Grade 4 + DIGITAL. EL Strategies. DOK 14 RTI Tiers 13. Flexible Supplemental K8 ELA & Math Online & Print


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1 Standards PLUS Flexible Supplemental K8 ELA & Math Online & Print Grade 4 SAMPLER Mathematics EL Strategies DOK 14 RTI Tiers Minute Lessons Assessments Consistent with CA Testing Technology Standards PLUS Targeted Intervention Ready to Teach RTI Tier Materials PRINT + DIGITAL Writing Program EL Strategies Performance Lessons Integrated Projects Written directly to the CA Standards by CA Educators
2 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 Standards Plus Lessons provide: Whole Class Instruction Targeted Intervention Intense Intervention Standards PLUS is Seven Programs in One: MINUTE LESSONS DOK 12 / RTI Tiers 12 Researchbased, Direct Instruction, K8, ELA and Math lessons. Written to the state standards. PERFORMANCE LESSONS DOK 3 Students deepen and apply their knowledge into new applications. ASSESSMENTS DOK 12 Weekly formative assessments monitor student progress. Online assessments help students master digital item types. INTEGRATED PROJECTS DOK 4 Students apply knowledge to realworld situations. STANDARDS PLUS DIGITAL DOK 13 / RTI Tiers 13 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 12 / RTI Tiers 23 Scaffolded lessons assigned based on assessment results. Digital program automates this process. WRITING PROGRAM (ELA Only) DOK 14 / RTI Tiers 12 Includes lessons on every writing genre. Writing performance lessons include skills trace, prompts, and rubrics. HOMEWORK/ PARENT CONNECTION (COMING SOON) 2
3 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
4 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 twodimensional 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 twosided 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 14 on your own. For problems 13, 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 14, 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
5 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 twodimensional figures. Point: a precise location or place, usually represented by a dot Line: a straight line that goes on forever or infinitely Line Segment: a part of a line X = Point X, or X A B = Line AB, or AB C D = Line segment CD, or CD Example: Draw and label the geometric objects in the table below. Write object names a second way. Geometric Object Name Point T Line PQ Line Segment XY Directions: Complete the Table. Geometric Object Name 1. Point F Draw the Object Draw the Object Write Object Name Another Way PQ XY Write Object Name Another Way Sample Daily Lesson  Student Response Page 2. Line AB 3. Line Segment RS 4. Explain the difference between a line and a line segment. 5
6 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 twodimensional 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
7 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 twodimensional figures. Example A: Ray: Angle: B A B = Ray AB, or AB. A Vertex C Example B: Draw the geometric objects in the table below. = angle BAC, or CAB. Geometric Object Name Draw the Figure Write Object Name Another Way Geometric Object Name Draw the Figure Write Object Name Another Way Ray BC Directions: Complete the table. BC Angle LMN Angle EFG EFG Angle QRS Geometric Object Name Draw the Figure Write Object Name Another Way Geometric Object Name Draw the Figure Write Object Name Another Way Sample Daily Lesson  Student Response Page 1. Angle ABC 3. Angle PQR 2. Ray QR 4. Angle DEF 5. Explain the attributes of an angle. Use the word vertex in your explanation. 7
8 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 twodimensional 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 15 on your own. For problems 13 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 45, 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
9 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 twodimensional figures. Parallel lines are two lines that never cross because they are the same distance apart for their entire length. Perpendicular lines are lines that cross or intersect at right angles (90 ). Examples: A. X Y B. Line QR is perpendicular to line ST. C D S Q R These lines are. T Directions: Write whether each pair of lines is parallel, perpendicular, or neither Sample Daily Lesson  Student Response Page Directions: Draw pairs of lines that make the statement true. 4. Draw line LM parallel to line XY. 5. Draw line DE perpendicular to line FG. 9
10 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 twodimensional figures. Sample Daily Lesson Teacher Lesson Plan Lesson Objective: Students will identify angles, parallel lines, and perpendicular lines in twodimensional figures. Introduction: Today we are going to learn how to identify angles, parallel lines, and perpendicular lines in twodimensional figures. Twodimensional 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 90degree 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 twodimensional 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 13 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 twodimensional 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
11 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 twodimensional figures. Parallel: two lines that never cross because they are the same distance for their entire length Perpendicular: lines that intersect or cross at a 90degree angle Example A: Example B: Q A B R S Acute angle is less than 90 C D X Z Right angles (2) Y Obtuse angle is greater than 90 Obtuse angle M Acute angle Parallel sides Perpendicular sides N O Right angle is exactly 90 Notice the box in the corner. This tells that it is a right angle M N O P W X Right angles Obtuse angle Acute angle Parallel sides Perpendicular sides Right angle Obtuse angles Acute angles Parallel sides Y Z Perpendicular sides 3. Explain why a quadrilateral without perpendicular sides does not have any right angles. Sample Daily Lesson  Student Response Page 11
