Grade 4 + DIGITAL. EL Strategies. DOK 1-4 RTI Tiers 1-3. Flexible Supplemental K-8 ELA & Math Online & Print

Standards PLUS Flexible Supplemental K-8 ELA & Math Online & Print Grade 4 SAMPLER Mathematics EL Strategies DOK 1-4 RTI Tiers 1-3 15-20 Minute Lessons Assessments Consistent with CA Testing Technology Standards PLUS Targeted Intervention Ready to Teach RTI Tier 1-2-3 Materials PRINT + DIGITAL Writing Program EL Strategies Performance Lessons Integrated Projects Written directly to the CA Standards by CA Educators

Close the Achievement Gap EL STRATEGIES All Standards Plus lessons explicitly teach communication skills, strategies, and conventions that meet the goal of EL Instruction. Standards PLUS Includes: Standards PLUS is so much more READY TO TEACH RTI / TIER 1-2-3 Standards Plus Lessons provide: Whole Class Instruction Targeted Intervention Intense Intervention Standards PLUS is Seven Programs in One: 15-20 MINUTE LESSONS DOK 1-2 / RTI Tiers 1-2 Research-based, Direct Instruction, K-8, ELA and Math lessons. Written to the state standards. PERFORMANCE LESSONS DOK 3 Students deepen and apply their knowledge into new applications. ASSESSMENTS DOK 1-2 Weekly formative assessments monitor student progress. Online assessments help students master digital item types. INTEGRATED PROJECTS DOK 4 Students apply knowledge to real-world situations. STANDARDS PLUS DIGITAL DOK 1-3 / RTI Tiers 1-3 Lessons and assessments match the the digital format of the state test. Students transfer their knowledge into a digital learning environment. TARGETED INTERVENTION LESSONS DOK 1-2 / RTI Tiers 2-3 Scaffolded lessons assigned based on assessment results. Digital program automates this process. WRITING PROGRAM (ELA Only) DOK 1-4 / RTI Tiers 1-2 Includes lessons on every writing genre. Writing performance lessons include skills trace, prompts, and rubrics. HOMEWORK/ PARENT CONNECTION (COMING SOON) 2

Sample Lessons Included in this Booklet Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Geometry (Geometry Standards 4.G.1 4.G.3) 1 Points, Lines, and Line Segments 2 Draw and Distinguish Between Rays and Angles 3 Draw and Distinguish Between Parallel and Perpendicular Lines Identify Angles, Parallel, and Perpendicular 4 Lines in Two- Dimensional Figures E1 Evaluation Identify Geometric Objects 5 6 Classify Two- Dimensional Figures Based on Their Sides Classify Two- Dimensional Figures Based on Angle Measurement 7 Classify Special Triangles 8 Classifying Quadrilaterals Evaluation Classifying Two Dimensional E2 Figures P9 Performance Lesson #9 Lines, Angles, Figures (4.G.1, 4.G.2) 4.MD.5: Recognize angles as geometric shapes that are 4.G.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two- dimensional figures. 4.G.2: Classify two- dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. See the lesson index for the entire program on pages 28-35. 3

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Points, Lines, and Line Segments Lesson: #1 Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Lesson Objective: Students will draw and distinguish between points, lines, and line segments. Introduction: Today we are going to learn to draw points, lines, and line segments. Sample Daily Lesson- Teacher Lesson Plan Instruction: A point is a precise location or place, usually represented by a dot. Points are given letter names. Point X is symbolized as a dot with the letter name. In geometry, a line is defined as a straight line that goes on forever or infinitely. It is signified as a straight line with arrows at both ends. Typically two points are labeled on the line, so we call the line by those two points. Line AB is a line with arrows at each end, and two points labeled A and B. Notice that there are two ways to write the name for a line. A line segment is a part of a line. When a line segment is drawn, there are no arrows on the ends. It has a definite start and finish point. Line segment CD is a straight line, with no arrows and two endpoints labeled point C and point D. Notice the two ways to write the name. Guided Practice: In the example we will complete the table by drawing the figures indicated in each row. When we draw these geometric figures, it is important that we draw and label them properly. For the first figure, we will draw Point T. When drawing a point, simply draw a dot, and label it with a letter. Another way to indicate a point is to simply write the letter. Notice the T in the last column. For the second figure, we will draw Line PQ. When drawing a line, first draw a line, then add arrows to each end. Label two points on the line with letters to name the line. Another way to indicate a line is to write the two letters and draw a two-sided arrow above them. For the third figure, we will draw Line Segment XY. When drawing a line segment, first draw the line, and then place endpoints on both ends. This shows the line segment is finite, or having a definite beginning and end. Label the endpoints of the segment with letters. Another way to write a line segment is to write the two letters and draw a line with two endpoints above them. Independent Practice: Complete problems 1-4 on your own. For problems 1-3, complete the table by drawing each geometric figure stated in the left column and writing the object name a second way. For problem 4, explain the differences between a line and a line segment. Review: Discuss the answers to problems 1-4, taking the time to reinforce the difference between a line and line segment. Closure: Today we reviewed how to draw and distinguish between points, lines, and line segments. Turn to your partner and tell them how lines and line segments are related. Answers: 1. F, F 3. R S RS 2. A B AB 4. Answers may vary. Lines have arrows on each end and are infinite. Line segments do not have arrows and have a dot at the beginning and end. 4

