Bradley County Schools MATH Pacing Guide

Transcription

1 Bradley County Schools MATH Pacing Guide The following pages are a suggested pacing guide for Mathematics. This pacing guide is designed to assist the teacher in planning for the entire school year and to complete the necessary skills before TCAP for grades 3-5. All lessons for the Envision text are listed in the order in which they appear in the book along with thecorresponding Tennessee State Performance Indicator (SPI) or Check for Understanding (CFU). Some Things to Know Before Using This Pacing Guide The first column of the pacing guide is a guide to let the teacher know approximately how much material must be covered in each of the nine week grading periods. Grades 3-5 need to look closely at this column because some of the grading periods have more lessons than there are days. Consolidation of some lessons may be appropriate in order to get through the necessary lessons before TCAP. A day is set aside between each of the topics for assessment and differentiation of instruction. The second column list the number of the lesson from the Envision textbook. Some of the lessons in grades 3-5 are written in red saying 'Post TCAP'. This is the recommendation of the book publisher, but teachers need to look at these lessons to make sure it is not something that needs to be introduced. All of the 'Post TCAP' lessons are added at the end of the year. It is important to get as many of these lessons covered before the end of the year as possible. Column three list the Tennessee SPI or CFU that is covered in the lesson according to the publisher. Since this is the first year of the textbook adoption, teachers may need to look closely to make sure that all SPI's are covered in the depth needed. Using this list as a guide, all SPI's are covered before the TCAP testing window. An attempt has been made to assign all words from the Tennessee list to the topic which it would seem the most logical. Teachers need to be mindful of this list because some are not presented in the text. The next column is a place for the teacher to write in their own. Remember that the Tech Coaches have worked diligently to put all of the resources associated with the new textbook on the web at The state is also working on a website of additional resources at This website is being updated regularly with new ideas. It may be a little hard to navigate but it will be a great resource in years to come. The kindergarten guide has one more column than the others. This column contains the Common Core Standard that is related to each lesson. These are the standards that kindergarten teachers are responsible for teaching during the year Some lessons have no Common Core Standard connected to them, but it is important to cover these lessons to prepare for first grade. This column will be added for the other grades as we move up the adoption of Common Core Standards.

2 1st Nine Weeks Lesson 1-1 SPI Identify the place value of a specified digit in a number and the quantity it represents. Lesson 1-2 SPI Identify the place value of a specified digit in a number and the quantity it represents. ( Also SPI (Read and write numbers from hundredths to hundred-thousands in numerals and in words.) and CFU (Compose and decompose quantities according to place value.) Lesson 1-3 Reviews SPI Compare and order numbers up to 10,000 using the words less than, greater than, and equal to, and the symbols <, >, =. Lesson 1-4 Post TCAP Lesson 1-5 CFU Connect operations with decimals to money and make estimates. Lesson 1-6 SPI Determine the correct change from a transaction. Lesson 1-7 CFU Translate between symbolic, numerical, verbal, or pictorial representations of a whole number pattern or relationship. Lesson 2-1 Lesson 2-2 Lesson 2-3 CFU Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning. Post TCAP SPI Solve contextual problems using whole numbers, fractions, and decimals. GRADE 4 Topic 1 Numeration decimal base-ten system greater than / less than numeral digit dollar expanded form Topic 2 Adding and Subtracting Whole Numbers commutative property associative property distributive whole number fraction See Click on "Curriculum Links" Go to the heading 'Mathematics' Everything from Envisions is there along with plenty of additional web-based resources from which to choose

3 1st Nine Weeks Lesson 2-4 Reviews SPI Solve contextual problems involving the addition (with and without regrouping) and subtraction (with and without regrouping) of twoand three digit whole numbers. Lesson 2-5 Reviews SPI Solve contextual problems involving the addition (with and without regrouping) and subtraction (with and without regrouping) of twoand three digit whole numbers. Lesson 2-6 Reviews SPI Solve contextual problems involving the addition (with and without regrouping) and subtraction (with and without regrouping) of twoand three digit whole numbers. Lesson 2-7 SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 3-1 Lesson 3-2 Lesson 3-3 Lesson 3-4 Reviews SPI Identify various representations of multiplication and division. SPI Find factors, common factors, multiples, and common multiples of two numbers. CFU Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning. (Also SPI Verify a conclusion using the commutative, associative and distributive properties.) CFU Identify factors of whole numbers and model factors and products beyond basic multiplication facts using arrays and area models. Also CFU (Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning) and SPI (Verify a conclusion using the commutative, associative and distributive properties). relationship computation equations inverse operations Topic 3 Multiplying Meanings and Facts factor multiple product patterns array inverse relationships Pattern Rules

