Unit: Operations and Algebraic Thinking

Transcription

1 Unit: Operations and Algebraic Thinking Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of addition to, taking from, putting together, taking apart and comparing, with unknowns in all positions, e.g. by using drawing and equations with a symbol for the unknown number to represent the problem. Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols. i Use concrete, pictorial, and verbal representaions to develop an understanding of invented and conventional symbolic notations. i Connect number words and numerals to the quantities they represent, using various physical models and representations. Develop and use strategies for wholenumber computations, with a focus on addition and subtraction. i Build new mathematical knowledge through problem solving. Solve problems that arise in mathematics and in other contexts. Apply and adapt a variety of appropriate astrategies to solve problems. Monitor and reflect on the process of mathematical problem solving. Recognize reasoning and proof as fundamental aspects fo mathematics. i Make and investigate mathematical conjectures. i Develop and evaluate mathematical arguments and proofs. i Select and use various types of reasoning and methods of proof. i

2 Unit: Operations and Algebragic Thinking Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of addition to, taking from, putting together, taking apart and comparing, with unknowns in all positions, e.g. by using drawing and equations with a symbol for the unknown number to represent the problem. Create and use representations to organize, record, and communicate mathematical ideas. ii Select, apply, and translate among mathematical representations to solve problems. ii Use representations to model and interpret physicak, social and mathematical phenomena. ii Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers. 2.2 Fluently add and subtract within20 using mental strategies. By the end of Grade 2 know from memory all sums of two one-digit numbers. Develop fluency with basic number cominations for additon and subtraction. i 2.3 Determine whether a group of objects (up to 20) has an odd or even number of member; wirte an equation to express and even number as a sum of two equal addends. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers. Recognize, describe, and extend patters such as sequences fo sounds and shapes or simple numeric patterns and translate i from one representation to another. Analyze how both repeating and growing patters are generated. i 2.4 Use addition to find a total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.

3 Unit: Numbers and Operations in Base Ten Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. Count with understandin and recognize "how many" in sets of objects. Use multiple models to develop initial understandings of place value and the base-ten number system. 2.2 Count within 1000; skip count by 5's, 10's, and 100's. Count with understandin and recognize "how many" in sets of objects. Use multiple models to develop initial understandings of place value and the base-ten number system. Connect number words and numerals to the quantities they represent, using various physical models and representations. 2.3 Read and write numbers to 1000 using base ten numerals, number names, and expanded form. Connect number words and numerals to the quantities they represent, using various physical models and representations. 2.4 Compare two three-digit numbers based on meanings of hundreds, tens, and ones digits, using <, =, > symbols to record the results of comparisions. Connect number words and numerals to the quantities they represent, using various physical models and representations. 2.5 Fluently add and subtract within 100 using strategies based on place value, propreties of operations, and/or the relationship between addition and subtraction. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations. Understand the effects of adding and subtracting whole numbers. 2.6 Add up to four two-digit numbers using strategies based on place vale and properties of operations. Measure the perimeter of quadralaterals with sides that measure in 2-digit numbers. Expressions; Unit 5 L Add and subtract within 1000 using concrete models or drawings and stategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the Understand the effects of adding and strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundrends, tens and tens, ones and ones;and sometimes it is necessary to subtracting whole numbers. compose or decompose tens and hundreds. 2.8 Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a giving number Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and caculators. i

4 Unit: Numbers and Operations in Base Ten 2.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. i Use the language of mathematics to express mathematical ideas precisely. i

5 Unit: Measurement & Data Measure the length of an object by selecting and using appropiate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Understand how to measure using nonstandard and standard units. Measure with multiploe copies of units of the same size, such as paperclips laid end to end. Use tools to measure. Develop common referents for measures to make comparisions and estimates. Pose questions and gather data about themselves and their surroundings. 2.2 Measure the length of an ojbect twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of th unit chosen. Compare and order objects according to these attributes. Understand how to measure using nonstandard and standard units. Select an appropriate unit and tool for th eattribute being measured. Use repetitation of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick. Develop common referents for measures to make comparisions and estimates.

6 Unit: Measurement & Data 2.3 Estimate lengths using units of inches, feet, centimeters, and meters. Select an appropriate unit and tool for the attribute being measured. Use tools to measure. 2.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Understand how to measrue using nonstandard and standard units. Measure with multiple copies of units of the same size, such as paper clips laid end to end. Use tools to measure. Develop common referents for measures to make comparisons and estimates. Pose questions and gather data about themseleves and their surroundings. 2.5 Use addition and subtraction within 100 to solve word problems involving lengths that are give in the same units. Compare and order objects according to these attributes. Understand how to measure using nonstandard and standard units. Select an appropriate unit and tool for th eattribute being measured.

7 Unit: Measurement & Data 2.5 Measure with multiple copies of units of the same size, such as paper clips laid end to end. Use repetitation of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick. Use tools to measure. 2.6 Represent whole numbers as lenghts from 0 on a number line diagram with equally spaced points corresponding to the numbers 0,1,2, and represent whole number sums and differences, within 100 on a number line diagram. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and caculators. i 2.7 Tell and write time from analog and digital colocks to the nearest five minutes, using a.m. and p.m. 2.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and cents symbols appropriately. Monitor and feflect on the process of mathematical problem solving. 2.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the Measure terrarium plants and graph measurements by making a line plot, wher the horizontal scale is marked off I wholenumber results. units. Terrarium Plants, graph paper Completed graphs 0 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. Represent data using concrete objects, pictures and graphs.

8 Unit: Geometry G- Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Recognize, name, build, draw, compare, and sort two-and three-dimensional shapes ii Describe attributes and parts of two-and three-dimensional shapes. ii Recognize geometric shapes and structures in the environment and specify their location. G-2.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. Develop common referents for measures to make comparisons and estimates. G-2.3 Partition circles and rectangles into 2,3, or 4 equal shares. Describe the shares using the words halves, thirds, and half of, a third, of, etc. and describe the whole as 2 halves, 3 thirds, 4 fouths. Recognize that equal shares of identical wholes need not have the same shape. Count with understanding and recognize "how many" in sets of objects.

9 Unit: Operations and Algebragic Thinking