Curriculum Map: Grade 4 Math Course: Math 4 Sub-topic: General Grade(s): None specified Unit: Creating a Community of Mathematical Thinkers Timeline: Week 1 The purpose of the Establishing a Community of Mathematical Thinkers Module is to launch the important mathematical processes and practices that will support the growth and independence of our students as mathematical thinkers in a learning community. what big ideas) as a result "Students will understand Mathematical thinkers effectively use their understanding, knowledge and skills. Mathematical thinkers learn through collaboration and problem solving. I can attack a math problem and solve it (MP1) I can make sense of a problem (MP2) I can prove my answer (MP3) I can assist others when I do not agree with their answer (MP3) I can use the appropriate vocabulary and symbols to represent a problem or solution (MP4) I can use math tools to help me solve/show how I solved a problem (MP5) I can explain the steps I used to solve a problem, and I am careful in my calculations (MP6) I can use what I already know to help me solve a new problem (MP7) I can use multiple ways to find a solution to a problem (MP8) Why problem solve (or why think mathematically)? How does participation in a community of learners support thinking and learning? How do structures, strategies, and routines in problem solving support thinking and learning? How does productive mathematical thinking support critical thinking, growth and independenc Page 1 of 11
Unit: Unit 1 Multiplicative Thinking Timeline: Week 2 to 6 The purpose of this learning unit is for students to interpret multiplication equations as comparisons, with an emphasis on algebraic thinking and making generalizations about number relationships. what big ideas) as a result "Students will understand Numbers can be represented and compared in many ways. In what ways can products and quotients be interpreted? Computations involve taking apart and combining numbers using a variety of approaches. Numbers can be classified by attributes. How can numbers be identified through multiplication? In what ways can numbers be composed and decomposed? I can develop and apply number theory concepts to represent and solve problems including the four operations. I can interpret products of whole numbers. I can solve multiplication story problems with products to 100 involving situations of equal groups. I can solve for the unknown in a multiplication equation involving 3 whole numbers. I can multiply using the commutative and distributive properties. I can solve division problems by finding an unknown factor (i.e. solve 32/8 by finding that number that makes 32 when multiplied by 8) I can fluently multiply with products to 100 using strategies. I can explain patterns among basic multiplication facts by referring to properties of the operation I can multiply whole numbers from 1-9 by multiples of 10 from 10-90 using strategies based on place value and properties of operations. I can demonstrate that the area of a rectangle with whole-number side lengths can be found by multiplying the side lengths. I can represent the product of two numbers as the area of a rectangle with side lengths equal to those two numbers. I can use the area model for multiplication to illustrate the distributive property. I can find the area of a figure that can be decomposed into non-overlapping rectangles. I can make a comparison statement to match a multiplication equation. I can write a multiplication equation to represent a verbal statement of a multiplicative comparison. I can solve story problems involving a multiplicative comparison using multiplication or division. I can solve multi-step story problems involving only whole numbers, using addition, multiplication, and division. I can find all factor pairs for a whole number between 1 and 100. I can demonstrate an understanding that a whole number is a multiple of each of its factors. I can determine whether a whole number between 1 and 100 is a multiple of a given 1-digit number. I can determine whether a whole number between 1 and 100 is prime or composite. CC.2.1.4.B.2 (Focus) Use place-value understanding and properties of operations to perform multi-digit arithmetic. CC.2.2.4.A.1 (Focus) Represent and solve problems involving the four operations. CC.2.2.4.A.2 (Focus) Develop and/or apply number theory concepts to find factors and multiples. CC.2.4.4.A.1 (Practiced) Solve problems involving measurement and conversions from a larger unit to a smaller unit. Page 2 of 11
