CoreConnects Mathematics Sample Pages - Grades K-2

Professional Development for College and Career Readiness

Teaching a deep understanding of math content and how to use math in the real world

Teacher Resource

Manual

GradesK-2

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©2014 This information is confidential and proprietary to Catapult Learning™. For internal distribution only.

CoreConnects: Mathematics

Teaching Math Skills to Achieve Common Core Outcomes

Levels K-2

Confidentiality Statement

This information is confidential and proprietary to Catapult Learning™. It is for internal use and distribution only.

Distribution of this document beyond employees of Catapult Learning™ is strictly prohibited.

External Distribution: In the event that any proprietary or confidential information is disclosed, intentionally or otherwise to a School District/Schools, its employees, agents or assigns, the School District/Schools agrees to hold same in strictest confidence and not to disclose same to any other person for any reasons nor utilize same within the School District or Schools without prior written approval by Catapult Learning.

The School District/Schools further agree to use all efforts at its disposal to assure that its employees, agents or assigns are aware of the confidential and proprietary nature of the subject matter, and do not disclose same to any other person for any reasons nor utilize same without prior written approval by Catapult. The School District/Schools acknowledges that unauthorized disclosure of Catapult’s proprietary and confidential information may cause Catapult irreparable harm and may entitle Catapult to injunctive relief in a court of competent jurisdiction.

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CoreConnects: Mathematics 3 ©2014 This information is confidential and proprietary to Catapult Learning™. For internal distribution only.

Table of Contents

Overview

Common Core General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Building Performance Character Traits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

How to use the Teaching Math Skills sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

Recommended Manipulatives and Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Skills Sheets at a Glance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Standards for Mathematical Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Directed Math Activity Format/DMA Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

Sequence of TMS K-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Skills Sheets

K.CC.A – Know number names and the count sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

K.CC.B – Count to tell number of objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

K.CC.C – Compare numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

K.OA.A – Understand addition as putting together and adding to,

and understand subtraction as taking apart and taking from . . . . . . . . . . . . . . . . . . . . . . . . . . 47

K.NBT.A – Work with numbers 11–19 to gain foundations for place value . . . . . . . . . . . . . . . . . 51

K.MD.A – Describe and compare measurable attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

K.MD.B – Classify objects and count the number of objects in categories . . . . . . . . . . . . . . . . . . 55

K.G.A – Identify and describe shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

K.G.B – Analyze, compare, create, and compose shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

1.OA.A – Represent and solve problems involving addition and subtraction . . . . . . . . . . . . . . . . . 63

1.OA.B – Understand and apply properties of operations and the

relationship between addition and subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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CoreConnects: Mathematics – Teaching Math Skills Levels K-2 – Table of Contents

1.OA.C – Add and subtract within 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

1.OA.D – Work with addition and subtraction equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

1.NBT.A – Extend the counting sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

1.NBT.B – Understand place value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

1.NBT.C – Use place value understanding and properties of operations

to add and subtract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

1.MD.A – Measure lengths indirectly and by iterating length units . . . . . . . . . . . . . . . . . . . . . . . 89

1.MD.B – Tell and write time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

1.MD.C – Represent and interpret data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

1.G.A – Reason with shapes and their attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

2.OA.A – Represent and solve problems involving addition and subtraction . . . . . . . . . . . . . . . . . 107

2.OA.B – Add and subtract within 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

2.OA.C – Work with equal groups of objects to gain foundations for multiplication . . . . . . . . . . . 117

2.NBT.A – Understand place value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

2.NBT.B – Use place value understanding and properties of operations to add and subtract . . . 127

2.MD.A – Measure and estimate lengths in standard units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

2.MD.B – Relate addition and subtraction to length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

2.MD.C – Work with time and money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

2.MD.D – Represent and interpret data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

2.G.A – Reason with shapes and their attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

Performance Tasks

K-2 Performance Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Performance Task Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Performance Task Rubric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

