Unit | Timeframe | Big Ideas (Statements or Essential Questions) | Major Learning Experiences from Unit |
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1:Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10 | | Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10 In Module 1 students build on their knowledge of addition and arrays to connect repeated addition to multiplication. They begin to name the factors in multiplication as either the size of a group or the number of groups. WIth a foundation of multiplication, they relate this work to division. Students begin to apply the commutative and distributive properties of multiplication. Students use skip counting by factors of 2,3,4,5, and 10. Students discover the inverse relationship between multiplication and |
I can draw and interpret models of multiplication and division using equal-sized groups and arrays I can interpret the factors and products in multiplication using repeated addition of equal sized groups. I can distinguish between the number of groups and the size of groups in multiplication and division. I can give real-life examples of how to use multiplication and division to find the total number of objects in equal-sized groups/arrays. I can draw and interpret models of multiplication and division using arrays. I can interpret the factors and products in multiplication involving arrays. I can draw and interpret models of division using equal shares. I can understand the dividend (number of objects being divided) is the product of the number of groups and of how many in a group. I can use an equation to represent a division problem as a multiplication problem with an unknown factor. I can interpret the dividend and divisor of a division problem using equal shares or arrays. I can determine the unknown number in a multiplication or division equation relating three whole numbers. I can apply the commutative property of multiplication as strategies to multiply. I can apply the distributive property of multiplication as strategies to multiply and divide. I can use multiplication and division within 100 to solve word problems involving repeated addition of equal groups, arrays and measurement quantities, using symbols for unknown quantities. I can express multiplication and division problems using expressions and equations. I can use strategies to multiply and divide within 100
I can explain that multiplication and division are inverse operations. |
2:Place Value and Problem Solving with Units of Measure | | Place Value and Problem Solving with Units of Measure In this module students explore units of measure and further develop their estimation strategies. They use their understanding of place value and estimation to round to the nearest ten and hundred. They solve problems involving measurement units and use strategies based on place value to solve multi-digit addition and subtraction. | I can tell and write time to the nearest minute using both an analog and a digital clock. I can find and write fractions of an hour. I can measure time intervals in minutes. I can add and subtract time intervals in minutes I can fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations and/or the inverse relationship between addition and subtraction. I can measure and estimate liquid volumes of objects in liters. I can solve one-step word problems involving volume by drawing models and pictures. I can round to the nearest ten or hundred and use this as a tool for estimation
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3:Multiplication and Division with Units of 0, 1, 6-9, and Multiples of 10 | | Multiplication and Division with Units of 0, 1, 6-9, and Multiples of 10 Module 3 continues students on their journey toward fluency with multiplication and division within 100. Students revisit the commutative and distributive properties. There is emphasis on word problems involving unknowns in any position. In this module, students are introduced to the associative property and use it to make use of structure in word problems. Special consideration is given to working with factors 0 and 1 and how they relate to division.
| I can write and solve multiplication and division equations with an unknown to solve problems. I can use my knowledge of the relationship between multiplication and division to find unknowns in fact-family equations. I can demonstrate the Distributive Property of Multiplication using a rectangle by tiling, drawing a picture and writing the associated equations. I can demonstrate the Commutative Property of Multiplication using models and equations. I can explain the Associative Property of Multiplication using both pictures and equations. I can use mathematical properties as strategies to help me multiply and divide. I can use multiplication within 100 to solve word problems involving repeated addition of equal groups, arrays and measurement quantities, using symbols for unknown quantities. I can use division within 100 to solve word problems involving equal groups, equal shares, arrays and measurement quantities, using symbols for unknown quantities. I can solve 2 step problems using addition, subtraction, multiplication, and division. I can solve 2 step problems using a letter to represent unknown quantities. I can check the reasonableness of my answers to 2 step problems by using mental math strategies, including estimation and rounding.
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4:Multiplication and Area | | Multiplication and Area In this module students explore area as an attribute of 2-dimensional figures and relate it to their understanding of multiplication. | I understand and can explain meaning of the "area of a shape" I can draw and explain what a unit square is. I can explain the relationship between square units and area. I can tile a rectangle to find its area. I can find the area of a rectangle by multiplying the side lengths. I can explain how various methods for finding area (tiling, counting squares, multiplying side lengths) are related. I can draw rectangles with a given area on grid paper and label their side lengths. I can solve real-world problems involving the area of a rectangle. I can draw and interpret models of multiplication by partitioning the area of a rectangle. I can interpret the factors and products in multiplication by partitioning the area of a rectangle.