Unit: Unit 2 Multi-Digit Multiplication and Early Division Timeline: Week 7 to 11 The purpose of this learning unit is to build multiplicative reasoning with an emphasis on multi digit multiplication and early division with remainders, and apply number sense to develop models and strategies to become more efficient with this practice. what big ideas) as a result "Students will understand Multiplicative reasoning is about understanding which operation is appropriate. Strategies play an important role in computation What helps determine whether to use multiplication or division in a problem? How does place value effect computation? How are the properties useful when solving problems? How does multiplication help identify attributes of numbers? I can solve for the unknown in a multiplication or division equation involving 3 whole numbers. I can multiply using the commutative and associative property. I can fluently divide with dividends to 100 with strategies. I can solve story problems involving money using addition, multiplication, and division of whole numbers. I can solve multi-step story problems involving only whole numbers, using addition, subtraction multiplication and division. I can solve multi-step story problems involving only whole numbers, using multiplication. I can demonstrate an understanding that a whole number is a multiple of each of its factor. I can determine whether a whole number between 1 and 100 is prime or composite. I can solve single step story problems involving division with remainders. I can demonstrate an understanding that a multi-digit number, each digit represents ten times what it represents the place to its right. I can multiply a 2- or 3- digit whole number by a 1-digit whole number using strategies based on place value and the properties of operations. I can multiply two 2-digit numbers using strategies based on place value and the properties of operations. I can use equations or rectangular arrays to explain strategies for multiplying with multi-digit numbers. I can divide a 2-digit number by a 1-digit number, with a remainder, using strategies based on place value, the properties of operations or the relationship between multiplication and division. I can use a rectangular array to explain strategies for dividing a multi-digit number by a 1-digit number. I can apply the area formula for a rectangle to solve a problem. I can make comparison statements to match a multiplication equation. I can solve story problems involving a multiplication comparison using multiplication or division. CC.2.1.4.B.2 (Mastered) Use place-value understanding and properties of operations to perform multi-digit arithmetic. Page 3 of 11
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Unit: Unit 3 Fractions and Decimals Timeline: Week 12 to 16 The purpose of this Learning unit is for students to develop an understanding of fractions and decimals with an emphasis on an applied and visual approach to their relationship. what big ideas) as a result "Students will understand Proportional reasoning helps understand fractions. Fractions and decimals express a relationship between two numbers. How are fractions used in real life? How are fractions and decimals similar and different? Fractions and decimals are both parts of a whole. I can recognize equivalent fractions I can generate a fraction equivalent to fraction a/b by multiplying the numerator (a) and the denominator (b) by the same number I can compare two fractions with different numerators and different denominators using symbols >,=, and <. I can explain why one fraction must be greater than or less than another fraction. I can demonstrate an understanding that a comparison of fractions is valid only when they refer to the same whole. I can write an equation showing a fraction a/b as the sum of a number of the unit fraction 1/b. I can explain addition of fractions as joining parts referring to the same whole. I can express a fraction as the sum of other fractions with the same denominator in more than one way. I can add and subtract fractions and mixed numbers with like denominators. I can solve story problems involving addition and subtraction of fractions and mixed numbers referring to the same whole and with like denominators. I can express a fraction with denominator 10 as equivalent fraction with denominator 100. I can add a fraction with denominator 10 to a fraction with denominator 100 by rewriting the first fraction as an equivalent fraction with denominator 100. I can represent decimal numbers with digits to the hundredths place using place value models. I can write fractions with denominator 10 or 100 in decimal notation. I can compare two decimal numbers with digits to the hundredths place using the symbols >, =, and < to record the comparison. CC.2.1.4.C.1 (Focus) Extend the understanding of fractions to show equivalence and ordering. CC.2.1.4.C.2 (Focus) Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. CC.2.1.4.C.3 (Focus) Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). CC.2.4.4.A.1 (Practiced) Solve problems involving measurement and conversions from a larger unit to a smaller unit. Page 5 of 11