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Performance Task Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

Level K (1) Jellybean Fun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Level K (2) Shapes All Around Us . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

Level 1 (1) Class Play . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Level 1 (2) Who Dunnit? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Level 1 (3) Puzzle Pieces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Level 2 (1) Exploring Problem Solving Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Level 2 (2) Preparing for New Students . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Level 2 (3) The School Olympics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

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How to Use the Teaching Math Skills Sheets

The Teaching Math Skills sheets are designed to assist teachers in approaching Common Core Standards in the classroom. Each TMS Skills Sheet addresses a Common Core cluster within each domain of the Common Core State Standards for Math.

TMS Sheets are not intended to be used only once. Many of them cover many standards and can and should be used until the teacher feels that those standards have been addressed to sufficiently meet the needs of the students s/he is teaching. Although the Standards for Mathematical Practice are not outlined within these lesson suggestions, teachers should continue to provide opportunities for these practices for students.

An example for the top of a TMS Skills Sheet for Level 2 follows. Note the following:

• The objective which is the cluster, is indicated.

• The prerequisite standards for the skill indicate what is expected to be known at the end of the level prior to the current level.

• The standards for the current grade-level skills are indicated.

» If the current cluster is considered a Major Cluster, it will be indicated with a * in the objective.

» If the current cluster contains a Required Fluency, that standard will be indicated with a ◊.

• Students that show mastery of the current cluster can be challenged to explore the growth cluster.

Performance Task: Exploring Problem Solving Strategies

The skills sheets will each be set up with the following sections: Review and Pre-assessment, Instruction, Scaffolding, and Evidence of Learning.

Review and Pre-assessment

This section provides a set of review and pre-assessment questions. As noted above, they will align to the pre-requisite skills required for the current cluster. Students should have sufficient knowledge of these review items in order to continue with instruction at this level. If they do not, the teacher will refer to the pre-requisite cluster, and start instruction with that skills sheet.

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CoreConnects: Mathematics – How to Use the Teaching Math Skills Sheets

Instruction

This section will present several instructional activities that pertain to the current level cluster. They are bulleted activities that follow a Directed Math Activity Format. Within the instruction, specific Practice Standards have been indicated. Teachers should be looking for student engagement in these areas. Each instructional activity is designed to cover one or two class sessions, depending on session length.

Scaffolding

It is rare that all students will be working at the exact same pace and at the exact same level. A few options are provided to give either additional support or an additional challenge to those students who may need it.

Evidence of Learning

Once an adequate amount of time has been spent on the standards and cluster, the teacher will need to look for evidence of learning. At the end of each skills sheet, there will be a bulleted list of what is expected of students upon mastery of this cluster.

These skills sheets have been provided as a guide for instruction. Teachers are encouraged to supplement with additional activities that align to the standards indicated.

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Teaching Math Skills 3.G.A3.G

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Objective: Reason with shapes and their attributes

Pre-Requisite

Reason with shapes and their attributes: drawing shapes,

partitioning rectangles and circles

(2.G.A.1, 2.G.A.2, 2.G.A.3)

Current

Reason with shapes and their attributes: geometric planes

and solids

(3.G.A.1, 3.G.A.2)

Performance Task: What’s in Your Garden?

Growth

Reason with shapes and their attributes: figures with perpendicular

and parallel lines, symmetry

(4.G.A.1, 4.G.A.2, 4.G.A.3)

Review & Pre-AssessmentHave students draw each shape and tell how many sides and corners.