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Draw and Distinguish Between Rays and Angles Lesson: #2 Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Lesson Objective: Students will draw and distinguish between rays and angles. Introduction: Today we are going to learn to draw rays and angles. A ray is a portion of a line that starts at a point and goes in a particular direction to infinity. An angle is a shape formed by two rays that start from the same point. This point is called the vertex. Instruction: To draw a ray, make a straight line with a point on one end and an arrow on the other. Rays are given letter names so they can be recognized. Look at Example A. Ray AB is symbolized as a point with the letter A next to it, and a letter B on the line toward the arrow. When naming a ray, the letter at the endpoint always comes first, ray AB. Sample Daily Lesson- Teacher Lesson Plan Angles are named for the point on the two rays that meet at the vertex. For example, ray AB and ray AC form angle BAC or angle CAB. The vertex of the angle is always the middle letter in the angle name. Guided Practice: Look at Example B. We will draw each figure described in the table. First, we will draw Ray BC. When drawing a ray, draw a line with a point at one end and an arrow on the other end extending out in one direction. (Model drawing the ray.) Label the point B and label the arrow C. Next, we will draw Angle EFG. When drawing an angle, draw two rays with a common vertex. (Model this.) Label the vertex F, and each of the rays E and G. Guide students through the rest of the objects in the table. Draw these objects on the board for students to check their own work. Independent Practice: Complete problems 1 5 on your own. Complete the chart by drawing the correct geometric figures and write your answer to question 5 on the lines provided. Review: Discuss the answers to problems 1 5. Closure: Today we reviewed how to draw and discuss the attributes of rays and angles. Answers: 1. Angle ABC; ABC; students draw and label an angle with a vertex at B. 2. Ray QR; QR ; students draw and label ray QR with the endpoint at Q. 3. Angle PQR; PQR; students draw and label angle PQR with the vertex at Q. 4. Angle DEF; DEF; students draw and label angle DEF with the vertex at E. 5. Answers will vary. It is made with two rays that have the same endpoint, called a vertex. 6

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Draw, Distinguish Between Parallel and Perpendicular Lines Lesson: #3 Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Lesson Objective: Students will draw and distinguish between parallel and perpendicular lines. Introduction: Today we are going to learn about parallel and perpendicular lines. Instruction: Look at the top of your page. Today we will be working with parallel and perpendicular lines. Parallel lines are two lines that are the same distance apart for their entire length. This means that parallel lines never cross or intersect. Perpendicular lines are lines that cross or intersect at right angles (90 o ). Sample Daily Lesson- Teacher Lesson Plan Guided Practice: In Example A, look at the two lines. On the space below the lines XY and CD, write if the two lines are parallel, perpendicular, or neither. These lines are parallel because they are the same distance apart and they will never intersect. Next, look at Example B. Read the statement and draw two lines that make this statement true. Line QR is perpendicular to line ST because they intersect at right angles. Make sure you draw two lines that intersect at 90 o. Connect points S and T. Then connect points Q and R. Independent Practice: Complete problems 1-5 on your own. For problems 1-3 write if each pair of lines is parallel, perpendicular, or neither. Notice that the small box in problem 1 indicates the angle is a 90 o angle. In problems 4-5, draw pairs of lines that will make the written statement true. Review: Review correct answers, emphasizing the justification for each pair of lines. Closure: Today we reviewed how to draw and distinguish between parallel and perpendicular lines. Turn and tell your partner the most important thing to remember about both parallel lines and perpendicular lines. Answers: 1. Perpendicular 2. Parallel 3. Neither 4. L M 5. X Y D F E G 8

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Angles, Parallel and Perpendicular Lines in Figures Lesson: #4 Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Sample Daily Lesson- Teacher Lesson Plan Lesson Objective: Students will identify angles, parallel lines, and perpendicular lines in two-dimensional figures. Introduction: Today we are going to learn how to identify angles, parallel lines, and perpendicular lines in two-dimensional figures. Two-dimensional shapes have only two dimensions: width and height. They have no thickness. Instruction: Look at the top of your page. In Example A there are three types of angles. An acute angle is any angle that is less than 90 degrees. An obtuse angle is any angle that is greater than 90 degrees, and a right angle is one that is exactly 90 degrees and is formed by two perpendicular lines. Perpendicular lines intersect or cross at a 90-degree angle. Parallel lines are two lines that never cross because they are the same distance apart for their entire length. We can find all types of angles around us, including those in twodimensional figures. A two-dimensional figure is a closed shape that is made up of a combination of line segments and angles. Guided Practice: In Example B, we see a quadrilateral, with four sides and four angles. We can see that side AC and side CD are perpendicular because they form a right angle at C. So, angle ACD is a right angle. Write the name of the right angle in the space provided. Name the other right angle. Find the obtuse angle and write its name in the space provided (ABD). Remember that an obtuse angle is greater than 90 degrees. (Guide students through identifying and writing the acute angle.) Do you see a pair of parallel sides? (Students should identify the top and bottom sides or line segments AB and CD.) Write in the space provided: AB CD. Do you see any perpendicular sides? (Students should identify line segments AB and AC or AC and CD.) Write AB AC and AC CD. Independent Practice: Complete problems 1-3 on your own. Identify all angles, parallel sides, and perpendicular sides that you see in these figures. If the figure does not contain a type of angle or set of lines, write the word none in the space provided. Review: Review correct answers. Closure: Today we reviewed how to identify angles, parallel lines, and perpendicular lines in two-dimensional figures. Turn and tell your partner the most important types of angles and lines they would find in a perfect square. Answers: 1. *Right angle: MNP & NPO *Obtuse angle: OMN *Acute angle: MOP *Parallel sides: MN PO *Perpendicular sides: NP PO and MN NP *Students may reverse the order of the letters and still be correct. 2. *Right angles: none *Obtuse angle: XWY & WXZ *Acute angle: WYZ & XZY *Parallel side: WX YZ *Perpendicular sides: none *Students may reverse the order of the letters and still be correct. 3. Answers may vary. Right angles are made from perpendicular sides. If a shape has no perpendicular sides there cannot be a right angle. 10