Unit: Unit 4 Addition, Subtraction, Measurement Timeline: Week 17 to 21 The purpose of this learning unit is to investigate strategies used in addition and subtraction by critically thinking about which strategy would be most efficient based on the numbers with an emphasis on the traditional algorithm. what big ideas) as a result "Students will understand The relationship among the operations and their properties promote computational fluency. Numeric fluency includes both the understanding of and the ability to appropriately use numbers. What we measure affects how we measure it. How and when can numbers be manipulated for application purposes? How do I know which mathematical operation and strategy to use? What makes a computation strategy both effective and efficient? How does measurement help describe our world using numbers? I can solve multi-step story problems involving only whole numbers using addition, subtraction, multiplication, and division. I can demonstrate an understanding that in a multi-digit number, each digit represents ten times what it represents in the place to its right. I can read and write multi-digit whole numbers represented with base ten numerals, number names, and expanded form. I can compare pairs of multi-digit numbers using the symbols <, >, and = to record comparisons. I can round multi-digit whole numbers to the nearest hundred, thousand, and ten thousand. I can fluently add and subtract multi-digit whole numbers, using an algorithm or another strategy. I can use the standard algorithm with fluency to add and subtract multi=digit whole numbers. I can identify the relative sizes of a centimeters, meters, and kilometers. I can identify the relative size of grams and kilograms. I can identify the relative size of ounces and pounds. I can identify the relative size of milliliters and liters. I can identify the relative size of seconds, minutes, and hours. I can express a measurement in a larger unit in terms of a smaller unit within the same system of measurement. I can record equivalent measurements in different units from the same system of measurement using a 2-column table. I can solve story problems involving distance and time using addition and subtraction of whole numbers. I can solve story problems involving distance and time using addition and subtraction of whole numbers. I can solve story problems involving liquid volume and mass using addition, subtraction, multiplication, and division of whole numbers. I can solve story problems that involve expressing measurements given in a larger unit in terms of a smaller unit within the same system of measurement. I can use a diagram to represent measurement quantities. Page 6 of 11
CC.2.1.4.B.2 (Focus) Use place-value understanding and properties of operations to perform multi-digit arithmetic. CC.2.2.4.A.1 (Focus) Represent and solve problems involving the four operations. CC.2.4.4.A.1 (Practiced) Solve problems involving measurement and conversions from a larger unit to a smaller unit. CC.2.4.4.A.2 (Practiced) Translate information from one type of data display to another. Page 7 of 11
Unit: Unit 5 Geometry & Measurement Timeline: Week 22 to 26 The purpose of this learning unit is to introduce geometric concepts including analyzing, classifying, measuring, and comparing with an emphasis on angles. The purpose also addresses geometric measurement which includes area and perimeter. what big ideas) as a result "Students will understand Points, lines, and angles are the foundation of geometry Geometry helps build logic, reasoning and problem solving. How does geometric relationships help solve problems? How can attributes help identify shapes? I can identify an angle as a geometric figure formed where two rays share a common endpoint I can measure angles by identifying the fraction of the circular arc between the points where the two rays forming the angle intersect the circle whose center is at the end points of those rays I can use a protractor to measure angles in whole degrees I can sketch an angle of a specified measure I can decompose an angle into non-overlapping parts I can express the measure of an angle as the sum of the angle measures of the non-overlapping parts into which it has been decomposed. I can solve problems involving find the unknown angle in a diagram, using addition and subtraction I can demonstrate an understanding that angle measure is additive I can identify points, lines, line segments, rays, and angles (right, acute, obtuse), parallel lines, and perpendicular lines in 2-D figures I can draw angles (right, acute, and obtuse), parallel lines and perpendicular lines. I can classify 2-D figures based on the presence of absence of parallel lines, perpendicular lines, and angles of a specified size I can identify right triangles. I can identify and draw lines of symmetry. I can identify figures with line symmetry I can apply the area and perimeter formulas for rectangles to solve problems. I can identify the measure of an angle by identifying the total number of one-degree angles through which it turns CC.2.3.4.A.1 (Focus) Draw lines and angles and identify these in two-dimensional figures. CC.2.3.4.A.2 (Focus) Classify two-dimensional figures by properties of their lines and angles. CC.2.3.4.A.3 (Focus) Recognize symmetric shapes and draw lines of symmetry. CC.2.4.4.A.1 (Practiced) Solve problems involving measurement and conversions from a larger unit to a smaller unit. CC.2.4.4.A.6 (Focus) Measure angles and use properties of adjacent angles to solve problems. Page 8 of 11