12 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 twodimensional 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
13 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
14 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify Twodimensional Figures Lesson: #5 Standard: 4.G.2 Classify twodimensional 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 twodimensional 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 twodimensional 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 twodimensional 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 twodimensional 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
15 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify Twodimensional Figures Lesson: #5 Standard: 4.G.2 Classify twodimensional 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. Example: Parallelogram Trapezoid Right Triangle Parallel Sides Both Perpendicular Sides Parallelogram Trapezoid Right Triangle Rectangle Directions: Draw the following figures on the Venn Diagram according to their sides. Sample Daily Lesson  Student Response Page Parallel Sides Perpendicular Sides Both 15
16 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify Twodimensional Figures Lesson: #6 Standard: 4.G.2 Classify twodimensional 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 twodimensional 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 twodimensional 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
17 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify Twodimensional Figures Lesson: #6 Standard: 4.G.2 Classify twodimensional 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. Right: Acute: Obtuse: Right Triangle Square Parallelogram Equilateral Triangle 1 Right Angle 4 Right Angles 2 Acute Angles 3 Equal Sides 2 Acute Angles 4 Equal Sides 2 Obtuse Angles 3 Equal Acute Angles Example: Classify each figure above (some figures fit into more than one category). At Least One Right Angle At Least One Acute Angle At Least One Obtuse Angle Right Triangle Right Triangle Directions: Classify each figure below (some figures fit into more than one category). At Least One Right Angle At Least One Acute Angle At Least One Obtuse Angle Sample Daily Lesson  Student Response Page Rhombus Rectangle Right Triangle Square Equilateral Triangle Parallelogram Pentagon 17
18 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify triangles Lesson: #7 Standard: 4.G.2 Classify twodimensional 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 14 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
19 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classify triangles Lesson: #7 Standard: 4.G.2 Classify twodimensional 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. Right Triangle Obtuse Triangle Classifying Special Triangles Acute Equilateral Triangle Triangle Isosceles Triangle Scalene Triangle Example: 1' 2' 3' Angles Sides Directions: Write the name of each triangle as it would be classified by both its angles and sides. 1. Angles Sides 5" 5" 5" 2. 8" 8" Sample Daily Lesson  Student Response Page 12" 3. 8" 4" 10" 4. 2" 2" 3" 19
20 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying quadrilaterals Lesson: #8 Standard: 4.G.2 Classify twodimensional 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 twodimensional 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 foursided 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 13 on your own. Use the diagram to help you answer the questions. Review: Review and discuss correct answers to problems 13. 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
21 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying quadrilaterals Lesson: #8 Standard: 4.G.2 Classify twodimensional 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. All foursided, two dimensional objects are quadrilaterals. Rectangle: Parallelogram: Square: Example: At least one right angle Classifying Quadrilaterals Both At least one pair of parallel sides Directions: Using the diagram above, answer the questions below. 1. Why does the square fit into both sections of the diagram? Sample Daily Lesson  Student Response Page 2. Circle the shape with exactly one right angle. Explain why it is in its appropriate place on the diagram. 3. Draw a figure that is not a square but would still fit in the same Venn Diagram section as the square. 21
22 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying twodimensional 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 twodimensional 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
23 Common Core Standards Plus Mathematics Grade 4 Domain: Geometry Focus: Classifying twodimensional figures Evaluation: #2 Equilateral Isosceles Scalene 15' 5' 5' 6' 6' 5' 12' 17' Acute Obtuse Right 5' Parallel Lines Quadrilateral Directions: Answer problems 14. 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
24 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 twodimensional figures. 4.G.2: Classify twodimensional 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 (Student Worksheet) Protractor Lesson Objective: The students will classify twodimensional 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 18, E1E2. The students will also review the content and academic vocabulary in the Measurement and Data Standard 6. Students will: Draw a twodimensional figure that has parallel lines. Classify parallel and perpendicular lines in twodimensional 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 ) 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