Domain: Geometry Common Core Standards Plus Mathematics Grade 4 Focus: Identify Geometric Objects Evaluation: #1 The weekly evaluation may be used in the following ways: As a formative assessment of the students progress. As an additional opportunity to reinforce the vocabulary, concepts, and knowledge presented during the week of instruction. Standard: 4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. Procedure: Read the directions aloud and ensure that students understand how to respond to each item. Sample Assessment - Teacher Lesson Plan If you are using the weekly evaluation as a formative assessment, have the students complete the evaluation independently. If you are using it to reinforce the week s instruction, determine the items that will be completed as guided practice, and those that will be completed as independent practice. Review: Review the correct answers with students as soon as they are finished. Answers: 1. (4.G.1) Ray BA or BA 2. (4.G.1) MNO or OMN ( ONM, NMO) 3. (4.G.1) A C or B C B A 4. (4.G.1) ST VU and SV TU 5. (4.G.1) Answers may vary. An obtuse angle is greater than 90. A right angle is made from perpendicular lines. The lines of an obtuse angle are not parallel or perpendicular. 12

Domain: Geometry Common Core Standards Plus Mathematics Grade 4 Focus: Identify Geometric Objects Evaluation: #1 Point Line Ray Parallel Lines Perpendicular Lines Acute Angle Obtuse Angle Vertex Right Angle Directions: Write the correct answers on the line provided. 1. Write the correct name for this figure. 2. Name an acute angle in the figure below. M O 4. Name two sets of parallel sides in the figure below. S T N B 3. Draw angle ABC. Make sure you label the vertex correctly. A Sample Assessment - Student Response Page V U 5. Explain the differences between a right angle and an obtuse angle. 13

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify Two-dimensional Figures Lesson: #5 Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Lesson Objective: Students will classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines. Introduction: Today we are going to learn how to recognize parallel or perpendicular lines in a two-dimensional figure and classify figures according to their sides. Lines can be classified as parallel and perpendicular. Remember, two lines are parallel if they never intersect or cross, and two lines are perpendicular if they intersect or cross at right angles (90 ). Sample Daily Lesson- Teacher Lesson Plan Instruction: Many two-dimensional figures are made of line segments or sides. The endpoints of the sides are called vertices. The plural of vertex is vertices. Look at the first figure. This is a parallelogram. It has two sets of parallel sides. The next figure is called a trapezoid and has only one pair of parallel sides. The last figure is a right triangle; it has one pair of perpendicular sides. Guided Practice: Look at the figures below the Venn Diagram. Let s draw the figures in the correct places on the Venn Diagram. A parallelogram has one set of parallel lines. We will draw that on the left side of the diagram. Where would you draw the trapezoid? It has both parallel sides and perpendicular sides so it goes in the oval in the middle of the diagram. Now draw the right triangle and a rectangle in the Venn Diagram. (The right triangle should be on the right, and the rectangle should be in the center.) Independent Practice: You will now complete the Venn Diagram at the bottom of your page on your own. Place the figures in the Venn Diagram by drawing them. Make sure you can justify why you chose where to draw each of the figures. Review: Review how each figure should be classified. Draw the shapes on the projected image. (Teacher draws or selects students to draw.) Closure: Today we reviewed how to classify two-dimensional figures based on their types of sides. Turn and tell your partner the most important thing is why there is only one right triangle on the perpendicular side of the Venn Diagram. Answers: Parallel Sides Perpendicular Sides Both 14

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify Two-dimensional Figures Lesson: #6 Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Lesson Objective: Students will classify two-dimensional figures based on angle measurement. Introduction: Today we will be using right, acute, and obtuse angles to classify figures. A right angle measures 90 degrees, an acute angle measures less than 90 degrees, and an obtuse angle measures greater than 90 degrees. Instruction: Today we will review how to recognize figures and classify them according to their angles. Look at the figures at the top of the page. A right triangle always has a right angle and two acute angles. A square has four right angles as shown. A parallelogram has two acute angles and two obtuse angles. An equilateral triangle has three equal sides and three equal acute angles. Sample Daily Lesson- Teacher Lesson Plan Guided Practice: Look at the categories and notice how each is labeled. We are going to sort the figures from the top of the page into categories according to their characteristics. Let s start with the right triangle. Why is it placed in the At Least One Right Angle category? (Discuss.) You can see we have placed the right triangle in two categories. Why does it fit in the second category? A right triangle has two acute angles. Could a right triangle fit in the final category? No. A right triangle has one right angle and two acute angles, so it doesn t fit in the final category. Let s sort the rest of the shapes together. (last box) Independent Practice: You will now categorize the figures shown at the bottom of your page on your own. Place the figures in the correct category. Make sure you can justify where you placed each of the figures. Figures can be placed in more than one category. Review: Review what figures are in each category. Closure: Today we reviewed how to classify two-dimensional figures based on their angles. Turn to your partner and try to think of a shape that you could place into the portion of the diagram that has all three angles. Answers: Students may use the figure letter or shape name At Least One Right Angle At Least One Acute Angle At Least One Obtuse Angle Rectangle Right Triangle Square Pentagon Rhombus Right Triangle Equilateral Triangle Parallelogram Rhombus Parallelogram Pentagon 16