4 1st Nine Weeks Lesson 3-5 CFU Identify factors of whole numbers and model factors and products beyond basic multiplication facts using arrays and area models. Also CFU (Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning). Lesson 3-6 CFU Identify factors of whole numbers and model factors and products beyond basic multiplication facts using arrays and area models. Lesson 3-7 SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 4-1 Lesson 4-2 CFU Use models to understand division as the inverse of multiplication, partitioning, and repeated subtraction. CFU Use models to understand division as the inverse of multiplication, partitioning, and repeated subtraction. CFU Understand that division by zero is Lesson 4-3 undefined. Lesson 4-4 CFU Use models to understand division as the inverse of multiplication, partitioning, and repeated subtraction. Lesson 4-5 SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 5-1 Lesson 5-2 Reviews SPI Compute multiplication problems that involve multiples of ten using basic number facts. CFU Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning. Topic 4 Division Meanings and Facts division divisor dividend quotient Topic 5 Multiplying by 1-digit Numbers reasonableness

5 1st Nine Weeks Lesson 5-3 Post TCAP Lesson 5-4 CFU Identify the range of appropriate estimates, including over-estimate and under-estimate. Also CFU Understand the relationship between use of answers and the accuracy of the number. Lesson 5-5 CFU Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently. Also CFU (Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning). Lesson 5-6 SPI Solve problems using whole number multi-digit multiplication. Lesson 5-7 SPI Solve problems using whole number multi-digit multiplication. Lesson 5-8 SPI Solve problems using whole number multi-digit multiplication. Also SPI (Solve contextual problems using whole numbers, fractions, and decimals). Lesson 6-1 SPI Use letters and symbols to represent an unknown quantity and write a simple mathematical expression. Also CFU (Translate between symbols and words to represent quantities in expressions or equations), CFU (Translate between symbolic, numerical, verbal, or pictorial representations of a whole number pattern or relationship), SPI (Make generalizations about geometric and numeric patterns), SPI (Represent and analyze patterns using words, function tables, and graphs). Topic 6 Patterns and Expressions conclusion conjecture expression ordered pair function table

6 2nd Nine Weeks 1st Nine Weeks Lesson 6-2 SPI Represent and analyze patterns using words, function tables, and graphs. Also CFU (Translate between symbolic, numerical, verbal, or pictorial representations of a whole number pattern or relationship), and SPI (Represent and analyze patterns using words, function tables, and graphs). Lesson 6-3 CFU Create, explain and use a rule to generate terms of a pattern or sequence. Also CFU (Translate between symbolic, numerical, verbal, or pictorial representations of a whole number pattern or relationship), and SPI (Represent and analyze patterns using words, function tables, and graphs). Lesson 6-4 SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 7-1 Lesson 7-2 Lesson 7-3 Lesson 7-4 Reviews SPI Compute multiplication problems that involve multiples of ten using basic number facts. Post TCAP CFU Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently. Also CFU Use commutative, associative, and distributive properties of numbers including oral descriptions of mathematical reasoning. SPI Solve problems using whole number multi-digit multiplication. Topic 7 Mulitiplying by 2-digit Numbers

7 2nd Nine Weeks Lesson 7-5 SPI Solve problems using whole number multi-digit multiplication. AlsoCFU Multiply two- and three-digit whole numbers and CFU Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a singledigit divisor accurately and efficiently. Lesson 7-6 SPI Solve problems using whole number multi-digit multiplication. Lesson 7-7 CFU Solve multi-step problems of various types using whole numbers, fractions, and decimals. Also SPI Solve problems using whole number multi-digit multiplication. Lesson 8-1 Lesson 8-2 Lesson 8-3 Lesson 8-4 Lesson 8-5 CFU Divide three-digit whole numbers by one-digit divisors fluently with pencil and paper. Post TCAP CFU Understand the role of the remainder in division. CFU Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently. CFU Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently. Also SPI (Solve problems using whole number division with one- or two-digit divisors). Topic 8 Dividing by 1-digit Divisors remainder prime composite

