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|4.1 Students will apply procedures of multiplication and division on whole numbers. |

|Big Ideas: |

|Multiplication and division both have groups of equal size as well as two factors and a multiple (e.g.  4 x 7 = 28 and 28 / 7 = 4) |

|Multiplication finds the total in all the groups (product); division finds the missing part when we know one factor and the product. |

|Essential Questions: |

|What is the same about multiplication and division? |

| How are multiplication and division different? |

|  |

|Key Vocabulary |Terms that May be Used: |

| |multiplication, product, division, quotient, divisor, remainder, multiple, factor |

|Key Concepts |Multiplication and division of whole numbers with fluency |

|What students need to know |Solve multiplication and division problems efficiently |

|Key Skills |Develop conceptual awareness of multiplication and division by building arrays, noting multiplication patterns, |

|What students need to be able to do: |using concrete representations, and understanding fact families. |

| |Multiply with fluency facts 0-10 (4.1.A) |

| |Divide with fluency facts 0-10 (4.1.A) |

| |Identify factors and multiples of a number (4.1.B) |

| |Solve single and multi-step word problems involving multiplication and division (with and without remainders); |

| |verify solutions (4.1.J and 4.1.I) |

|Related Standards |3rd grade standards: |

| |3.2.D: Apply and explain strategies to compute multiplication facts to 10x10 and the related division facts |

| |(including skip counting, double-doubles, think 10, and decomposition of arrays). |

| |3.2.E: Quickly recall those multiplication facts for which one factor is 1,2,5, or 10 and the related division |

| |facts. |

|Resources |Trailblazers Unit 3: Lesson 1 |

| |Trailblazers Unit 4: Lesson 1, 2, 3, 5, 6 |

| |Trailblazers Unit 6: Lesson 7 |

| |Trailblazers Unit 7: Lesson 2, 3, 4 |

| |See: S Drive for additional resources |

| |Daily Word Problems by Evan-Moor |

| |Van de Walle: pg. 88-93 (math facts) |

|4.1 Students will apply procedures of multiplication and division on whole numbers. |

|Big Ideas: |

|Multiplication and division both have groups of equal size as well as two factors and a multiple (e.g.  4 x 7 = 28 and 28 / 7 = 4) |

|Multiplication finds the total in all the groups (product); division finds the missing part when we know one factor and the product. |

|Between any two place values, the value is ten times bigger or smaller than the one next to it. (e.g. 1000 is ten times bigger than 100) |

|Essential Questions: |

|What is the same about multiplication and division? |

| How are multiplication and division different? |

| How does the base ten system apply to multiplication and division? |

|Key Vocabulary |Terms that May be Used: |

| |multiplication, product |

|Key Concepts |There are many ways to multiply 3 and 1 digit numbers. |

|What students need to know |Numbers can be multiplied by 10, 100, 1000. |

|Key Skills |Multiply a one-digit number by two and three digit numbers using the standard algorithm (part of 4.1.F) |

|What students need to be able to do: |Multiply by multiples of 10, 100, 1000 to extend place value concepts to large numbers through millions (4.1.D)|

| |Compare the values represented by digits in whole numbers using place value. Example : 4,000,000 is a 100 x |

| |more than 40,000 (4.1.E) |

| |Solve single and multi-step word problems involving multiplication and division (with and without remainders); |

| |verify solutions (4.1.I and 4.1.J) |

|Related Standards |4.4.A Equalities and Inequalities: |

| |Solve equations and inequalities using letters, boxes and other symbols |

| |Example: 5 x m = 40 or 5 x 8 > 5 x 4 |

| |Estimate products to find reasonable solutions to problems. Example 28 x 120 is approximately 30 x 100 which |

| |equals 3000 (4.1.H) |

|Resources |Trailblazers Unit 6 Lessons 4, 6 |

| |Trailblazers Unit 7 Lesson 4, 7 |

| |Trailblazers Unit 11 Lessons 1, 2, 3 |

| |Daily Word Problems – Evan Moor |

| |See S Drive for additional resources |

| |Van de Walle: 113-116, 118 |

|4.1 Students will apply procedures of multiplication and division on whole numbers. |

|Big Ideas: |

|Multiplication and division both have groups of equal size as well as two factors and a multiple (e.g.  4 x 7 = 28 and 28 / 7 = 4) |

|Multiplication finds the total in all the groups (product); division finds the missing part when we know one factor and the product. |