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify triangles Lesson: #7 Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Lesson Objective: Students will classify triangles, by angle and side. Introduction: Today we are going to review how to recognize and classify triangles. Triangles are given names according to their angles as well as the length of their sides. Sample Daily Lesson- Teacher Lesson Plan Instruction: Look at the top of your page. The three names we give triangles according to their angles are right, obtuse, and acute. A right triangle has one right angle, an obtuse triangle has one obtuse angle, and an acute triangle has three acute angles. Additionally, triangles are named for the length of their sides. The names triangles can be called based on their sides are equilateral, isosceles, and scalene. An equilateral triangle has three sides that are the same length, an isosceles triangle has two sides that are the same length, and a scalene triangle has three sides that are all different lengths. Many times when we name triangles, we just use one name. A triangle can be called by two names, by their angles or by their side measures. For example, a right triangle that has two sides the same length is a right, isosceles triangle. Usually, when a triangle is labeled with both names, the angle classification is stated first. Guided Practice: Look at the triangle in the example. First, we are going to classify this triangle by its angles. This triangle has one angle that is obtuse; therefore it is an obtuse triangle. Write obtuse in the first blank. Next, we will look at the length of its sides. This triangle has three sides that are all different lengths, so it is a scalene triangle. Write scalene in the second blank next to the triangle. We can call this triangle an obtuse, scalene triangle. Independent Practice: Complete problems 1-4 on your own. Write the name of the triangle according to its angle in the first blank, and named by the sides in the second blank. Review: Review correct answers. Discuss any questions that come up. Closure: Today we reviewed how to classify triangles by their angles and lengths of their sides. Turn and tell your partner the most important reason why an equilateral triangle could also be considered an isosceles triangle. Answers: 1. acute, equilateral 2. obtuse, isosceles 3. right, scalene 4. acute, isosceles 18

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying quadrilaterals Lesson: #8 Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Lesson Objective: Students will classify and draw quadrilaterals according to specific features. Introduction: Today we are going to review how to recognize and classify quadrilaterals. Quadrilaterals are two-dimensional figures that have four sides and four angles. They are classified according to their sides and angles. Sample Daily Lesson- Teacher Lesson Plan Instruction: Look at the top of your page. All four-sided objects are quadrilaterals. Quadrilaterals are classified according to more than one feature. Like triangles, they are classified by both their angles and side lengths. For example, a quadrilateral with two pairs of parallel sides, four right angles, and opposite sides that are equal in length is classified as a rectangle. A parallelogram is a figure that has two pairs of parallel sides and opposite sides that are equal. A parallelogram is not a rectangle because it does not have right angles, but a rectangle is a parallelogram since it has two pairs of parallel sides and opposite sides that are equal. Additionally, a square is a rectangle and a parallelogram, but neither of them can be a square, because a square also has all four sides of equal length. Guided Practice: Look at the Venn Diagram. Take a moment to examine the quadrilaterals in each section of the diagram, and how they are classified. What figure on the diagram is incorrectly classified? Why? Allow students time to discuss this with their partners before calling on a student to answer. Discuss why the trapezoid in the upper left section should be in the overlapping section with the parallel sides. Make sure students understand how to read the Venn Diagram. Independent Practice: Complete problems 1-3 on your own. Use the diagram to help you answer the questions. Review: Review and discuss correct answers to problems 1-3. Closure: Today we reviewed how to classify quadrilaterals according to their features. Answers: 1. The square fits in the center because it is a quadrilateral that has at least one right angle, and at least one pair of parallel sides. 2. Circle the shape in the bottom left corner. It is a quadrilateral with one right angle and no parallel sides. 3. Students should draw a rectangle or a trapezoid with a right angle in the center. 20

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying two-dimensional figures Evaluation: #2 The weekly evaluation may be used in the following ways: As a formative assessment of the students progress. As an additional opportunity to reinforce the vocabulary, concepts, and knowledge presented during the week of instruction. Standard: 4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Sample Assessment - Teacher Lesson Plan Procedure: Read the directions aloud and ensure that students understand how to respond to each item. If you are using the weekly evaluation as a formative assessment, have the students complete the evaluation independently. If you are using it to reinforce the week s instruction, determine the items that will be completed as guided practice, and those that will be completed as independent practice. Review: Review the correct answers with students as soon as they are finished. Answers: 1. (4.G.2) right, isosceles triangle 2. (4.G.2) one 3. (4.G.2) two 4. (4.G.2) C 5. (4.G.2) or equivalent 22

Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying two-dimensional figures Evaluation: #2 Equilateral Isosceles Scalene 15' 5' 5' 6' 6' 5' 12' 17' Acute Obtuse Right 5' Parallel Lines Quadrilateral Directions: Answer problems 1-4. In problem 5, draw the figure described. 1. What is the complete name of this figure? 2. How many pairs of parallel sides does this figure have? 3. How many acute angles does this figure have? Sample Assessment - Student Response Page 4. Circle the letter next to the figure that has all of the features listed. Two pairs of parallel sides Opposite sides that are equal No right angles A. square B. rectangle C. parallelogram D. trapezoid 5. Draw a quadrilateral that has two right angles, and one pair of parallel sides. 23