• Square ( , 4 sides, 4 corners)

• Circle ( , 0 sides, 0 corners)

• Triangle ( , 3 sides, 3 corners)

• Rectangle ( , 4 sides, 4 corners)

Have students identify the two-dimensional geometric shape in an object:

• (circle) • (rectangle)

• (triangle) • (circle)

InstructionEXPLORING THE ATTRIBUTES OF PLANE FIGURES:

• Place plane figures on the table (e.g., square, triangle, and rectangle). Allow the students some time to explore them. Review the following definition: A plane figure is made up of lines and segments that connect to create sides and corners. Have students identify the shapes on the table. Explain that these shapes are called plane figures. Look at our definition. Ask if the figures have sides and corners. (yes) Have students look at the square and identify how many sides and how many corners it has. (4 sides, 4 corners) Have students look at the triangle and identify the number of sides and corners. (3 sides, 3 corners) Continue examining the remaining shapes in a similar manner. (PS.2, PS.3, PS.5, PS.6)

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3.G.A Teaching Math Skills3.

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• Have students draw the following chart and examine the shapes to fill in the sides and corners. Discuss all responses. (PS.3, PS.5, PS.6)

Figure Number of Sides Number of CornersSquare (4) (4)Triangle (3) (3)

Rectangle (4) (4)Pentagon (5) (5)

• Draw the following shapes on the board. Have the students write how many sides and corners each shape has and record it on their papers. (PS.1, PS.2, PS.6)

1. 2. 3. 4.

Sides 4 5 6 3Corners 4 5 6 3

5. 6. 7. 8.

Sides 4 4 4 4Corners 4 4 4 4

• Challenge students to find 3-5 examples of plane figures in the classroom. Once they have selected their figures, have students draw them and identify the number of corners and sides. Discuss all of the different plane figures in the classroom. (PS.2, PS.6, PS.7)

CATEGORIZING QUADRILATERALS:

• Explain that we categorize shapes to help organize them. Explain that the categories can for broken into smaller categories. For example, mammals can be broken into the subcategory “people” and that can be broken into “boys and girls.” Explain that quadrilaterals are a larger category that can be broken into subcategories. Remind students that quadrilaterals have four sides. Review the following subcategories: parallelogram (4 sides, one pair of parallel sides); rectangle (4 sides, two pairs of parallel sides, 4 right angles); and square (4 sides, two pairs of parallel sides, 4 right angles, 4 equal sides). (PS.2, PS.6)

• Fold a sheet of paper in half and in half again so that it is broken up into 4 horizontal sections. Label the top quadrilateral, the next section parallelogram, the next section, rectangle, and the last section square. Provide students with a variety of quadrilaterals. Start off with all of the shapes in the top quadrilateral section. Have students move the shapes down one at a time until they find the best placement on the chart. (PS.5, PS.6, PS.7)

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Teaching Math Skills 3.G.A3.G

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• Discuss the final placement of the quadrilaterals: Can any shape fit into a better category? Can some shapes go into more than one category? (PS.2, PS.3, PS.6, PS.7)

• Challenge students to find a pattern. Lead them to see that the shapes fit into all of the categories above them. (PS.6, PS.7, PS.8)

EXPLORING THE ATTRIBUTES OF GEOMETRIC SOLIDS:

• Provide students with several different geometric solids (e.g., cone, cylinder, cube, pyramid, sphere), and allow them to explore their attributes. Discuss their observations. Review the following terms: Flat surfaces are called faces. Two or more faces join at an edge. Edges join at a corner. Ask if anyone can name the shapes on the table. Allow the students to name all of the shapes they can. Supply the names for the shapes that are not known. Explain that these kinds of shapes are called solids. Ask which of these solids has a face. Students should answer cube, cylinder, cone, and pyramid (answers may vary if different shapes are provided). Ask which solids have an edge. Students should answer cube and pyramid. If edges come together to make corners, ask what are the two shapes that would have corners. Students should answer cube and pyramid. Ask why only two solids have corners. Students should answer because they are the only two solids with edges. (PS.3, PS.5, PS.6, PS.7)

• Draw the following chart on the board. Have the students create it on their paper. Challenge students to examine each shape and fill in the chart. Discuss the results. (PS.5, PS.6)

Figure Number of faces Number of edges Number of cornersPyramid (5) (8) (5)

Cube (6) (12) (8)Cylinder (2) (0) (0)