8 2nd Nine Weeks Lesson 8-6 CFU Understand and use a reliable algorithm for multiplying multi-digit numbers and dividing numbers by a single-digit divisor accurately and efficiently. Also CFU (Divide three-digit whole numbers by one-digit divisors fluently with pencil and paper), and SPI Solve problems using whole number division with one- or two-digit divisors. TN - 1 SPI Solve problems using whole number division with one- or two-digit divisors. Lesson 8-7 CFU Divide three-digit whole numbers by one-digit divisors fluently with pencil and paper. Lesson 8-8 SPI Find factors, common factors, multiples, and common multiples of two numbers. Lesson 8-9 GLE Identify prime and composite numbers. Lesson 8-10 CFU Solve multi-step problems of various types using whole numbers, fractions, and decimals. Also SPI (Solve problems using whole number division with one- or two-digit divisors). TN - 2* CFU Develop a story problem that illustrates a given multiplication or division number sentence. Lesson 9-1 Lesson 9-2 Lesson 9-3 Lesson 9-4 Lesson 9-5 Lesson 9-6 TN - 3* SPI Classify lines and line segments as parallel, perpendicular, or intersecting. CFU Classify angles and triangles as obtuse, acute, or right. CFU Measure and draw angles Determine if a figure is a polygon. SPI Identify acute, obtuse, and right angles in 2-dimensional shapes. SPI Identify acute, obtuse, and right angles in 2-dimensional shapes. CFU Identify the basic parts of circles. Topic 9 Lines, Angles, and Shapes Previously Introduced: intersecting lines Parallel perpendicular polygons angles lines line segments

9 2nd Nine Weeks TN - 4* CFU Understand the definition of degree as it relates to the circle. Lesson 9-7 SPI Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument. Also CFU (Identify geometric or physical attributes that are appropriate to measure in a given situation). Lesson 10-1 Lesson 10-2 Lesson 10-3 Lesson 10-4 Lesson 10-5 Lesson 10-6 Lesson 10-7 Reviews Identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as division of two whole numbers. Reviews CFU Identify fractions as parts of whole units, as parts of sets, as locations on number lines, and as division of two whole numbers. CFU Identify the range of appropriate estimates, including over-estimate and under-estimate. SPI Generate equivalent forms of common fractions and decimals and use them to compare size. Also CFU Generate equivalent forms of whole numbers, decimals, and common fractions (e.g., 1/10, ¼, ½, ¾). CFU Generate equivalent forms of whole numbers, decimals, and common fractions (e.g., 1/10, ¼, ½, ¾). SPI Convert improper fractions into mixed numbers and/or decimals. SPI Generate equivalent forms of common fractions and decimals and use them to compare size. Also SPI Use the symbols <, > and = to compare common fractions and decimals in both increasing and decreasing order. obtuse acute right vertex / vertices radius / radii diameter Topic 10 Adding and Subtracting Fractions and Mixed Numbers numerator denominator equivalent unit fraction common fraction mixed number proper fraction improper fraction convert

10 3rd Nine Weeks 2nd Nine Weeks Lesson 10-8 Extends: SPI Use the symbols <, > and = to compare common fractions and decimals in both increasing and decreasing order. Lesson 10-9 SPI Generate equivalent forms of common fractions and decimals and use them to compare size. Adding and Subtracting Fractions Lesson 11-1 SPI Add and subtract proper fractions with like and unlike denominators and simplify the answer. Also SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 11-2 SPI Add and subtract proper fractions with like and unlike denominators and simplify the answer. Also SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 11-3 SPI Add and subtract proper fractions with like and unlike denominators and simplify the answer. Also SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 11-4 SPI Add and subtract proper fractions with like and unlike denominators and simplify the answer. Also SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 12-1 TN-5 SPI Read and write numbers from hundredths to hundred-thousands in numerals and in words. Also CFU (Match the spoken, written, concrete (including base ten blocks), and pictorial representations of decimals), and CFU (Compose and decompose quantities according to place value). CFU Understand decimal notation as an extension of the base-ten number system. Topic 11 Topic 12 Understanding Decimals