Teacher Lesson Plan Common Core Standards Plus Mathematics Grade 4 Performance Lesson #9 Domain: Geometry Standard Reference: 4.G.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. 4.G.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. Required Student Materials: Student Pages: St. Ed. Pgs. 177-179 (Student Worksheet) Protractor Lesson Objective: The students will classify two-dimensional figures by their lines or angles, recognize and identify right triangles, and classify triangles by their measurement. Sample Performance Lesson - Teacher Lesson Plan Overview: Students will review the content and academic vocabulary as addressed in Common Core Standards Plus Geometry Lessons 1-8, E1-E2. The students will also review the content and academic vocabulary in the Measurement and Data Standard 6. Students will: Draw a two-dimensional figure that has parallel lines. Classify parallel and perpendicular lines in two-dimensional figures. Recognize and categorize right triangles. Classify triangles by measuring the interior angles of triangles. Explain their thinking when classifying figures. Guided Practice: (Required Student Materials: St. Ed. Pg. 177) Review the vocabulary terms: parallel and perpendicular lines. Review the vocabulary terms: right angle, acute angle, obtuse angle, parallel lines, and perpendicular lines. Review how to identify right triangles, acute triangles, and obtuse triangles. Review the symbol for a right angle and the symbols for other angles. Review how to use a protractor to measure an angle. (Angle measurement is covered in Measurement and Data Standards 6 and 7.) Independent Practice: (Required Student Materials: St. Ed. Pgs. 177-179) Students will work with a partner to complete the three problems. Remind students to check their work to be certain they complete all parts of each problem. Review & Evaluation: Option 1: Students join another group and explain their work product to the new group. Students collect any feedback prior to making revisions or additions to their papers. Option 2: Teacher selects students answers to display and discusses possible answers with the class. Option 3: Teacher collects students papers and evaluates them for students ability to demonstrate conceptual understanding of the standard and ability to explain thinking. 24

Student Page 1 of 3 Common Core Standards Plus Mathematics Grade 4 Performance Lesson #9 Domain: Geometry Vocabulary: Lines: Parallel lines: Never intersect or meet and equal distance from one another. Perpendicular lines: Intersect to form a right angle 90 o. Angles: Right angle: An angle of exactly 90 o. @ Acute angle: An angle of less than 90 o. Y Obtuse angle: Angle of more than 90 o. K Triangles: Have three angles and three sides; the measurement of the 3 angles always total exactly 180 0. Right triangle: Includes a right angle 90 o. Acute triangle: All angles measure less than 90 o. Obtuse triangle: Has one angle with a measure greater than 90 o. Directions: Complete all parts of each problem. 1. a) Draw a two- dimensional figure that has parallel lines. b) Label the parallel lines with the word parallel. c) Label the right angles in the figure with the right angle symbol. d) Explain how you know the figure you drew has parallel lines. Sample Performance Lesoon - Student Repsone Page Explanation: 25

Student Page 2 of 3 Common Core Standards Plus Mathematics Grade 4 Performance Lesson #9 Domain: Geometry 2. a) Look at the two- dimensional figures below. b) Which of the figures has perpendicular lines? c) Label the figures that have perpendicular lines with the word perpendicular. d) Explain how you know the other figures do not have perpendicular lines. 1: F Sample Performance Lesson - Student Response Page 2: 3: 4: 5: n p A X Explanation: 26

Student Page 3 of 3 Common Core Standards Plus Mathematics Grade 4 Performance Lesson #9 Domain: Geometry 3. A a) Look at the triangles below. b) Use a protractor to measure the interior angles of each triangle. c) Label each interior angle with its measurement. d) Classify each triangle (right, acute, obtuse) by the measure of its largest interior angle. e) Identify and label any right triangles. f) Explain how you know that a triangle is a right triangle. B C D Sample Performance Lesoon - Student Repsone Page Explanation: 27

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Number and Operations in Base Ten (Number and Operations in Base Ten Standards 4.NBT.1 4.NBT.6) 1 Identify Place Value 30 3 2 Identify Place Value up to 1,000,000 32 4 4.NBT.1: Recognize that in a multi- digit whole 3 Understand Place Value Patterns number, a digit in one place represents ten times 34 5 4 Understand Place Value Patterns what it represents in the place to its right. 36 6 E1 Evaluation Place Value 38 7 5 Word Form of Numbers 40 9 4.NBT.2: Read and write multi- digit whole 6 Expanded Form numbers using base- ten numerals, number 42 10 7 Standard Form names, and expanded form. Compare two multi- digit numbers based on meanings of the digits in 44 11 8 Whole Number Forms each place, using >, =, and < symbols to record the 46 12 results of comparisons. E2 Evaluation Forms of Numbers 48 13 9 Compare Numbers 50 15 4.NBT.2 10 Compare Numbers 52 16 11 Rounding Numbers 4.NBT.3: Use place value understanding to round 54 17 12 Rounding Numbers multi- digit whole numbers to any place. 56 18 Evaluation Comparing and Rounding Whole E3 Numbers 4.NBT.2, 4.NBT.3 58 19 P1 Performance Lesson #1 Understanding Numbers (4.NBT.1, 4.NBT.2, 4.NBT.3) 60 21 23 3 13 Add Multi- digit Whole Numbers 64 25 14 Add Multi- digit Whole Numbers 66 26 15 Subtract Multi- digit Whole Numbers 4.NBT.4: Fluently add and subtract multi- digit 68 27 16 Subtract Multi- digit Whole Numbers whole numbers using the standard algorithm. 70 28 Evaluation Add and Subtract Multi digit E4 Whole Numbers 72 29 17 Multiplication of Whole Numbers 4.NBT.5: Multiply a whole number of up to four 74 31 digits by a one- digit whole number, and multiply 18 Multiplication of Whole Numbers 76 32 two two- digit numbers, using strategies based on 19 Multiplication of Whole Numbers place value and the properties of operations. 78 33 20 Multiplication of Whole Numbers Illustrate and explain the calculation by using equations, rectangular arrays, and/or area 80 34 E5 Evaluation Multiplication of Whole Numbers models. 82 35 21 Dividing Whole Numbers 4.NBT.6: Find whole- number quotients and 84 37 remainders with up to four digit dividends and 22 Dividing Whole Numbers one- digit divisors, using strategies based on place 86 38 value, the properties of operations, and/or the 23 Dividing Whole Numbers 88 39 relationship between multiplication and division. 24 Dividing Whole Numbers Illustrate and explain the calculation by using 90 40 E6 Evaluation Dividing Whole Numbers equations, rectangular arrays, and/or area models. 92 41 25 Dividing Whole Numbers 94 43 26 Dividing Whole Numbers 96 44 27 Dividing Whole Numbers 4.NBT.6 98 45 28 Dividing Whole Numbers 100 46 E7 Evaluation Dividing Whole Numbers 102 47 P2 Performance Lesson #2 Working with Operations (4.NBT.4, 4.NBT.5, 4.NBT.6) 104 49 52 3 TE Page St. Ed. Page DOK Level 28 2013 Learning Plus Associates

