Grade Five Growing With Mathematics

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Mathematics in Our World 1.1-Sets the stage. 1.2 1.3 1.4 1.5-NSO 8 - Identify and use relationships between operations to solve problems Initial Assessment - 1 day Going over assessment-1 day Topic 1 <1 wk Initial Assessment After the Initial Assessment you may or may not need to teach 1.2, 1.3, and-or 1.4. Maintaining Skills pages important and will review a lot of skillsconcepts Properties of Polygons and Circles 2.1-2.2-G 1 Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. 2.2-G 2 Use standard language to describe line, segment, ray,angle, skew, parallel and perpendicular 2.3-G 2 Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular 2.3-G 7* Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. 2.3-M 1 Identify and select appropriate units to measure angles; i.e., degrees. 2.3-M 7 Use benchmark angles (e.g.; 45º, 90º, 120º) to estimate the measure of angles, and use a tool to measure and draw angles. Topic 2 2.1 Briefly review 2.2 Missing skew, parallel and perpendicular G 2 review term: ray 2.3 G7--Using Practice page 19 in Student Book point out it s not the length of either side 2.4 Do Extra Help! * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 1

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Properties of Polygons and Circles Using Division 2.4-G 3* Label vertex, rays, interior and exterior for an angle 2.4-G5* Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. 2.4-M 1 Identify and select appropriate units to measure angles; i.e., degrees 2.4-M 7 Use benchmark angles (e.g.; 45º, 90º, 120º) to estimate the measure of angles, and use a tool to measure and draw angles. 2.5-G 4* Describe and use properties of congruent figures to solve problems 2.5-G2 Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. 3.1 Reviews factors and common factors 3.2 NSO7 Review properties of mathematics through the long division algorithm. 3.3 - DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 3.4-NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 3.5-NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 3.5-DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate Topic 2 Topic 3 2.1 Briefly review 2.2 Missing skew, parallel and perpendicular G 2 review term: ray 2.3 G7--Using Practice page 19 in Student Book point out it s not the length of either side 2.4 Do Extra Help! 3.5 NSO 13 only in assessment Extend DAP6 to include explain what each does and does not indicate about the set of data. * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 2

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Using Division (cont.) about the set of data. Topic 3 3.5 NSO 13 only in assessment Investigating Length and Perimeter Adding and Subtracting Common Fractions 4.1 -M5 Make conversions within the same measurement system while performing computations. 4.2 -M5 Make conversions within the same measurement system while performing computations. 4.3 Social Studies 4.4 Social Studies 4.5 -M 6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 5.1 -NSO 10 Justify why fractions need common denominators to be added or subtracted 5.1-NSO 12 Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 5.1-NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 5.2 -NSO 10 Justify why fractions need common denominators to be added or subtracted 5.2-NSO 12 Use physical models, points of reference, and Topic 4 6 days Topic 5 Extend DAP6 to include explain what each does and does not indicate about the set of data. See 11.5 Teacher s Guide * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 3

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Adding and Subtracting Common Fractions (cont.) Analyzing Everyday Data equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 5.3 -NSO3 Identify and generate equivalent forms of fractions, decimals and percents. 5.4 -NSO 2* Use various forms of one to demonstrate the equivalence of fractions 5.4-NSO 12 Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 5.5-NSO 12 Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 6.1-DAP 2 Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 6.1-DAP3 Read and interpret increasingly complex displays of data. 6.2-DAP 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 6.2-DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 6.3-DAP 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 6.3-DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. Topic 5 Topic 6 <3 wk which includes Periodic Assessment Change the Assessing the Lesson to select and construct an appropriate graph as opposed to telling the students to construct a bar graph. Ask why they chose the graph they chose. 6.1 N 10-Daily Number Sense starter and N 12 6.2 N 10- Daily Number Sense starter and N 12 6.3 N 10- Daily Number Sense starter and N 12 6.4 N 10- Daily Number Sense starter and N 12 6.5 N 10- Daily Number Sense starter and N 12 * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 4

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Analyzing Everyday Data (cont.) Working with Large Numbers Using Multiplication 6.4-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs. 6.4-M7 6.5-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs. 6.5-DAP 2 Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 6.5-DAP 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. 7.1 7.2 7.3 7.4 7.5 8.1-NSO 9* Use order of operations, including use of parentheses, to simplify numerical expressions. 8.1-PFA 4 Create and interpret the meaning of equations and inequalities representing problem situations. 8.2-NSO13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 8.3-NSO13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of Topic 6 <3 wk which includes Periodic Assessment Topic 7 <4 days Skip lessons but complete Maintaining Skills pg 92, 94, 100, 102. Topic 8 Before Topic 7 do Periodic Assessment for Topics1-6 pages 47-50 6.2, 6.3, 6.5 Students are not asked to determine appropriate data. Extend DAP6 to include explain what each does and does not indicate about the set of data. 8.5 Do Extra Challenge Inequalities need to be supplemented * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 5