11 3rd Nine Weeks Lesson 12-2 SPI Use the symbols <, > and = to compare common fractions and decimals in both increasing and decreasing order. Also SPI (Compare decimals using concrete and pictorial representations). Lesson 12-3 CFU Understand and use decimal numbers up to hundredths and write them as fractions. Also CFU (Generate equivalent forms of whole numbers, decimals, and common fractions (e.g., 1/10, ¼, ½, ¾)). TN - 6 SPI Convert improper fractions into mixed numbers and/or decimals. Lesson 12-4 CFU Use models, benchmarks, and equivalent forms to compare fractions/decimals and locate them on the number line. Also CFU (Compare equivalent forms whole numbers, fractions, and decimals to each other and to benchmark numbers) and SPI (Generate equivalent forms of common fractions and decimals and use them to compare size). Lesson 12-5 SPI Locate and place mixed numbers on the number line. Lesson 12-6 CFU Use models, benchmarks, and equivalent forms to compare fractions/decimals and locate them on the number line. Lesson 13-1 Post TCAP Lesson 13-2 Post TCAP Lesson 13-3 SPI Add and subtract decimals through hundredths. Also CFU Match the spoken, written, concrete (including base ten blocks), and pictorial representations of decimals. Topic 13 Operations with Decimals

12 3rd Nine Weeks Lesson 13-4 SPI Add and subtract decimals through hundredths. Also SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 13-5 SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 13-6 SPI Solve contextual problems using whole numbers, fractions, and decimals. Lesson 13-7 SPI Solve contextual problems using whole numbers, fractions, and decimals. Also CFU Use age-appropriate books, stories, and videos to convey ideas of mathematics. Lesson 14-1 Lesson 14-2 Lesson 14-3 Lesson 14-4 Lesson 14-5 CFU Estimate areas of rectangles in square inches and square centimeters. Also CFU Recognize that a measure of area represents the total number of same-sized units /that cover the shape without gaps or overlaps. CFU Recognize that a measure of area represents the total number of same-sized units /that cover the shape without gaps or overlaps. Also CFU (Connect area measure to multiplication using a rectangular area model) and SPI (Solve problems involving area and/or perimeter of rectangular figures). CFU Recognize that area does not change when 2-dimensional figures are cut apart and rearranged. Also SPI Solve problems involving area and/or perimeter of rectangular figures. SPI Solve problems involving area and/or perimeter of rectangular figures. Post TCAP Topic 14 Area and Perimeter area perimeter square unit accuracy

13 3rd Nine Weeks Lesson 14-6 SPI Solve problems involving area and/or perimeter of rectangular figures. Lesson 14-7 SPI Solve problems involving area and/or perimeter of rectangular figures. Lesson 14-8 SPI Solve problems involving area and/or perimeter of rectangular figures. Lesson 14-9 SPI Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument. Lesson 15-1 CFU Recognize two-dimensional faces of three-dimensional shapes. TN - 7 SPI Identify attributes of simple and compound figures composed of 2- and 3- dimensional shapes. Lesson 15-2 Post TCAP Lesson 15-3 Post TCAP Lesson 15-4 Post TCAP Lesson 15-5 SPI Make generalizations about geometric and numeric patterns. Lesson 16-1 Lesson 16-2 SPI Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight. Also CFU (Measure using ruler, meter stick, clock, thermometer, or other scaled instruments). SPI Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight. Also CFU Measure liquids using both standard units and metric units. Topic 15 Solids face of a polyhedron Topic 16 Ratio and Percent

14 3rd Nine Weeks Lesson 16-3 SPI Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight. Lesson 16-4 SPI Convert measurements within a single system that are common in daily life (e.g., hours and minutes, inches and feet, centimeters and meters, quarts and gallons, liters and milliliters). Lesson 16-5 SPI Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight. Lesson 16-6 SPI Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight. Also CFU Measure liquids using both standard units and metric units. Lesson 16-7 SPI Determine appropriate size of unit of measurement in problem situations involving length, capacity or weight. Lesson 16-8 SPI Convert measurements within a single system that are common in daily life (e.g., hours and minutes, inches and feet, centimeters and meters, quarts and gallons, liters and milliliters). TN - 8* CFU Recognize the use of decimals in metric measures. Also SPI Determine situations in which a highly accurate measurement is important. Lesson 16-9 SPI Convert measurements within a single system that are common in daily life (e.g., hours and minutes, inches and feet, centimeters and meters, quarts and gallons, liters and milliliters). Lesson CFU Measure using ruler, meter stick, clock, thermometer, or other scaled instruments. Lesson CFU Measure using ruler, meter stick, clock, thermometer, or other scaled instruments. Lesson CFU Measure using ruler, meter stick, clock, thermometer, or other scaled instruments.