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Operations and Algebraic Thinking (Operations and Algebraic Thinking Standards 4.OA.1 4.OA.5) 1 Commutative Property of Multiplication 4.OA.2: See Week 2. 118 53 2 Represent Verbal Statements as Equations 4.OA.1: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. TE Page St. Ed. Page 120 54 3 Represent Verbal Statements as Equations 122 55 4 Represent Verbal Statements as Equations 124 56 E1 Evaluation Multiplicative Comparison 4.OA.1, 4.OA.2 126 57 5 Multiplicative Comparison Problems 4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 128 59 6 Multiplicative Comparison Problems 130 60 7 Multiplicative Comparison Problems 132 61 8 Distinguish Multiplicative & Additive Comparisons 134 62 E2 Evaluation Multiplicative Comparison 136 63 9 Multiplicative Comparison Problems 4.OA.2 138 65 10 Multiplicative Comparison Problems 140 66 11 Multistep Word Problems 4.OA.3 142 67 12 Multistep Word Problems 144 68 E3 Evaluation Word Problems 4.OA.2, 4.OA.3 146 69 13 Multistep Addition & Subtraction Word Problems 4.OA.3: Solve multistep word problems posed with whole numbers and having whole- number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 148 71 14 Multistep Multiplication Word Problems 150 72 15 Multistep Word Problems 152 73 16 Multistep Word Problems 154 74 E4 Evaluation Multistep Word Problems 156 75 17 Division Word Problems with Remainders 4.OA.3 158 77 18 Division Word Problems with Remainders 160 78 19 Division Word Problems with Remainders 162 79 20 Division Word Problems with Remainders 164 80 E5 Evaluation Solving Division Word Problems with Remainders 166 81 21 Multiples of Whole Numbers 4.OA.4: Find all factor pairs for a whole number in 168 83 22 Finding Factor Pairs for Whole Numbers the range of 1-100. Recognize that a whole 170 84 number is a multiple of each of its factors. 23 Finding Factor Pairs for Whole Numbers Determine whether a given whole number in the 172 85 24 Recognize Prime and Composite Numbers E6 Evaluation Multiples and Factors range 1-100 is a multiple of a given one- digit number. Determine whether a given whole number in the range 1-100 is prime or composite. 174 176 86 87 DOK Level P3 Performance Lesson #3 Understanding Operations (4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4) 178-179 89 92 3 2013 Learning Plus Associates 29

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Operations and Algebraic Thinking (4.OA.1 4.OA.5) 25 Generating Arithmetic Patterns 4.OA.5: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule Add 3 and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way. TE Page St. Ed. Page 184 93 26 Identifying the Rule for Arithmetic Patterns 186 94 27 Generate Geometric Patterns 188 95 28 Identifying the Rule for Geometric Patterns 190 96 E7 Evaluation Pattern Rules 192 97 Identify and Explain Features of Arithmetic 29 Patterns 194 99 Identify and Explain Features of Geometric 30 196 100 Patterns 4.OA.5 31 Generate Growing Shape Patterns 198 101 32 Identify the Rule for Growing Shape Patterns 200 102 E8 Evaluation Feature of Patterns 202 103 P4 Performance Lesson #4 Generate and Analyze Patterns (4.OA.5) 204 105 106 3 Integrated Project 1: It s a Number s Game (4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4, 4.OA.5, 4.NBT.1, 4.NBT.2, 4.NBT.3, 4.NBT.4, 4.NBT.5, 4.NBT.6) Prerequisite Common Core Standards Plus Domains: Number and Operations in Base Ten and Operations and Algebraic Thinking DOK Level 209-213 107 110 4 Product: A board game that includes the game board, rules, and cards with at least 10 questions/problems (and their answers) related to each of nine categories. Overview: In this project the students will work in groups of 2 4 to create a board game that shows an understanding of all of the standards taught in the Number and Operations in Base Ten and Operations and Algebraic Thinking Domains. The students will write at least 90 (10 in each category) questions or problems with an answer key for each in the following categories: Place Value of Whole Numbers Representing, Comparing, and Rounding Numbers Adding Multi digit Numbers Subtracting Multi digit Numbers Multiplying Multi digit Numbers Dividing Multi digit Numbers Writing Equations Pattern Rules Making a Model The students will write the rules of play, design the game board, and create the cards. They will include dice, a spinner, or any other item needed to play the game. They will present and explain their game to the class when the project is complete. 30 2013 Learning Plus Associates