|Between any two place values, the value is ten times bigger or smaller than the one next to it. (e.g. 1000 is ten times bigger than 100) |

|Essential Questions: |

|What is the same about multiplication and division? |

| How are multiplication and division different? |

| How does the base ten system apply to multiplication and division? |

|Key Vocabulary |Terms that May be Used: |

| |multiplication, product, represent, array |

|Key Concepts |Solve multi-digit multiplication problems |

|What students need to know | |

|Key Skills |Represent multiplication of a two-digit number by a two-digit number with place value models (4.1.C) |

|What students need to be able to do: |Multiply a two digit number by a two and three digit number using the standard algorithm and other methods (part|

| |of 4.1.F) |

| |Estimate products to find reasonable solutions to problems. Example 28 x 120 is approximately 30 x 100 which |

| |equals 3000 (4.1.H) |

| |Solve single and multi-step word problems involving multiplication and division (with and without remainders); |

| |verify solutions (4.1.I and 4.1.J) |

|Related Standards | |

|Resources |Trailblazers Unit 6, lesson 7 |

| |Trailblazers Unit 11, Lesson 4, 5, 7 |

| |Daily Word Problems by Evan-Moor |

| |See S Drive for additional resources |

| |Van de Walle pg. 120 |

| |

|4.1 Students will apply procedures of multiplication and division on whole numbers. |

|Big Ideas: |

|Multiplication and division both have groups of equal size as well as two factors and a multiple (e.g.  4 x 7 = 28 and 28 / 7 = 4) |

|Multiplication finds the total in all the groups (product); division finds the missing part when we know one factor and the product. |

|Between any two place values, the value is ten times bigger or smaller than the one next to it. (e.g. 1000 is ten times bigger than 100) |

|Essential Questions: |

|What is the same about multiplication and division? |

| How are multiplication and division different? |

| How does the base ten system apply to multiplication and division? |

|Key Vocabulary |Terms that May be Used: |

| |multiplication, product, estimate, approximate, rounding |

|Key Concepts |Estimate multiplication problems |

|What students need to know | |

|Key Skills |Mentally multiply two digit numbers by numbers through 10 and by multiples of 10 (4.1.G). Examples: |

|What students need to be able to do: |4 x 32 = (4 x 30) + ( 4 x 2) |

| |4 x 99 = 400 – 4 |

| |25 x 30 = 75 x 10 |

| |Fluently and accurately multiply two digit number by a two and three digit number using the standard algorithm |

| |and other methods |

|Related Standards | |

|Resources |Trailblazers Unit 7 Lesson 6, 7 |

|4.3 Students will understand and apply systematic procedures to determine the area and perimeter of figures composed of rectangles. |

|Big Idea: Area is a measure of covering expressed in square units. |

|Area of a rectangle can be determined using multiplication. |

|There is a relationship between area and perimeter. |

|Essential Questions: What is area? |

|How do we find area? |

|How are area and perimeter related? |

|Key Vocabulary |Terms that May be Used: |

| |area, congruent, formula, perimeter |

| | |

| |Related vocabulary: Hexagon, pentagon, polygon, regular polygon |

|Key Concepts |Area |

|What students need to know |Perimeter |

|Key Skills |Determine the approximate area of a figure using square units (4.3.B) |

|What students need to be able to do: |Determine congruence of two- dimensional figures (4.3.A) |

| |Determine the areas of figures that can be broken down into rectangles (4.3.D) |

| |Determine the perimeter and area of rectangles using formulas (L x W and 2L + 2W) and explain why the formulas |

| |work (4.3.C) |

| |Demonstrate that rectangles with the same area can have different perimeters; and that rectangles with the same|

| |perimeter can have different areas (4.3.E) |

| |Solve single and multi-step word problems involving perimeters and areas of rectangles and verify the solutions|

| |(4.3.F) |

|Related Grade Level Expectations |Connections between multiplication and area should be emphasized whenever possible. |

|Resources |Trailblazers Unit 2 Lesson 1 |

| |Trailblazers Grade 3 Unit 5 |

| |Trailblazers Grade 5 Unit 15 lesson 1 |

| |Conceptual Unit on Area (created by NTPS) |

| |Using the Standards: Measurement, Grade 4 |

| |pgs. 26-30, 35- 40, 66-72, 74-79 |

| |See S Drive for additional resources |

| | |

|4.4 E Students will analyze and describe data |

|Big Idea: Data can be analyzed and organized in different ways. |

|Essential Questions: How do you analyze data? |

|Key Vocabulary |Terms that May be Used: |

| |line plots, pictographs, charts, bar graphs, median, mode, range, data |

|Key Concepts | |

|What students need to know |Median, mode and range can be used to analyze data |