15 4th Nine Weeks Prior to TCAP Lesson 17-1 Lesson 17-2 Lesson 17-3 Lesson 17-4 TN - 9* Lesson 17-5 SPI Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs). SPI Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs). Reviews SPI Interpret a frequency table, bar graph, pictograph, or line plot. SPI Graph and interpret points with whole number or letter coordinates on grids or in the first quadrant of the coordinate plane. Also CFU Explain how the components of a coordinate system are used to determine location. CFU Explore properties of paths between points. SPI Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs). Lesson 17-6 Prepares for CFU Use measures of central tendency to compare two sets of related data. Lesson 17-7 SPI Given a set of data or a graph, describe the distribution of the data using median, range, or mode. TN - 10* CFU Use measures of central tendency to compare two sets of related data. Lesson 17-8 CFU Develop and use stem-and-leaf plots. Lesson 17-9 CFU Interpret and prepare pie charts using appropriate measurements of angles. TN - 11* CFU Evaluate how well various representations show the collected data. Lesson SPI Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs). Topic 17 Equations and Graphs pictograph line plot frequency table / tally chart vertical horizontal Scale of instrument / graph coordinate system quadrant measures of central tendency (mean, median, and mode) stem-and-leaf plot range

16 4th Nine Weeks Prior to TCAP Lesson 18-1 Reviews SPI Express mathematical relationships using number sentences/equations. Lesson 18-2 CFU Find an unknown quantity in simple equations using whole numbers, fractions, decimals, and mixed numbers. Lesson 18-3 CFU Find an unknown quantity in simple equations using whole numbers, fractions, decimals, and mixed numbers. Lesson 18-4 Post TCAP Lesson 18-5 CFU Translate the details of a contextual problem into diagrams and/or numerical expressions, and express answers using appropriate units. Lesson 19-1 SPI Identify images resulting from reflections, translations, or rotations. Lesson 19-2 SPI Identify images resulting from reflections, translations, or rotations. Lesson 19-3 SPI Identify images resulting from reflections, translations, or rotations. TN - 12 CFU Examine transformations in the coordinate plane. Also CFU Predict the results of a transformation of a geometric shape. TN - 13* CFU Design and analyze simple tilings and tessellations. Lesson 19-4 Reviews SPI Determine if two figures are congruent based on size and shape. Lesson 19-5 CFU Determine whether a geometric shape has line and/or rotational symmetry. Also CFU Draw lines of symmetry in 2-dimensional figures. Lesson 19-6 CFU Determine whether a geometric shape has line and/or rotational symmetry. Topic 18 Equations Topic 19 Transformations, Congruence, and Symmetry transformation symmetry reflect rotate translate congruent line of symmetry tiling / tessellation

17 4th Nine Weeks After TCAP 4th Nine Weeks Prior to TCAP Lesson 19-7 SPI Compare objects with respect to a given geometric or physical attribute and select appropriate measurement instrument. Lesson 20-1 Prepares for SPI List all possible outcomes of a given situation or event. Lesson 20-2 SPI List all possible outcomes of a given situation or event. Lesson 20-3 CFU Determine a simple probability. Lesson 20-4 CFU Translate the details of a contextual problem into diagrams and/or numerical expressions, and express answers using appropriate units. Lesson 1-4 Prepares for CFU Explore different methods of estimation including rounding and truncating. Lesson 2-2 Prepares for CFU Explore different methods of estimation including rounding and truncating. Lesson 5-3 Prepares for CFU Explore different methods of estimation including rounding and truncating. Lesson 7-2 Prepares for CFU Explore different methods of estimation including rounding and truncating. Lesson 8-2 Prepares for CFU Explore different methods of estimation including rounding and truncating. Lesson 13-1 Prepares for CFU Explore different methods of estimation including rounding and truncating. Lesson 13-2 Prepares for SPI Estimate fraction and decimal sums or differences. Lesson 14-5 Prepares for SPI Solve contextual problems that require calculating the area of triangles and parallelograms. Lesson 15-2 Prepares for CFU Build, draw, and work with prisms by means of orthogonal views, projective views, and nets. Topic 20 Probability Post TCAP Preparing for 5th Grade

18 4th Nine Weeks After TCAP Lesson 15-3 Prepares for CFU Build, draw, and work with prisms by means of orthogonal views, projective views, and nets. Lesson 15-4 Prepares for CFU Quantify total volume as filling space with same-sized units of volume without gaps or overlap. Lesson 18-4 Prepares for CFU Solve single-step linear inequalities and graph solutions on a number line.