Common Core Standards Plus - Math Grade 4 Lesson Index Domain Lesson Focus Standard(s) Measurement and Data (Measurement and Data Standards 4.MD.1 4.MD.7) 1 2 3 Relative Size of Measurement Units Customary Measurement Equivalents Comparing Customary Measurements 4.MD.1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two- column table. For example, know that 1 ft is 12 times as long as 1 in. Express the 230 232 234 111 112 113 4 Relative Size of Measurement Units 236 114 Evaluation Customary Measurement Equivalents 5 Measurement Conversion E1 length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24),... TE Page St. Ed. Page 238 115 240 117 6 Measurement Conversion 242 118 7 Metric Measurement Equivalents 4.MD.1 244 119 8 Comparing Metric Measurements 246 120 E2 Evaluation Metric Measurement Equivalents 248 121 9 Word Problems Involving Measurement Units 4.MD.2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 250 123 10 Word Problems Involving Measurement Units 252 124 11 Word Problems Involving Measurement Units 254 125 12 Word Problems Involving Measurement Units 256 126 E3 Evaluation Word Problems with Measurement Units 258 127 P5 Performance Lesson #5 Conversion Factor (4.MD.1, 4.MD.2) 260 129 132 3 13 Finding Perimeter of a Rectangle 4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. 266 133 14 Finding Area of a Rectangle 268 134 15 Perimeter/Area in Real World Problems 270 135 16 Perimeter/Area in Real World Problems 272 136 Evaluation Perimeter and Area of a E4 Rectangular Figure 274 137 P6 Performance Lesson #6 Area and Perimeter (4.MD.3) 276 139 140 3 17 Create a Line Plot 4.MD.4: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. 280 141 18 Reading a Line Plot 282 142 19 Solve Problems Using a Line Plot 284 143 20 Solve Problems Using a Line Plot 286 144 E5 Evaluation Line Plots 288 145 P7 Performance Lesson #7 Plotting Data (4.MD.4) 290 147 148 3 DOK Level 2013 Learning Plus Associates 31

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Measurement and Data (Measurement and Data Standards 4.MD.1 4.MD.7) Geometry (Geometry Standards 4.G.1 4.G.3) 21 Concepts of Angles 4.MD.5: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a) an angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a one- degree angle, and can be used to measure angles. b) An angle that turns through n one- degree angles is said to have an angle measure of n degrees. TE Page St. Ed. Page 294 149 22 Using a Protractor to Measure Angles 296 150 4.MD.6: Measure angles in whole number 23 Using a Protractor to Measure Angles degrees using a protractor. Sketch angles of 298 151 24 Using a Protractor to Sketch Angles specified measure. 300 152 E6 Evaluation Measurement of Angles 4.MD.5, 4.MD.6 302 153 25 Composing and Decomposing Angles 4.MD.7: Recognize angle measure as additive. When 304 155 26 Finding Unknown Angles an angle is decomposed into non- overlapping parts, the angle measure of the whole is the sum of the 306 156 27 Finding Unknown Angles angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a 308 157 28 Angles in Real World Problems diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the 310 158 E7 Evaluation Angles unknown angle measure. 312 159 P8 Performance Lesson #8 All About Angles (4.MD.5, 4.MD.6, 4.MD.7) 314 161 163 3 1 Points, Lines, and Line Segments 326 165 2 Draw and Distinguish Between Rays and Angles 328 166 3 4.G.1: Draw points, lines, line segments, rays, Draw and Distinguish Between Parallel and angles (right, acute, obtuse), and perpendicular Perpendicular Lines and parallel lines. Identify these in two- 330 167 dimensional figures. Identify Angles, Parallel, and Perpendicular 4 Lines in Two- Dimensional Figures 332 168 E1 Evaluation Identify Geometric Objects 334 169 Classify Two- Dimensional Figures Based on 5 Their Sides 336 171 Classify Two- Dimensional Figures Based on 4.G.2: Classify two- dimensional figures based on 6 the presence or absence of parallel or 338 172 Angle Measurement perpendicular lines, or the presence or absence of 7 Classify Special Triangles angles of a specified size. Recognize right 340 173 8 Classifying Quadrilaterals triangles as a category, and identify right triangles. 342 174 Evaluation Classifying Two Dimensional E2 Figures 344 175 P9 Performance Lesson #9 Lines, Angles, Figures (4.G.1, 4.G.2) 346 177 179 3 9 Line of Symmetry 350 181 10 Line of Symmetry 4.G.3: Recognize a line of symmetry for a two- dimensional figure as a line across the figure such 352 182 11 Line of Symmetry that the figure can be folded along the line into matching parts. Identify line- symmetric figures 354 183 and draw lines 12 Line of Symmetry 356 184 of symmetry. E3 Evaluation Lines of Symmetry 358 185 P10 Performance Lesson #10 Symmetry (4.G.3) 360 187 188 3 DOK Level 32 2013 Learning Plus Associates

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Integrated Project #2: A Place to Play (4.NBT.4, 4.NBT.5, 4.NBT.6, 4.MD.1, 4.MD.2, 4.MD.3, 4.MD.4, 4.MD.5, 4.MD.5a, 4.MD.5b, 4.MD.6, 4.MD.7, 4.G.1, 4.G.2, 4.G.3) Prerequisite Common Core Standards Plus Domains: Measurement & Data and Geometry TE Page St. Ed. Page DOK Level 365-369 189 191 4 Product: A park design that includes specific features. Overview: In this project, the students will design a park that includes specified features. They will create a schematic for the park that shows every feature including: green spaces (grass, shrubs, trees), benches, walkways, playground equipment, ball fields, etc. They will use common tools to provide a precise visual of the park. Each student will present his/her park design orally. 2013 Learning Plus Associates 33