| | |

|Key Skills |Read, interpret and explain data: line plots, pictographs, charts, frequency tables, and bar graphs |

|What students need to be able to do: |Summarize the data using median, mode and range (4.4.E) |

| |Determine median, mode, and range from a set of data (4.4.E) |

|Related Grade Level Expectations | |

|Resources |Trailblazers(for median, mode and range): Unit 1 Lesson 2, 3,5 |

| |Using the Standards Data and Probability, pgs 42-48, 54, 59, 60, 69 |

| |See grade 5 Using the Standards Data and Probability for additional resources |

| |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, Chapter 11 |

|4.4 B-C Students will understand how measurement units (including time) are converted. |

|Big Idea: Units are standard and relate to each other, therefore can be converted. |

|We use different units to measure different attributes. |

|Essential Questions: What are the standard units of measurement and how can they be converted? |

|The unit of measurement must match the attribute being measured. |

|Key Vocabulary |Terms that May be Used: |

| |Previously introduced: |

| |Time: second, minute, hour, day, week, month, year |

| |Weight: ounce, pound |

| |Capacity: cup, pint, quart, gallon |

| |Length: centimeter, meter |

| | |

| |New vocabulary: |

| |Length: millimeter, kilometer |

| |Capacity: milliliter, deciliter, liter, kiloliter |

| |Mass: milligram, gram, kilogram |

| | |

| |Abbreviations for all of the above |

|Key Concepts |Elapsed time |

|What students need to know |Standard units of measurement (metric and U.S. customary) |

|Key Skills |Estimate and determine elapsed time using a calendar, digital clock and analog clock (4.4.C) |

|What students need to be able to do: |Convert measurements within the U.S. system and metric system (capacity, length, weight). |

| |Solve single and multi-step problems involving unit conversions, including time, within the U.S. or metric |

| |system (4.4.B) |

|Related Standards |Students use ideas of multiplication and division as they do basic measurement conversions. |

|Resources |Daily Word Problems by Evan Moor |

| |Using the Standards: Measurement, Grade - pgs. 9-12, 14-25, 31-34, 42, 43, 46-48,51, 53, 54, 56, 57, 59, 62, |

| |64, 65, 88, 92, 93, 97, 98 |

| |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, pages 269 – 271 (telling |

| |time) |

| |See S: Drive for additional resources |

| | |

|4.4 F-H Students will understand when events are certain or impossible and more likely, less likely, or equally likely. |

|Big Idea: Probability can be used to predict outcomes. |

|Essential Questions: How can we predict and communicate the outcomes of events? |

|Why it is important to be able to predict outcomes of events? |

|Key Vocabulary |Terms that May be Used: |

| |Equally likely, impossible, less likely, likely, more likely, unlikely, certain |

| | |

|Key Concepts |Probability |

|What students need to know | |

|Key Skills | |

|What students need to be able to do: |Describe and compare the likelihood of events using the vocabulary of probability (4.4.F) |

| |Determine a simple probability from a context that includes pictures, spinners, coins, chips, marbles, or number|

| |cubes (4.4.G) |

| |Express probability as a number from 0 to 1 (4.4.G) |

| |Display the results of probability using tallies, frequency tables, graphs, pictures and fractions and interpret|

| |the results (4.4.H) |

|Related Standards | |

|Resources |Trailblazers Unit 14: Lesson 1, 2, 3, 4, 5 and 6 |

| |Using the Standards Data and Probability pages 80 – 84, 90-99 |

| |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, pages 339 - 347 |

| |See S: Drive for additional resources |

| | |

|4.4 D Students will apply understanding of the location of points on a coordinate grid in the first quadrant. |

|Big Idea: Ordered pairs (coordinates) specify locations on a coordinate grid. |

|Essential Questions: How are points graphed and identified on a coordinate grid? |

| |

|Key Vocabulary |Terms that May be Used: |

| |Coordinate, graph, grid, location, ordered pair, point, x-axis, y-axis, plot |

|Key Concepts |Coordinate Grid |

|What students need to know |Ordered Pair (coordinates) |

|Key Skills |Graph (plot) and identify points in the first quadrant using ordered pairs (coordinates) (4.4.D) |