25 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 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 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
26 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
27 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
28 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 Identify Place Value up to 1,000, NBT.1: Recognize that in a multi digit whole 3 Understand Place Value Patterns number, a digit in one place represents ten times Understand Place Value Patterns what it represents in the place to its right E1 Evaluation Place Value Word Form of Numbers NBT.2: Read and write multi digit whole 6 Expanded Form numbers using base ten numerals, number Standard Form names, and expanded form. Compare two multi digit numbers based on meanings of the digits in Whole Number Forms each place, using >, =, and < symbols to record the results of comparisons. E2 Evaluation Forms of Numbers Compare Numbers NBT.2 10 Compare Numbers Rounding Numbers 4.NBT.3: Use place value understanding to round Rounding Numbers multi digit whole numbers to any place Evaluation Comparing and Rounding Whole E3 Numbers 4.NBT.2, 4.NBT P1 Performance Lesson #1 Understanding Numbers (4.NBT.1, 4.NBT.2, 4.NBT.3) Add Multi digit Whole Numbers Add Multi digit Whole Numbers Subtract Multi digit Whole Numbers 4.NBT.4: Fluently add and subtract multi digit Subtract Multi digit Whole Numbers whole numbers using the standard algorithm Evaluation Add and Subtract Multi digit E4 Whole Numbers Multiplication of Whole Numbers 4.NBT.5: Multiply a whole number of up to four digits by a one digit whole number, and multiply 18 Multiplication of Whole Numbers two two digit numbers, using strategies based on 19 Multiplication of Whole Numbers place value and the properties of operations Multiplication of Whole Numbers Illustrate and explain the calculation by using equations, rectangular arrays, and/or area E5 Evaluation Multiplication of Whole Numbers models Dividing Whole Numbers 4.NBT.6: Find whole number quotients and remainders with up to four digit dividends and 22 Dividing Whole Numbers one digit divisors, using strategies based on place value, the properties of operations, and/or the 23 Dividing Whole Numbers relationship between multiplication and division. 24 Dividing Whole Numbers Illustrate and explain the calculation by using E6 Evaluation Dividing Whole Numbers equations, rectangular arrays, and/or area models Dividing Whole Numbers Dividing Whole Numbers Dividing Whole Numbers 4.NBT Dividing Whole Numbers E7 Evaluation Dividing Whole Numbers P2 Performance Lesson #2 Working with Operations (4.NBT.4, 4.NBT.5, 4.NBT.6) TE Page St. Ed. Page DOK Level 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 (Operations and Algebraic Thinking Standards 4.OA.1 4.OA.5) 1 Commutative Property of Multiplication 4.OA.2: See Week 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 Represent Verbal Statements as Equations Represent Verbal Statements as Equations E1 Evaluation Multiplicative Comparison 4.OA.1, 4.OA 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 Multiplicative Comparison Problems Multiplicative Comparison Problems Distinguish Multiplicative & Additive Comparisons E2 Evaluation Multiplicative Comparison Multiplicative Comparison Problems 4.OA Multiplicative Comparison Problems Multistep Word Problems 4.OA Multistep Word Problems E3 Evaluation Word Problems 4.OA.2, 4.OA 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 Multistep Multiplication Word Problems Multistep Word Problems Multistep Word Problems E4 Evaluation Multistep Word Problems Division Word Problems with Remainders 4.OA Division Word Problems with Remainders Division Word Problems with Remainders Division Word Problems with Remainders E5 Evaluation Solving Division Word Problems with Remainders Multiples of Whole Numbers 4.OA.4: Find all factor pairs for a whole number in Finding Factor Pairs for Whole Numbers the range of Recognize that a whole number is a multiple of each of its factors. 23 Finding Factor Pairs for Whole Numbers Determine whether a given whole number in the Recognize Prime and Composite Numbers E6 Evaluation Multiples and Factors range is a multiple of a given one digit number. Determine whether a given whole number in the range is prime or composite DOK Level P3 Performance Lesson #3 Understanding Operations (4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4) Learning Plus Associates 29
30 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 Identifying the Rule for Arithmetic Patterns Generate Geometric Patterns Identifying the Rule for Geometric Patterns E7 Evaluation Pattern Rules Identify and Explain Features of Arithmetic 29 Patterns Identify and Explain Features of Geometric Patterns 4.OA.5 31 Generate Growing Shape Patterns Identify the Rule for Growing Shape Patterns E8 Evaluation Feature of Patterns P4 Performance Lesson #4 Generate and Analyze Patterns (4.OA.5) 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 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 Learning Plus Associates