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Using Multiplication (cont.) Thinking Visually 9.1 9.2 9.3 9.4 9.5 Working with Time 10.1 10.2 10.3 10.4 10.5 Adding and Subtracting Decimal Fractions strategies. 8.3-NSO7 Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. 8.4 - skip 8.5-NSO 5* Recognize and identify perfect squares and their roots 8.5-PFA 1 Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 11.1- NSO 3 Identify and generate equivalent forms of fractions, decimals and percents 11.2- NSO 11 Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. 11.3-NSO 6* Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money 11.3-PFA 6* Describe how the quantitative change in a Topic 8 8.5 Do Extra Challenge Inequalities need to be supplemented * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 Skip Skip Topic 11 6

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Adding and Subtracting Decimal Fractions (cont.) Relating Volume, Capacity, and Weight variable affects the value of a related variable. 11.4- NSO 11 Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. 11.5 skip 12.1-M 3 Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects. 12.1-M 4 Demonstrate understanding of the differences among linear units, square units and cubic units. 12.2-M 4 Demonstrate understanding of the differences among linear units, square units and cubic units. 12.2-M 6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 12.3 -M 3 Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects 12.3-M 4 Demonstrate understanding of the differences among linear units, square units and cubic units. 12.4-M 5 Make conversions within the same measurement system while performing computations. 12.5-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs. 12.5-DAP 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collected and display data, and clearly communicate findings. 12.5-DAP 5 Modify initial conclusions, propose and justify new interpretations and predictions as additional data are Topic 11 Topic 12 After Topic 12 take the Periodic Assessment for Topics 1-12. 12.1 works with volume but not the comparison between area and volume 12.5 DAP4 Students are not asked to determine appropriate data. * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 7

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Relating Volume, Capacity, and Weight (cont.) collected. Topic 12 After Topic 12 take the Periodic Assessment for Topics 1-12. 12.1 works with volume but not the comparison between area and volume 12.5 DAP4 Students are not asked to determine appropriate data. Exploring Multiplication of Fractions Using Division to Find Rates 13.1 13.2 13.3 13.4 13.5 14.1-NSO 8 Identify and use relationships between operations to solve problems. 14.1-NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 14.2-NSO 1 Use models and visual representation to develop the concept of ratio as part-to-part and part-towhole, and the concept of percent as part-to-whole. 14.3 NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 14.4-DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate Skip Topic 14 Reviewed throughout the year. * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 8

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Using Division to Find Rates (cont.) Relating Circumference and Diameter Relating Circumference and Diameter Working with Fractions and Decimals about the set of data. 14.5- NSO 1- Use models and visual representation to develop the concept of ratio as part-to-part and part-towhole, and the concept of percent as part-to-whole. 15.1 skip 15.2 -G 1 Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. 15.3-G 1 Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. 15.3-PFA 3 Use variables as unknown quantities in general rules when describing patterns and other relationships. 15.4-G 1 Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of π. 15.5-M 7 Use benchmark angles (e.g.; 45º, 90º, 120º) to estimate the measure of angles, and use a tool to measure and draw angles. 16.1 (6 th grade indicator) skip 16.2-NSO 13- Estimate the results of computations involving whole numbers, fractions and decimals, using a Topic 14 Topic 15 <1 wk Topic 15 <1 wk May be used as an extension. Topic 16 Be certain to give students multiple opportunities to draw their own circles. * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 9

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Working with Fractions and Decimals Working with Area variety of strategies. 16.3-NSO 12 Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. 16.3-PFA 5 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 16.4-NSO 8 Identify and use relationships between operations to solve problems. 16.5-NSO 1 Use models and visual representation to develop the concept of ratio as part-to-part and part-towhole, and the concept of percent as part-to-whole. 17.1-M 6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 17.2-M6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 17.3-M 6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 17.3- PFA 5 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 17.4-M 6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 17.5 (6 th grade indicator) Topic 16 Topic 17 <1 wk 17.1 review as needed Topic 17 <1 wk 17.1 review as needed * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 10

