2nd Grade Mathematics

Unit 5: Geometry

Teacher Resource Guide 2012 - 2013In Grade 2, instructional time should focus on four critical areas:

1. Extending understanding of base-ten notation;Students extend their understanding of place value. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).

2. Building fluency with addition and subtraction;Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, methods to compute sums and differences of whole numbers in base-ten notation. They apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.

3. Using standard units of measure;Students recognize the need for standard units of measure (centimeter and inch) and they use rulers with the understanding that linear measure involves iteration (repetition) of units. They recognize that the smaller the unit, the more iterations they need to cover a given length.

4. Describing and analyzing shapesStudents describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.

2nd Grade 2012-2013 Page 1

2nd Grade Mathematics 2012-2013

Unit Time Frame Test By

TRIM

ESTE

R 1 1: Addition and Subtraction

(within 20) 7 weeks 8/27 - 10/12 October 12

2: Data/Measurement5 weeks 10/15 - 11/27 November 27

TRIM

ESTE

R 2

3: Addition and Subtraction (within 100- Developing Skills) 6 weeks 12/3 - 1/18 January 18

4: Addition and Subtraction (within 100- Fluency) 6 weeks 1/21 - 3/1 March 1

TRIM

ESTE

R 3 5: Geometry

5 weeks 3/4 - 4/12 April 12

6: Addition and Subtraction (within 1,000) 6 weeks 4/15 – 5/30 May 31

Math Wiki: http://dmps-mathematics.wikispaces.com/

2nd Grade 2012-2013 Page 2

Unit 5: Geometry March 4 – April 12 (5 weeks)

Big Ideas Essential Questions

Fractions describe a whole that has been partitioned into equal-sized shares.

What is a fraction?

Identifier Standards Mathematical Practices

STAN

DARD

S

2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

1) Make sense of problems and persevere in solving them.

2) Reason abstractly and quantitatively.

3) Construct viable arguments and critique the reasoning of others.

4) Model with mathematics.

5) Use appropriate tools strategically.

6) Attend to precision.

7) Look for and make use of structure.

8) Look for and express regularity in repeated reasoning.

2.G.3

2.G.2

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.

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

2nd Grade 2012-2013 Page 3

Unit 5: Geometry March 4 – April 12 (5 weeks)

Identifier Standards Bloom’s Skills ConceptsST

ANDA

RDS

2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.5 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

Remember (1)Apply (3)

Remember (1)

Recognize anddraw (shapes)

Identify (shapes)

attributeanglefacetrianglequadrilateralpentagon hexagoncube

2.G.3

2.G.2

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.

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

Apply (3)

Remember (1)

Partition (circles and rectangles)

Describe (the shares)

circlerectangleequal sharewholehalfthirdfourthtwo-halvesthree-thirds four-fourths

2nd Grade 2012-2013 Page 4

Unit 5: Geometry March 4 – April 12 (5 weeks)

Instructional Strategies for ALL StudentsCritical Reading Prior to Instruction:Teaching Student-Centered Mathematics K-3, Van de Walle & Lovin, Pearson, 2006, p. 252-254 & p. 186-191 (building resource, SPED)

Sorting and ClassifyingInstructional activities in geometry appropriate for grades K-2:

Involve lots of sorting and classifying. Seeing how shapes are alike and different is the primary focus. As students learn more content, the types of things that they notice will become more sophisticated. At an early stage they may talk about very nongeometric-sounding attributes of shape such as “fat” or even the color of pieces. When properties such as symmetry and number of sides and corners are introduced, students should be challenged to use these features to classify shapes.

Include a sufficient variety of examples of shapes so that irrelevant features do not become important. Students need ample opportunities to draw, build, make, put together, and take apart shapes in both two and three dimensions. These activities should be built around specific characteristics or properties so that students develop an understanding of geometric properties and begin to use them naturally. (Adapted from Van de Walle, 2006)

Sharing and the Concept of Fractional PartsThe first goal in the development of fractions should be to help children construct the idea of fractional parts of the whole – the parts that result when the whole or unit has been partitioned into equal-sized portions or fair shares. Children seem to understand the idea of separating a quantity into two or more parts to be shared fairly among friends. They eventually make connections between the idea of fair shares and fractional parts. Sharing tasks are, therefore, good places to begin the development of fractions. (Adapted from Van de Walle, 2006)

2nd Grade 2012-2013 Page 5

Unit 5: Geometry March 4 – April 12 (5 weeks)

Routines/Meaningful Distributed PracticeDistributed Practice that is Meaningful and PurposefulPractice is essential to learn mathematics. However, to be effective in improving student achievement, practice must be meaningful, purposeful, and distributed.

Meaningful: Builds on and extends understanding Purposeful: Links to curriculum goals and targets an identified need based on multiple data sources Distributed: Consists of short periods of systematic practice distributed over a long period of time

Routines are an excellent way to achieve the mandate of Meaningful Distributed Practice outlined in the Iowa Core Curriculum. The skills presented during routines do not necessarily reinforce the lesson concept for that day. Routines may be used to address a need for small increments of exposure to a skill or review of skills already taught. Routine activities may be repeated several days in a row, allowing for a build-up of conceptual understanding, or can be visited and re-visited over a period of time. Routines can be inserted as the schedule allows; in short intervals throughout the day or as a lesson opener or closer. Selection of the routine should be made based on informal teacher observation and formative assessments.

