Students will understand 1. what attributes determine a two or three dimensional shapes. Grade 2 Enduring Understandings

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1 Grade 2 Geometry Essential Questions: 1. Why are geometry and geometric figures relevant and important? 2. How can geometric ideas be communicated using a variety of representations? ******(i.e maps, grids, charts, spreadsheets) 3. How can geometry be used to solve problems about real-world situations, spatial relationships, and logical reasoning? Essential Vocabulary shapes, attributes, angles, faces, triangles, quadrilaterals, pentagons, hexagons, cubes, plane shapes, trapezoid, circle, rectangle, vertices, closed figure, partition, rectangle, square, row, column, tiles, area, equal shares, halves, thirds, whole, fourths, identical, divide, fraction form We want students to understand that geometry is all around us in 2 or 3D shapes. Geometric shapes have certain properties and can be transformed, compared, measured, and constructed. 2.G.1: 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. 1. the names of shapes (triangles, quadrilaterals, pentagons, hexagons, and cubes.) 2. the difference between two dimensional and three dimensional figures. 3. what angles and faces are. 1. what attributes determine a two or three dimensional shapes. 1. recognize specific attributes (such as number of angles or faces) 2. draw specific attributes (such as number of angles or faces) 3. identify shapes (triangles, quadrilaterals, pentagons, hexagons, and cubes) 2.G.2.: Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 1. that a rectangle can be divided into rows and columns. 1. that repeated rows and columns of equal sized squares will construct a rectangle. 1. partition a rectangle into same sized squares. 2. count the squares to find the area. 2.G.3.: Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

2 1. that circles can divided into equal parts (halves, thirds, fourths) 2. that rectangles can divided into equal parts (halves, thirds, fourths) 3. how to recognize one whole when written in fraction form 1. circles and rectangles can be divided into equal shares. 2. equal shares can be divided in different ways. 1. divide a circle or a rectangles into halves, thirds, and fourths. 2. read and write a fraction.

3 Grade 2 - Measurement Essential Questions: 1. How does estimation help you find a reasonable measurement? 2. How do you determine the tool and unit to help you accurately measure? 3. When do you need to measure? Essential Vocabulary measure, length, ruler, yardstick, meter stick, measuring tape, unit, non-standard measurement, inches, feet, centimeters, meters, estimate, length, difference, standard length unit, number line, analog clock, digital clock, a.m., p.m., dollar bills, quarters, dimes, nickels, pennies, $, cents symbol, cents, line plot, horizontal scale, whole number, picture graph, bar graph, data, categories, put together, take apart, compare We want students to understand when to measure, what tool and unit to use, and how to use estimation to find a reasonable measurement. 2.MD.1: Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 1. how to use a measuring tool to determine length 2. the difference between the metric and standard measurement systems 1. when to choose the appropriate tool when measuring length 1. accurately measure length using a variety of tools 2. differentiate between metric and standard 2.MD.2: Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 1. they can measure length with nonstandard objects (paper clips, unifix cubes, hands, etc.) 2. how to compare two different units of measurement 1. that measurement results relate to the size of the unit chosen (for example: it would take more unifix cubes than hands to measure the length of a desk) 1. measure an object with two different units 2. compare the different measurement results 2.MD.3: Estimate lengths using units of inches, feet, centimeters, and meters. 1. how to estimate length 1. which unit of measurement will result in a 2. inches, feet, centimeters, and meters reasonable estimate 1. make a estimate of length 2. determine the difference between inches, feet, centimeters, and meters

4 2.MD.4: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 1. how to measure length with standard units 2. how to compare length with standard units 3. how to find the difference between lengths with standard unit. 1. that objects have different lengths that can be compared numerically 1. find the difference in length between two objects using standard units 2.MD.5: Use addition and subtraction within 100 to solve word problems within a cultural context, including those of Montana American Indians, involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 1. how to add and subtract (within 100) 2. how to solve word problems involving length, using different strategies 3. Montana American Indians are a part of Montana culture 1. how to apply addition and subtraction strategies to solve word problems involving length 2. math applies to the real world, including cultural components 1. solve addition and subtraction word problems involving length 2. utilize different strategies for problem solving 2.MD.6: Represent whole numbers as lengths 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. 1. how to horizontally represent numbers to 100 (number line diagram) 2. how to use a number line to add and subtract numbers to that a number line can be a tool for solving addition and subtraction problems 1. build a number line with equally spaced points to add and subtract on a number line to 100

5 2.MD.7: Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 1. how to tell time to the nearest five minutes 2. how to write time to the nearest five minutes 3. how to tell time on both analog and digital clocks 4. when to use a.m. and p.m. 1. the life skill of being able to tell time on analog and digital clocks 1. tell and write time using analog and digital clocks 2. tell and write time using a.m. and p.m. 2.MD.8: Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 1. how to count money 2. solve word problems involving money 3. use appropriate money symbols 1. the life skill of being able to count money 2. the importance of recording money accurately 1. count money 2. solve money word problems and record the answer appropriately 2.MD.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 measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 1. how to measure length 2. how to make a line plot 1. that a line plot is the precursor to a bar graph 2. the data can be displayed visually 1. collect and display data on a line plot

6 2.MD.10: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set from a variety of cultural contexts, including those of Montana American Indians, with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph. 1. how to draw a picture graph 2. how to draw a bar graph 3. how to use a bar graph to add, subtract, and compare 4. Montana American Indians are a part of Montana culture 1. how to utilize graphs for understanding data 2. math applies to the real world, including cultural components 1. draw picture and bar graphs 2. use bar graphs to add, subtract, and compare