|What students need to be able to do: |Use ordered pairs (coordinates) to identify or name the location of points or objects |

|Related Standards | |

|Resources |Trailblazers Grade 4 – Unit 1: Lesson 5 (DAB) |

| |Trailblazers Grade 3 – Unit 8: Lesson 2 , 3 |

| |Navigating Geometry by NCTM pg. 40, Xs and Os (with modification) |

| |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, page 239, “Location Activities” |

|4.2 Understand the concept of fractions and decimals and the relationship between them. |

|Big Ideas: |

|Fractions and decimals are different ways to show the same value. |

| Equivalent fractions, mixed numbers and improper fractions are all ways to show fractional amounts. |

| The decimal point divides the whole from the parts. The left of the decimal point begins counting as ones and between any two place values the value is ten |

|times bigger or smaller than the one next to it. (e.g.  1 is ten times bigger than 1/10) |

|Essential Questions: |

|What is the same about fractions and decimals? |

|How can fractions be represented in different ways? |

|How does the base ten system apply to decimals? |

|Key Vocabulary |Terms that May be Used: |

| |= < > denominator, numerator, equal to, even, fraction, greater than, tenths, hundredths, least,|

| |less than, number line, place value, whole number, round, compare, decimal |

|Key Concepts |Compare, represent, and convert fractions and decimals |

|What students need to know |Fractions and decimals are a part of a whole |

|Key Skills |Represent decimal through hundredths with place value models, fraction equivalents and a number line (4.2.A) |

|What students need to be able to do: |Read, write, compare and order decimals through hundredths (4.2.B) |

| |Convert a decimal to a fraction (and vice versa) and visually represent the number (4.2.D) |

| |Compare and order decimals and fractions on number lines, lists, and using symbols of equality and inequality |

| |(, =) (4.2.E) |

| |Round fractions and decimals to the nearest whole number (4.2.H) |

| |Solve single and multi-step word problems involving comparison of decimals and fractions and verify the |

| |solutions (4.2.I) |

|Related Standards | |

|Resources |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, Chapter 5: Developing Fraction |

| |Concepts |

| |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, Chapter 7: Decimal and Percents|

| |Concepts |

| |Trailblazers – Grade 4 Unit 12: Lesson 1, 3, 4, 5, 6, 7, 8 (2 optional) |

| |See: S Drive for additional resources |

|4.2 Understand the concept of fractions and decimals and the relationship between them |

|Big Ideas: |

|Fractions and decimals are different ways to show the same value. |

| Equivalent fractions, mixed numbers and improper fractions are all ways to show fractional amounts. |

| The decimal point divides the whole from the parts. The left of the decimal point begins counting as ones and between any two place values the value is ten |

|times bigger or smaller than the one next to it. (e.g.  1 is ten times bigger than 1/10) |

|Essential Questions: |

|What is the same about fractions and decimals? |

|How can fractions be represented in different ways? |

|How does the base ten system apply to decimals? |

|Key Vocabulary |Terms that May be Used: |

| |= < > denominator, numerator, equal to, even, fraction, greater than, greatest, least, less than, |

| |number line, common factors, compare, equivalent, mixed number, improper fraction, common denominator, simplify,|

| |lowest terms |

|Key Concepts |Compare, represent and convert fractions |

|What students need to know |Fractions can be represented in different ways (including mixed numbers and improper fractions). |

| |Fractions can be simplified |

|Key Skills |Convert a mixed number to a fraction (and vice versa) and visually represent the number (4.2.C) |

|What students need to be able to do: |Compare and order fractions (including mixed numbers and improper fractions) on number lines, lists, and with |

| |symbols of equality and inequality (, =) (4.2.E) |

| |Write a fraction equivalent to a given fraction (4.2.F) |

| |Simplify fractions using common factors 4.2.G) |

| |Solve single and multi-step word problems involving comparison of fractions (including mixed numbers and |

| |improper fractions) and verify the solutions (4.2.I) |

|Related Standards | |

|Resources |Teaching Student-Centered Mathematics Vol, 2, Grades 3-5, Van de Walle & Lovin, Chapter 5: Developing Fraction |

| |Concepts |

| |Trailblazers Unit 12: Lesson 1, 3, 4, 5, 6, 7, 8 (2 optional) |

| |See: S Drive for additional resources |

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