• Draw the following chart on the board. Have students create it on their paper. Encourage them to think about the items and fill in the spaces. Students can be encouraged to draw the items or you might draw the items for them (or bring in examples). Students can also use the shape that matches the item to find the answers. (PS.5, PS.6, PS.7)

Figure Number of faces Number of edges Number of cornersCereal box (6) (12) (8)Soup can (2) (0) (0)

Wedge of cheese (5) (9) (6)Globe (0) (0) (0)

MODELING FRACTIONAL PARTS:

• Draw 5 rectangles. Leave the first one whole, divide the second into two equal parts, the third into three equal parts, etc. Discuss the fractional parts that each rectangle is divided into (1 whole, halves, thirds, fourths and fifths). Place the fraction circles that represent a whole, halves, thirds, fourths, and fifths on the table (mixed-up). Ask for volunteers to assemble the fractions with the correct parts to make whole circles. (PS.3, PS.5, PS.6)

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3.G.A Teaching Math Skills3.

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• Shade in the rectangles as follows: 1/2, 2/3, 1/4, 2/5. Explain the fractional parts shaded. Have students draw a rectangle that represents 4/6. (PS.2, PS.3, PS.6)

• Choose 5-8 fractions. Have students draw a picture to show a shape (e.g., rectangle or circle) divided into equal fractional parts and identify the fraction pictured. (PS.2, PS.5, PS.6)

Scaffolding

Evidence of Learning• Students will be able to identify and categorize shapes based on their attribute.

• Given a shape, students will be able to partition it into equal areas.

• Students will be able to draw examples of a given shape.

• Students will be able to identify the fractional amount of a shape that is broken into equal parts.

Additional Support

• Allow struggling learners to work with a partner

• Allow students to use manipulatives such as: counters or tokens, base ten blocks, and multiplication flash cards when solving problems

• Guide students with questioning

• Provide students with geometric solids to count the edges, faces, and corners

• Have students work with two-dimensional objects only

Additional Challenge or Rigor

• Pair students with a struggling learner for peer tutoring

• Challenge students to think of examples not found in the classroom

• Have students create their own problems and answers to trade with a classmate

• Have students identify and explain a real- life application of fractions

• Challenge students to build a list of real-life geometric solids and identify the number of faces, corners, and edges

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Level 1 – Puzzle PiecesLevel 1

Answer Key/Teacher Guide

Teacher: This task will focus on students creating a puzzle out of a square. Have construction paper, scissors, and markers or crayons available for the students.

Common Core Standard Assessed Skill1.G.2 Compose two dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles,

and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

Part ASay: “Let’s make puzzles! Has anyone ever done a puzzle before? How do you think we can make our own puzzle?”

Teacher: Guide students to come to the conclusion that you need a starting image that can be cut into smaller pieces that fit together.

Say: “Draw a picture for your puzzle.”

Part BSay: “Sometimes puzzles come in funny shapes, but today we want to use shapes we have learned about. What shapes have we talked about?”

Teacher: Guide students to come up with triangles, rectangles, squares, trapezoids. Circles have also been learned, but these are not the best shapes for the puzzle.

Say: “Flip your picture over. Can you draw lines to divide your puzzle picture into smaller shapes?”

Teacher: Students can trace attribute blocks or use a ruler to make sure their shapes have straight lines.

Part CSay: “Cut your puzzle along the lines you drew to create your puzzle pieces.”

Teacher: Assist students with cutting as needed.

Say: “Trade your puzzle with a partner. Can you put your partner’s puzzle together?”

Teacher: Allow students time to work to put the puzzles together. Assist as needed.

Say: “What shapes did your partner use to create his or her puzzle?”

Teacher: If resources are available, allow students to explore tangrams, other puzzles, or similar online activities.

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CoreConnects: Mathematics – Level 1 – Puzzle PiecesLe

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CoreConnects Mathematics Sample Pages - Grades K-2