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Number and Operations Fractions (Number and Operations Fractions Standards 4.NF.1 4.NF.7) 1 Equivalent Fractions 4.NF.1: Explain why a fraction a/b is equivalent to a fraction (n x a) / (n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. TE Page St. Ed. Page 382 193 2 Equivalent Fractions 384 194 3 Comparing Fractions 4.NF.2 See Below 386 195 4 Comparing Fractions 388 196 Evaluation Equivalent Fractions and Comparing Fractions 5 Comparing Fractions E1 4.NF.1, 4.NF.2 390 197 4.NF.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as ½. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 392 199 6 Comparing Fractions 394 200 7 Equivalent Fractions 396 201 8 Equivalent Fractions 398 202 Evaluation Equivalent Fractions and Comparing Fractions 9 Add and Subtract Like Fractions E2 400 203 4.NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 402 205 10 Decomposing and Composing Fractions 4.NF.3b: Decompose a fraction into a sum of fractions with 404 206 the same denominator in more than one way, recording 11 Decomposing Fractions each decomposition by an equation. Justify 406 207 decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. 12 Decomposing Mixed Numbers 408 208 E3 Evaluation Composing and Decomposing Fractions 4.NF.3a, 4.NF.3b 410 209 P11 Performance Lesson #11 All About Fractions (4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b) 412-413 211 213 3 13 Adding Mixed Numbers 4.NF.3c: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. 418 215 14 Adding Mixed Numbers 420 216 15 Subtracting Mixed Numbers 422 217 16 Subtracting Mixed Numbers 424 218 E4 Evaluation Add and Subtract Mixed Numbers 426 219 17 Add Fractions to Solve Word Problems 428 221 DOK Level 18 Subtract Fractions to Solve Word Problems 430 222 19 20 E5 Add/Subtract Fractions to Solve Word Problems Add/Subtract Fractions to Solve Word Problems Evaluation Word Problems - Adding/ Subtracting Fractions 4.NF.3d: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. 432 223 434 224 436 225 P12 Performance Lesson #12 Adding and Subtracting Fractions (4.NF.3c, 4.NF.3d) 438 227 228 3 34 2013 Learning Plus Associates

Common Core Standards Plus - Math Grade 4 Lesson Index Common Core Standards Plus Mathematics Grade 4 Domain Lesson Focus Standard(s) Number and Operations Fractions (Number and Operations Fractions Standards 4.NF.1 4.NF.7) 4.NF.4a: Apply and extend previous understandings of multiplication 21 Multiply Fractions by Whole Numbers to multiply a fraction by a whole number. Understand a fraction a/b 442 229 22 Multiplying Fractions by Whole Numbers as a multiple of 1/b. For example use a visual fraction model to represent 5/4 as the product of 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). 444 230 23 Multiplying Fractions by Whole Numbers 446 231 4.NF.4b: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. Understand a fraction a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example use a visual fraction model to 24 Multiplying Fractions by Whole Numbers 448 232 E6 Evaluation Multiplying Fractions by Whole Numbers express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) TE Page St. Ed. Page 4.NF.4a, 4.NF.4b 450 233 25 Word Problems Multiplying Fractions 26 Word Problems Multiplying Fractions 4.NF.4c: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. 452 454 235 236 4.NF.4c, 4.NF.3d: Solve word problems involving addition 27 Operations in Fraction Word Problems and subtraction of fractions referring to the same whole and 456 237 28 Operations in Fraction Word Problems having like denominators, e.g., by using visual fraction models and equations to represent the problem. 458 238 Evaluation Operations in Fraction Word E7 Problems 4.NF.3c, 4.NF.4d 460 239 P13 Performance Lesson #13 Multiplying Fractions 462 241 242 3 4.NF.5: Express a fraction with denominator 10 as an 29 Converting Fractions - 10ths to 100ths equivalent fraction with denominator 100, and use this 466 243 30 Add Fractions technique to add two fractions with respective denominators 10 and 100. 468 244 4.NF.6: Use decimal notation for fractions with 31 Convert Fractions to Decimals denominators 10 or 100. For example, rewrite 0.62 as 470 245 32 Decimals on a Number Line 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 472 246 E8 Evaluation Converting Fractions 4.NF.5, 4.NF.6 474 247 33 Compare Decimals 476 249 34 Compare Decimals 4.NF.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons 478 250 35 Compare Decimals are valid only when the two decimals refer to the same whole. Record the results of comparisons with the 480 251 symbols >, =, or <, and justify the conclusions, e.g., by 36 Compare Decimals 482 252 using a visual model. E9 Evaluation Compare Decimals 484 253 P14 Performance Lesson #14 Fractions and Decimals (4.NF.5, 4.NF.6, 4.NF.7) 486-487 255 257 3 Integrated Project #3: An Illustrated Guide to Equivalence (4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.NF.4, 4.NF.4a, 4.NF.4b, 4.NF.4c, 4.NF.5, 4.NF.6, 4.NF.7) 493-497 258 261 4 Prerequisite Common Core Standards Plus Domains: Number and Operations Fractions Product: A booklet, pamphlet, or series of posters that explore and explain comparisons and equivalence between fractions, whole numbers, mixed numbers, and decimals. Overview: In this project, the students will each create an illustrated guide to equivalence that may be a booklet, a pamphlet, or a series of posters that use models and written explanations to teach the concepts of comparisons and equivalence between fractions, whole numbers, mixed numbers, and decimals. The students will write the text and draw models to explain all of the concepts. They will present their product to a group of peers and participate in a group discussion analyzing and commenting on each group member s work. DOK Level 2013 Learning Plus Associates 35

Standards Plus is Proven Effective in California Schools CALIFORNIA SBAC GROWTH RATE STANDARDS PLUS SCHOOLS SBAC GROWTH RATE* more than doubled OVER 83% of Schools that implemented Standards Plus in 2015-2016 more than doubled the California SBAC growth rate in one or more grade level. Standards Plus Closes the Achievement Gap with 7 Different Programs in One Standards Plus includes: Today s Lesson Performance Lessons Integrated Projects 15-20 Minute Direct Instruction Lessons in Print and Online Increase EL Performance with Equity ELA & Math in Grades K-8 Transfer of Knowledge to a Digital Learning Environment Intervention Materials Built-In Students Experience SBAC-Like Technology Fits into Every Budget starting at $10.00 www.standardsplus.org 1 877 505 9152 a Student