parallelogram Rectangle 51

13 Unit 4, Concept 3 Plane and Solid Shapes MG 1.3 Know and use the formulas for the volume of triangular prisms and cylinders; compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. Understand the properties of threedimensional figures Calculate the volumes of prisms and cylinders 9.2 Volume of a Rectangular Prism 9.3 Volume of a Triangular Prism 9.4 Volume of a Cylinder Prism Bases Right prism Circular cylinder Surface area Lateral surface 52

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