Unit | Timeframe | Big Ideas (Statements or Essential Questions) | Major Learning Experiences from Unit |
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1 | 25 | In Module 1, students extend their work with whole numbers. They begin with large numbers using familiar units (hundreds and thousands) and develop their understanding of millions by building knowledge of the pattern of times ten in the base ten system on the place value chart. They recognize that each sequence of three digits is read as hundreds, tens, and ones followed by the naming of the corresponding base thousand unit (thousand, million, billion). | Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. I can read and write multi-digit whole numbers using base-ten numerals. I can read and write multi-digit whole numbers using number names. I can read and write multi-digit whole numbers in expanded form (ie 235 = 200 + 30 +5 and 2x100+ 3x10 + 5x1). Recognize that 10 tens is 100, 10 hundreds is 1,000 so forth up to 1,000,000. I can apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10. I can compare two multi-digit numbers based on the meaning of the digits in each place. I can use the symbols <, >, and = to compare two multi-digit numbers. I can round multi-digit whole numbers to any place (with specific attention to thousands, ten thousands, hundred thousands, and millions places as these are new in Grade 4.) I can assess the reasonableness of answers to a multi-step real-world problem using the four operations using estimation strategies including rounding. I can use regrouping when adding multi-digit whole numbers. I can fluently add multi-digit whole numbers using the standard algorithm to sums less than or equal to 1,000,000. I can use regrouping when subtracting multi-digit whole numbers. I can fluently subtract multi-digit whole numbers using the standard algorithm (with the number that is to be subtracted less than or equal to 1,000,000. I can solve multi-step real-world problems using the four operations. I can assess the reasonableness of answers to a multi-step real-world problem using the four operations using mental computation.
| 2 | 7 | Module 2 uses length, mass and capacity in the metric system to convert between units using place value knowledge. Students recognize patterns of converting units on the place value chart, just as 1000 grams is equal 1 kilogram, 1000 ones is equal to 1 thousand. Conversions are recorded in two-column tables and number lines, and are applied in single- and multi-step word problems solved by the addition and subtraction algorithm or a special strategy. Mixed unit practice prepares students for multi-digit operations and manipulating fractional units in future modules. | I can use the four operations to solve word problems involving measurement, including conversion from a larger unit to a smaller unit. I can explain the relationship between kilometers, meters and centimeters, and provide examples of when to use each unit of measure. I can explain the relationship between kilograms and grams and provide examples of when to use each unit of measure. I can explain the relationship between milliliters and liters and provide examples of when to use each unit of measure. I can record equivalent measurements in a two-column table (t-chart) between two sizes of measurement units within the same system of units. I can represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. I can convert between measures, within the same system of measurement (i.e., kilograms to grams). I can use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money.
| 3 | 43 | In Module 3, students use place value understanding and visual representations to solve multiplication and division problems with multi-digit numbers. As a key area of focus for Grade 4, this module moves slowly but comprehensively to develop students’ ability to reason about the methods and models chosen to solve problems with multi-digit factors and dividends. | I can apply the area formula for rectangles in real-world and mathematical problems. I can apply the perimeter formula for rectangles in real-world and mathematical problems. I can provide a verbal statement of multiplicative comparison for a given multiplication equation. I can use multiplication to solve word problems that involve the use of drawings to represent multiplicative comparisons. I can use multiplication to solve word problems that involve equations with symbols to represent unknown numbers in a multiplicative comparison. I can use multiplication to solve word problems involving multiplicative comparisons using drawings. I can apply concepts of place value to recognize quotients and products in multiplication and division problems involving whole numbers and a factor of 10. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. I can multiply whole numbers up to four-digit by one-digit and two digit by two digit using strategies based on properties of operations, in particular the distributive property, and explain its connection to the area model. I can multiply whole numbers up to four-digits by one-digits and two-digit by two-digit using partial products. I can Illustrate and explain multiplication of whole numbers up to four-digit by one-digit and two digit by two digit using area models. I can solve multi-step real-world problems using the four operations in situations where a remainder must be interpreted. I can illustrate and explain division of whole numbers (with and without remainders) with up to four-digit dividends and one-digit divisors using rectangular arrays. I can illustrate and explain division of whole numbers (with and without remainders) with up to four-digit dividends and one-digit divisors using area models. I can find whole number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on place value (e.g. the relationship between 42 ÷ 6 and 420 ÷ 6). I can find whole-number quotients and remainders with up to 4-digit dividends and 1-digit divisors using partial quotients. I can find whole-number quotients and remainders with up to 4-digit dividends and 1-digit divisors using strategies based on mathematical properties of operations and decomposition by place value. I can find whole number quotients and remainders with up to four-digit dividends and one-digit divisors using strategies based on the relationship between multiplication and division. I can find all factor pairs of a whole number within 100. I can understand the meaning of the term multiple. I can determine whether a whole number within 100 is a multiple of a given one-digit number. I can determine whether a whole number within 100 is prime or composite. I can illustrate and explain division of whole numbers (with and without remainders) with up to four-digit dividends and one-digit divisors using equations.