7 Grade 2 Number Sense Essential Questions: 1. Why do we use numbers, what are their properties, and how does our number system function? 2. Why do we use estimation and when is it appropriate? 3. What makes a strategy effective and efficient and the solution reasonable? 4. How do numbers relate and compare to one another? Essential Vocabulary digit, number(s), amount(s), hundreds, tens, ones, equals, bundle, place value, three-digit number, count, skip-count, numbers, base-ten numerals, expanded form, compare, <, >, =, greatest, least, and smallest, addition, subtraction, sum, difference, operations, properties, regroup, addend, fact family, number sentence, and number statement, column addition, written method, compose and decompose, concrete models, mathematical drawings, mental math, communicate We want students to understand that all numbers have value, uses, types, and we use operations and reasonableness to work with them. 2.NBT.1: Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens called a hundred. b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 1. place value to the hundreds place 2. hundreds are represented by bundles of tens 3. digits have different values depending upon their place value 1. That digits have different amounts/values depending on their place value (hundreds, tens, and ones). 1. understand place value 2. represent three digit numbers 2.NBT.2.: Count within 1000; skip-count by 5s, 10s, and 100s. 1. that patterns determine how to skip-count 1. that counting is sequential (5s, 10s, 100s). 2. to apply patterns when skip-counting. 2. how to rote count, to 999 (from any number). 1. Count to 999 (from any starting point). 2. Skip-count by 5s, 10s, and 100s. *GFPS students will be able to count backwards to 999 as well.

8 2.NBT.3.: Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 1. number names 2. base ten numerals (number system) 3. expanded form 1. the placement of a digit dictates its value, how it is read, and written. 1. read and write numbers to 999 in both expanded form and word name 2.NBT.4: Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. 1. comparative symbols (<, >, and =). 2. how to compare three-digit numbers. 3. how to record the results of comparing numbers. 1. the comparative relationship between three-digit numbers. 1. compare three-digit numbers. 2. use appropriate tools when comparing numbers to (base-ten blocks, pictures, stamps, ). 2.NBT.5.: Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 1. fact families 2. the basic facts fluently 3. different strategies for addition and subtraction 4. how to add and subtract to there are multiple ways to solve addition and subtraction problems 1. Add and subtract (based on place value and properties of operations) 2. Use the relationship of fact families as a strategy for addition or subtraction 2.NBT.6.: Add up to four two-digit numbers using strategies based on place value and properties of operations. 1. how to add multiple (up to 4) two-digit numbers 1. there are multiple ways to solve addition problems 1. add up to 4 two-digit numbers using a variety of strategies

9 2.NBT.7.: Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 1. how to make models of addition and subtraction 2. how to draw addition and subtraction 3. how to add and subtract using a variety of written methods 1. that problems can be solved using models, drawings, and written methods 1. add and subtract using models, drawings, and a variety of written methods. 2. Understand subtraction of 3 digit numbers 2.NBT.8.: Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a given number a variety of strategies for mental math in both addition and subtraction. 1. how to apply a variety of strategies in mental math to solve addition and subtraction. 2. the value of mental math 1. mentally add 10 or 100 to a given number ( ) 2. mentally subtract 10 or 100 from a given number ( ) 2.NBT.9.: Explain why addition and subtraction strategies work, using place value and the properties of operations. 1. a variety of addition and subtraction strategies 2. there are different methods to communicate the mathematical strategies. 1. how to communicate the way that mathematical strategies work. 1. explain addition and subtraction strategies 2. communicate the strategies through words, drawing, or pictures.

10 Grade 2 Algebraic Thinking Essential Questions: 1. How do you use patterns to understand mathematics and model situations? 2. What is algebra? 3. How are the horizontal and vertical axes related? 4. How do algebraic representations relate and compare to one another? 5. How can we communicate and generalize algebraic relationships? Essential Vocabulary addition, subtraction, adding to, taking from, putting together, taking apart, comparing, equations, symbol, unknowns, sum, odd, even, equation, sum, equal addends, doubles, rectangular array, rows, columns, equation, sum, equal addends We want students to understand how we use patterns and relationships of algebraic representations to generalize, communicate, and model situations in mathematics. 2.OA.1: Use addition and subtraction within 100 to solve one- and two-step word problems involving situations within a cultural context, including those of Montana American Indians, of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 1. how to add and subtract within how to solve one and two step word problems. 3. how to solve for unknowns. 4. Montana American Indians are a part of Montana culture 3. how to apply addition and subtraction strategies to solve word problems 4. math applies to the real world, including cultural components 1. add and subtract within solve one and two step word problems 3. solve for unknowns 2.OA.2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. 1. basic math facts (within 20) 1. memorization of math facts is a life skill 1. fluently apply their basic math facts

11 2.OA.3: Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 1. doubles facts 2. odd and even 3. how to write an equation 1. what makes a number odd or even 2. doubles facts always result in an even sum 1. write their doubles facts in equation form 2. determine whether a number is odd or even 3. use a variety of strategies 2.OA.4: Use addition to find the 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. 1. how to make a model of a rectangular array 2. how to add up to 5 equal addends 3. how to write an addition equation 1. that arrays are visual models of equal addends 1. differentiate between columns and rows 2. express the total number of objects within a given array (up to 5 X 5) 3. add and record the equation of up to five equal addends