Unit: Unit 6 Multiplication & Division, Data and Fractions Timeline: Week 28 to 32 The purpose of this learning unit is to deepen the understanding and connection between multiplication and division with an emphasis on using strategies based on the relationship between multiplication and division as well as, place value and the properties of operations. This kind of algebraic thinking and reasoning helps students reason in a logical and orderly manner. what big ideas) as a result "Students will understand One representation may sometimes be more helpful than another. What helps determine which operation and strategy is appropriate for solving real world problems? Strategies play an important role in computation. Relationships among operations are essential for computing fluently. I can solve single step story problems involving division with remainders. I can solve multi-step story problems involving only whole numbers, using addition, multiplication and division. I can find all factor pairs for a whole number between 1 and 100. I can demonstrate an understanding that a whole number is a multiple of each of its factor, and determine whether a whole number between 1 and 100 is a multiple of a given 1 digit number. I can use the standard algorithm with fluency to add and subtract multi digit whole numbers. I can multiply a 2 or 3 digit whole number by a 1 digit whole number using strategies based on place value and the properties of operations. I can multiply two 2 digit numbers using strategies based on place value and the properties of operations. I can use equations or rectangular arrays to explain strategies for multiplying with multi-digit numbers. I can divide a 2 or 3 digit, using strategies based on place value, the properties of operations, or relationships between multiplication and division. I can divide a 2, 3, or 4 digit number by a 1 digit number, with or without a remainder, using strategies based on place value, the properties of operations, or the relationship between multiplication and division. I can use equations or rectangular arrays to explain strategies for dividing a multi-digit number by a 1 digit number. I can recognize and generate equivalent fractions. I can use a visual model to explain why a fraction a/b is equivalent to a fraction (n x a)(n x b) I can apply the area formula for a rectangle to solve a problem. I can apply the perimeter formula for a rectangle to solve a problem. I can make a line plot to display a data set comprising measurements take in halves, fourths, and eighths of a unit. CC.2.1.4.B.2 (Focus) Use place-value understanding and properties of operations to perform multi-digit arithmetic. CC.2.2.4.A.1 (Focus) Represent and solve problems involving the four operations. CC.2.4.4.A.1 (Focus) Solve problems involving measurement and conversions from a larger unit to a smaller unit. CC.2.4.4.A.2 (Practiced) Translate information from one type of data display to another. CC.2.4.4.A.4 (Practiced) Represent and interpret data involving fractions using information provided in a line plot. Page 9 of 11
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Unit: Unit 7 Reviewing and Extending Fractions, Decimals & Multi-digit Multiplication Timeline: Week 33 to 37 The purpose of this learning unit is to extend skills and concepts like recognizing and generating equivalent fractions, as well as comparing fractions with unlike denominators using visual models, benchmarks, and common denominators. Students review the strategies they have developed for multi-digit multiplication and practice the standard algorithm. what big ideas) as a result "Students will understand There are multiple representations for any number. Computational fluency includes understanding not only the meaning, but also the appropriate use of numerical operations. What effect do operations have on the relationship of numbers? How can numbers in different forms be compared or computed? I can multiply a whole number of up to four digits by a one digit whole number and multiply 2 two-digit numbers. M04.A-T.2.1.2 I can recognize and generate equivalent fractions M04.A-F.1.1.1. I can add and subtract fractions with unlike denominators. I can use equivalent fractions to add and subtract fractions with unlike denominators. I can compare fractions with unlike denominators. I can represent, compare, order, and add decimal fractions with denominators 10 and 100. CC.2.1.4.B.2 (Practiced) Use place-value understanding and properties of operations to perform multi-digit arithmetic. CC.2.1.4.C.1 (Practiced) Extend the understanding of fractions to show equivalence and ordering. CC.2.1.4.C.2 (Practiced) Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. CC.2.1.4.C.3 (Practiced) Connect decimal notation to fractions, and compare decimal fractions (base 10 denominator, e.g., 19/100). CC.2.2.4.A.1 (Practiced) Represent and solve problems involving the four operations. Page 11 of 11