| 4 | 20 | This module introduces points, lines, line segments, rays, and angles, as well as the relationships between them. Students construct, recognize, and define these geometric objects before using their new knowledge and understanding to classify figures and solve problems. With angle measure playing a key role in the work throughout the module, students learn how to create and measure angles, as well as how to create and solve equations to find unknown angle measures. In these problems, where the unknown angle is represented by a letter, students explore both measuring the unknown angle with a protractor and reasoning through the solving of an equation. This connection between the measurement tool and the numerical work lays an important foundation for success with middle-school geometry and algebra. Through decomposition and composition activities, as well as an exploration of symmetry, students recognize specific attributes present in two-dimensional figures. They further develop their understanding of these attributes as they classify two-dimensional figures. | I can draw and define a line and identify a line in two-dimensional figures. I can draw and define a line segment and identify a line segment in two-dimensional figures. I can draw and define a ray and identify a ray in two-dimensional figures. I can understand that angles are formed when two rays share an endpoint. I can draw and define an angle (right, acute, obtuse) and identify an angle in two-dimensional figures. I can draw and define perpendicular and parallel lines and identify perpendicular and parallel lines in two-dimensional figures. I can understand that angles are formed when two rays share an endpoint. I can understand that an angle that turns through 1/360 of a circle is called a "one degree angle". I can understand that an angle is measured with reference to a circle by considering the fraction of the circular arc between the points where the two rays intersect the circle. I can sketch angles of a specified measure using a protractor. I can measure angles in whole number degrees using a protractor. I can recognize angle measure as additive. I can solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. I can represent addition and subtraction problems to find unknown angles on a diagram using an equation with a symbol for the unknown angle measure. I can recognize lines of symmetry in 2-D figures. I can draw lines of symmetry in 2-D figures. I can understand that a line of symmetry in a 2-D figure represents the line across the figure such that the figure can be folded along the line into matching parts. I can recognize and identify right triangles. I can classify 2-D figures based on the presence or absence of parallel lines. I can classify 2-D figures based on the presence or absence of perpendicular lines. I can classify 2-D figures based on the presence or absence of angles of a specified size.