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Probability and Statistics 18.1-DAP2 Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 18.1-DAP 3 Read and interpret increasingly complex displays of data, such as double bar graphs. 18.1-DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 18.2-DAP 2 Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 18.2-DAP 3 Read and interpret increasingly complex displays of data, such as double bar graphs. 18.3-DAP 7* List and explain all possible outcomes in a given situation 18.3-DAP 8 Identify the probability of events within a simple experiment, such as three chances out of eight. 18.4-DAP 8 Identify the probability of events within a simple experiment, such as three chances out of eight. 18.5-DAP 2 Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. 18.5-DAP 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collected and display data, and clearly communicate findings. Algebraic Thinking 19.1-M 2* Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. Topic 18 <3 wk Topic 18 <3 wk Topic 19 After Topic 18, complete the Periodic Assessment 1-18 After Topic 18, complete the Periodic Assessment 1-18 Extend DAP6 to include explain what each does and does not indicate about the set of data. Be certain to complete the Daily Number Sense Starter for each lesson. (NSO 3) 18.5Students are not asked to determine appropriate data. Introduce the Cartesian Grid (four-quadrant * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 11

Grade Five Growing With Mathematics GWM Topic State Indicators-Lessons Lessons-Indicators: Pacing Assessment Comments Algebraic Thinking (cont.) 19.2-PFA5 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 19.3-PFA 1 Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 19.3-PFA 3 Use variables as unknown quantities in general rules when describing patterns and other relationships. 19.3-PFA5 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 19.4-PFA 1 Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 19.4-PFA5 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. 19.5-PFA 1 Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. 19.5-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs 19.5-PFA5 Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. Topic 19 * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 grid) 19.1 M2 Students are not asked to identify or compare paths. 19.1-19.3 G6. Students not asked to work with negative numbers. Introduce the Cartesian Grid (four-quadrant grid) 19.1 M2 Students are not asked to identify or compare paths. 19.1-19.3 G6. Students not asked to work with negative numbers. 12

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Polygons and Polyhedra Money and Time 20.1-M 6 Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. 20.2-20.3-20.4-G 8 Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net. 20.5-M 3 Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects. 20.5-G 8 Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net. 21.1 DAP 6 Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. 21.2- NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 21.3-21.4-M 5 Make conversions within the same measurement system while performing computations. 21.5-DAP 4 Determine appropriate data to be collected to answer questions posed by students or teacher, collected and display data, and clearly communicate findings. 21.5-M 5 Make conversions within the same measurement system while performing computations. Topic 20 Topic 21 <1 wk Complete the Daily Number Starter for this topic. 20.5 Connection needs to be made between surface area and volume; this lesson finds surface area but does not tie to meet the indicator. 21.3 N9 Be certain to complete Daily Number Sense Starter and the Maintaining Skills pages. 21.5 Students are not asked to determine appropriate data. * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 13

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Working with Division 22.1- NSO 13 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 22.2 22.3- PFA 4 Create and interpret the meaning of equations and inequalities representing problem situations. 22.4-PFA 4 Create and interpret the meaning of equations and inequalities representing problem situations. 22.5- NSO 1 Use models and visual representation to develop the concept of ratio as part-to-part and part-towhole, and the concept of percent as part-to-whole. Topic 22 <1 wk 22.1-2.5 Be certain to complete Daily Number Sense Starter and the Maintaining Skills pages. 22.2 Reviews 4 th grade indicator. 22.3-22.4 Inequalities need to be included. Exploring Percent 23.1- NSO 3 Identify and generate equivalent forms of fractions, decimals and percents. 23.2- NSO 3 Identify and generate equivalent forms of fractions, decimals and percents. 23.2-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs 23.3- NSO 3 Identify and generate equivalent forms of fractions, decimals and percents. 23.4 -NSO 13Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. 23.5-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs. Topic 23 * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 14

GWM Topic State Indicators-Lessons Lessons-Indicators: Grade Five Growing With Mathematics Pacing Assessment Comments Applying the Mathematics We Know 24.1-24.2 24.3 24.4-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs. 24.5-DAP 1 Read, construct and interpret frequency tables, circle graphs and line graphs. Topic 24 <1 wk Complete the Periodic Assessment for Topics 1-24. May not directly tie to content indicator, but does involve the mathematical processes. * This is the only lesson for this indicator NSO Number, Number Sense and Operations Standards PFA-Patterns, Functions and Algebra DAP-Data Analysis and Probability M Measurement G Geometry and Spatial Sense 4-17-07 15