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5 | | Fractions as Numbers on the Number Line In this module students build on previous part/whole work as they explore area models and fractions on a number line. Students work with specified units of halves, thirds, fourths, sixths and eighths but are exposed to units of fifths, ninths and tenths. | I can interpret the parts of a fractional number using correct names and notations. I can combine unit fractions to create other fractional quantities. I can deconstruct fractional quantities into their unit fraction parts. I can represent a unit fraction using shapes by partitioning a whole into equal parts and recognizing each part as a unit fraction. I can express whole numbers as fractions and represent them using shapes. I can recognize, using models, that two fractions are equivalent when they are the same size. I can represent my fraction comparisons using >, = or < symbols and can justify my comparison using visual models. I can compare fractions based on common numerators or denominators by using strategies (such as visual models) to reason about their size. I can recognize, using models, that two fractions are equivalent when they are the same size. I can recognize, using a number line, that two fractions are equivalent when they are located at the same point on the number line. I can generate simple equivalent fractions and explain why they are equivalent using visual models. I can recognize fractions that are equivalent to whole numbers and locate them on the number line. I can express whole numbers as fractions and represent them using shapes. I can express whole numbers as fractions and locate them on the number line. I can explain why it is necessary to have fractions refer to the same sized whole when comparing them by using visual models.
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6: Collecting and Displaying Data | | Collecting and Displaying Data This 10-day module builds on Grade 2 concepts about data, graphing, and line plots. The two topics in this module focus on generating and analyzing categorical and measurement data. By the end of the module, students are working with a mixture of scaled picture graphs, bar graphs, and line plots to problem solve using both categorical and measurement data. | I can draw scaled picture graphs to represent data in several categories. I can determine an appropriate value for the scale of my picture graph and accurately display the values in the graph key. I can use picture graphs to solve one- and two- step problems about data. I can draw bar graphs to represent data in several categories. I can determine an appropriate value for the scale of my bar graph, and accurately display the values in the graph key. I can solve one- and two-step "how many more" and "how many less" problems using the information presented in a scaled bar graph. I can write one- and two-step "how many more" and "how many less" problems using the information presented in a scaled bar graph. I can generate measurement data by measuring lengths using rulers marked with whole inches. I can generate measurement data by measuring lengths using rulers marked with halves of an inch. I can generate measurement data by measuring lengths using rulers marked with fourths of an inch.
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7: Geometry and Measurement Word Problems | | Geometry and Measurement Word Problems This 40-day final module of the year offers students intensive practice with word problems, as well as hands-on investigation experiences with geometry and perimeter. The module begins with solving one- and two-step word problems based on a variety of topics studied throughout the year, using all four operations. Next, students explore geometry. Students tessellate to bridge geometry experience with the study of perimeter. Line plots, familiar from Module 6, help students draw conclusions about perimeter and area measurements. Students solve word problems involving area and perimeter using all four operations. The module concludes with a set of engaging lessons that briefly review the fundamental Grade 3 concepts of fractions, multiplication, and division. | I can solve 2 step problems using addition, subtraction, multiplication, and division. I can solve 2 step problems using a letter to represent unknown quantities. I can check the reasonableness of my answers to 2 step problems by using mental math strategies, including estimation and rounding. I can sort and describe categories of shapes by their attributes. I can describe, draw and identify categories of quadrilaterals by their sides and angles, including rhombuses, rectangles and squares and also draw quadrilaterals that are not rhombuses, rectangles or squares. I can describe and draw triangles. I can find the perimeter of a polygon given its side-lengths. I can use my knowledge of polygons and perimeter to find unknown side-lengths. I can solve real-world and mathematical problems involving perimeter of polygons. I can generate measurement data by measuring lengths using rulers marked with whole inches. I can generate measurement data by measuring lengths using rulers marked with halves of an inch. I can generate measurement data by measuring lengths using rulers marked with fourths of an inch. I can solve 2 step problems using addition, subtraction, multiplication, and division. I can solve 2 step problems using a letter to represent unknown quantities. I can check the reasonableness of my answers to 2 step problems by using mental math strategies, including estimation and rounding.
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