31 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) 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 Relative Size of Measurement Units 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 Measurement Conversion Metric Measurement Equivalents 4.MD Comparing Metric Measurements E2 Evaluation Metric Measurement Equivalents 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 Word Problems Involving Measurement Units Word Problems Involving Measurement Units Word Problems Involving Measurement Units E3 Evaluation Word Problems with Measurement Units P5 Performance Lesson #5 Conversion Factor (4.MD.1, 4.MD.2) Finding Perimeter of a Rectangle 4.MD.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems Finding Area of a Rectangle Perimeter/Area in Real World Problems Perimeter/Area in Real World Problems Evaluation Perimeter and Area of a E4 Rectangular Figure P6 Performance Lesson #6 Area and Perimeter (4.MD.3) 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 Reading a Line Plot Solve Problems Using a Line Plot Solve Problems Using a Line Plot E5 Evaluation Line Plots P7 Performance Lesson #7 Plotting Data (4.MD.4) DOK Level 2013 Learning Plus Associates 31
32 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 Using a Protractor to Measure Angles MD.6: Measure angles in whole number 23 Using a Protractor to Measure Angles degrees using a protractor. Sketch angles of Using a Protractor to Sketch Angles specified measure E6 Evaluation Measurement of Angles 4.MD.5, 4.MD Composing and Decomposing Angles 4.MD.7: Recognize angle measure as additive. When Finding Unknown Angles an angle is decomposed into non overlapping parts, the angle measure of the whole is the sum of the Finding Unknown Angles angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a Angles in Real World Problems diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the E7 Evaluation Angles unknown angle measure P8 Performance Lesson #8 All About Angles (4.MD.5, 4.MD.6, 4.MD.7) Points, Lines, and Line Segments Draw and Distinguish Between Rays and Angles 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 dimensional figures. Identify Angles, Parallel, and Perpendicular 4 Lines in Two Dimensional Figures E1 Evaluation Identify Geometric Objects Classify Two Dimensional Figures Based on 5 Their Sides Classify Two Dimensional Figures Based on 4.G.2: Classify two dimensional figures based on 6 the presence or absence of parallel or Angle Measurement perpendicular lines, or the presence or absence of 7 Classify Special Triangles angles of a specified size. Recognize right Classifying Quadrilaterals triangles as a category, and identify right triangles Evaluation Classifying Two Dimensional E2 Figures P9 Performance Lesson #9 Lines, Angles, Figures (4.G.1, 4.G.2) Line of Symmetry Line of Symmetry 4.G.3: Recognize a line of symmetry for a two dimensional figure as a line across the figure such Line of Symmetry that the figure can be folded along the line into matching parts. Identify line symmetric figures and draw lines 12 Line of Symmetry of symmetry. E3 Evaluation Lines of Symmetry P10 Performance Lesson #10 Symmetry (4.G.3) DOK Level 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) 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 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 Learning Plus Associates 33
34 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 Equivalent Fractions Comparing Fractions 4.NF.2 See Below Comparing Fractions Evaluation Equivalent Fractions and Comparing Fractions 5 Comparing Fractions E1 4.NF.1, 4.NF 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 Comparing Fractions Equivalent Fractions Equivalent Fractions Evaluation Equivalent Fractions and Comparing Fractions 9 Add and Subtract Like Fractions E NF.3a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole Decomposing and Composing Fractions 4.NF.3b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording 11 Decomposing Fractions each decomposition by an equation. Justify 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 = /8 = 8/8 + 8/8 + 1/8. 12 Decomposing Mixed Numbers E3 Evaluation Composing and Decomposing Fractions 4.NF.3a, 4.NF.3b P11 Performance Lesson #11 All About Fractions (4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b) 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 Adding Mixed Numbers Subtracting Mixed Numbers Subtracting Mixed Numbers E4 Evaluation Add and Subtract Mixed Numbers Add Fractions to Solve Word Problems DOK Level 18 Subtract Fractions to Solve Word Problems 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 P12 Performance Lesson #12 Adding and Subtracting Fractions (4.NF.3c, 4.NF.3d) Learning Plus Associates
35 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 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) Multiplying Fractions by Whole Numbers 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 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 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 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 Operations in Fraction Word Problems having like denominators, e.g., by using visual fraction models and equations to represent the problem Evaluation Operations in Fraction Word E7 Problems 4.NF.3c, 4.NF.4d P13 Performance Lesson #13 Multiplying Fractions NF.5: Express a fraction with denominator 10 as an 29 Converting Fractions  10ths to 100ths equivalent fraction with denominator 100, and use this Add Fractions technique to add two fractions with respective denominators 10 and NF.6: Use decimal notation for fractions with 31 Convert Fractions to Decimals denominators 10 or 100. For example, rewrite 0.62 as Decimals on a Number Line 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram E8 Evaluation Converting Fractions 4.NF.5, 4.NF Compare Decimals Compare Decimals 4.NF.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons Compare Decimals are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by 36 Compare Decimals using a visual model. E9 Evaluation Compare Decimals P14 Performance Lesson #14 Fractions and Decimals (4.NF.5, 4.NF.6, 4.NF.7) 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) 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
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