| 5 | 45 | Students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers. This leads to the comparison of fractions and mixed numbers and the representation of both in a variety of models. Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes. Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations. | I can justify decomposition of fractions using a visual model. I can decompose a fraction into a sum of fractions with the same denominator in more than one way. I can record decomposition of fractions as an equation. I can show that any fraction is a multiple of its unit fraction, using a visual fraction model. I can use an understanding of a/b as a multiple of 1/b to multiply a fraction by a whole number, using visual models and expressions. I can show that any fraction is a multiple of its unit fraction, using an equation. I can understand a multiple of a/b as a multiple of 1/b. I can use an understanding of a/b as a multiple of 1/b to multiply a fraction by a whole number, using visual models and expressions. I can explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) using visual fraction models. I can show how the numbers and sizes of the parts differ, when I multiply the numerator and denominator of a fraction by the same number, even though the two fractions are the same size. I can recognize equivalent fractions using the principle a / b = (n x a)/(n x b) including fractions greater than 1. I can compare two fractions with different numerators and different denominators by comparing to a benchmark fraction such as 1/2. I can compare two fractions with different numerators and different denominators by creating common numerators or common denominators. I can use the symbols >, =, < to record the results of my fraction comparisons. I can justify comparison of fractions with different numerators and different denominators, example: by using a visual fraction model. I can recognize that comparisons of fractions are valid only when the two fractions refer to the same whole. I can understand addition of fractions as joining parts referring to the same whole. The whole can be a set of objects. I can understand subtraction of fractions as separating parts referring to the same whole. The whole can be a set of objects. I can solve word problems involving addition of fractions referring to the same whole and having like denominators. I can solve word problems involving subtraction of fractions referring to the same whole and having like denominators. I can use visual fraction models to solve word problems involving addition of fractions referring to the same whole. I can use visual fraction models to solve word problems involving subtraction of fractions referring to the same whole. I can use equations to solve word problems involving addition of fractions referring to the same whole. I can use equations to solve word problems involving subtraction of fractions referring to the same whole. I can add mixed numbers with like denominators by replacing each mixed number with an equivalent fraction. I can add mixed numbers with like denominators by using properties of operations. I can add mixed numbers with like denominators by using the relationship between addition and subtraction. I can subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction. I can subtract mixed numbers with like denominators by using properties of operations. I can subtract numbers with like denominators by using the relationship between addition and subtraction. I can solve word problems involving multiplication of a fraction by a whole number. I can represent and solve word problems involving multiplication of a fraction by a whole number with visual models. I can represent and solve word problems involving multiplication of a fraction by a whole number with equations.
| 6 | 20 | Students explore decimal numbers through their relationship with decimal fractions. They express numbers in both decimal and fraction forms. Students extend their understanding of fractions built in Module 5 to decimals. | I can use decimal notation for fractions with a denominator of 10. I can locate decimals on a number line. I can express a fraction with a denominator 10 as an equivalent fraction with a denominator 100. I can use decimal notation for fractions with a denominator of 100. I can explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) using visual fraction models. I can show how the numbers and sizes of the parts differ, when I multiply the numerator and denominator of a fraction by the same number, even though the two fractions are the same size. I can recognize equivalent fractions using the principle a / b = (n x a)/(n x b) including fractions greater than 1. I can understand that comparison of two decimals can only occur when the decimals refer to the same whole. I can compare two decimals to the hundredths place. I can justify the comparison of two decimals to the hundredths place (such as with a visual model). I can add two fractions with respective denominators 10 and 100 by expressing a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100. I can use the four operations to solve word problems involving measurement, including simple fractions or decimals. I can use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money.
| 7 | 20 | Students build their competencies in measurement as they relate multiplication to the conversion of measurement units. Throughout the module, students will explore multiple strategies for solving measurement problems involving unit conversion. | I can record equivalent measurements in a two-column table (t-chart) between two sizes of measurement units within the same system of units. I can explain the relationship between feet and inches and provide examples of when to use each unit of measure. I can explain the relationship between pounds and ounces and provide examples of when to use each unit of measure. I can convert between measures, within the same system of measurement (i.e., kilograms to grams). I can use the four operations to solve word problems involving measurement, including conversion from a larger unit to a smaller unit. I can use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money. I can use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money. I can use the four operations to solve word problems involving measurement, including conversion from a larger unit to a smaller unit. I can convert between measures, within the same system of measurement (i.e., kilograms to grams). I can use the four operations to solve word problems involving measurement, including conversion from a larger unit to a smaller unit. I can use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, or money. I can use the area formula for rectangles in real-world and mathematical problems. I can use the perimeter formula for rectangles in real-world and mathematical problems
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