Skill StandardUse addition and subtraction within 100 to solve one-and two-step word problems 2.OA.1

Fluently add and subtract within 20 2.OA.2

Tell and write time to nearest 5 minutes 2.MD.7Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies 2.MD.8Other skills students need to develop based on teacher observation and formative assessments.

2nd Grade 2012-2013 Page 6

Unit 5: Geometry March 4 – April 12 (5 weeks)

Lessons Teacher Directions StandardsAddressed

Geometrical Shapes

This unit is only 4 weeks and has a focus on shapes and fair shares (fractions). Map out the unit to ensure time to teach the fraction portion of this unit as well. Some of the geometry activities will only take a portion of your math time, so you may do more than one activity in one day. Once you complete the geometry activities, you may continue them throughout the unit.

Wiki: Quick Images- Shapes This can be done as a Routine/MDP throughout the unit. Discuss the attributes of each shape as the unit progresses. 2.G.1

Fractional Counting (Routine) This is similar to counting objects (one apple, two apples, three apples, etc.). We want students to be able to count by halves, thirds and fourths. They don’t have to switch to mixed numbers once they make a whole (i.e. ¼, 2/4, ¾, 4/4, 5/4, 6/4, etc.) This should be done as a routine during your MDP time throughout the unit.

Expressions: Unit 2, Lesson 2 Activities 1-3, p. 174(Draw Shapes)

2.G.1

Wiki: Shape Sorts Complete the activities multiple times, as needed. The activities can be slightly modified and used as a center activities

2.G.1

Wiki: Sorting Shape Cards Complete the activities multiple times, as needed. The activities can be slightly modified and used as a center activities

2.G.1

Expressions: Unit 10, Lesson 1, Activity 3, p. 722(Sort 2D Figures)

2.G.1

Wiki: Shape Searches 1-6 These activities can be done as centers 2.G.1Wiki: What’s My Shape Complete the activity multiple times, as needed. The activity can be slightly

modified and used as a center activity.2.G.1

Expressions: Unit 4, Lesson 1, Activity 1 (Define Shapes) Focus on the definitions portion of this lesson only 2.G.1Wiki: Building Rectangles 2.G.2Wiki: How Many Rectangles? Students may repeat this activity throughout the unit. 2.G.2Expressions: Unit 10, Lesson 5, Activities 1-2, p. 746 (Rectangles) 2.G.2Wiki: Is It A Rectangle? This can be given as an assessment 2.G.2Expressions: Unit 4, Lesson 2, Activities 1-2, p. 294 (Parallelograms)

2.G.1

Expressions: Unit 4, Lesson 3, Activities 1-2, p. 300 (Quadrilaterals)

2.G.1

Expressions: Unit 10, Lesson 2, Activities 1-2, p. 726 (Combine/Decompose Shapes)

Put two or more shapes together then name the new shape

Wiki: Separating shapes 1-6 A These can be done as centers. Separating Shapes A is easier than B. Some students may skip A and others may need to do A prior to B.Wiki: Separating shapes 1-6 B

2nd Grade 2012-2013 Page 7

Unit 5: Geometry March 4 – April 12 (5 weeks)

Lessons Teacher Directions StandardsAddressed

Fractions Some of the fraction activities will only take a portion of your math time, so you may do more than one activity in one day. Some of the activities should be done multiple times over the course of a few days.

2.G.3

Wiki: Quick Images- Shapes This can be done as a Routine/MDP throughout the unit. Discuss the attributes of each shape as the unit progresses. 2.G.1

Wiki: Fractional Counting (Routine) This is similar to counting objects (one apple, two apples, three apples, etc.). We want students to be able to count by halves, thirds and fourths. They don’t have to switch to mixed numbers once they make a whole (i.e. ¼, 2/4, ¾, 4/4, 5/4, 6/4, etc.) This should be done as a routine during your MDP time throughout the unit.

2.G.3

Wiki: Top & Bottom Numbers Please read this section about top and bottom numbers. It is not necessary to have this conversation with your students during one math block. Instead, it should be discussed throughout the unit.

2.G.3

Wiki: Linda & Ebony Sandwich 2.G.3Wiki: Correct Shares Should be done multiple times over the course of a few days. 2.G.3Wiki: Halves/Not Halves of a Rectangle 2.G.3Wiki: Folding and Folding Again 2.G.3Wiki: Same or Different 2.G.3Wiki: A Third of a Flag 2.G.3Wiki: Fraction Flags Can be modified and used as centers 2.G.3Expressions: Unit 13, Lesson 9, Activity 1, p. 1004 2.G.3Wiki: Fractional Parts Counting Should be done multiple times over the course of a few days.Wiki: More, Less or Equal to One Should be done multiple times over the course of a few days. 2.G.3

2nd Grade 2012-2013 Page 8