District 11 Educational Support Services
Mathematics












 

Grade 4: August Unit
 Estimation and Reasonableness (@10 days)

Overview
 Video introduction. August focuses on critical math skills and includes lessons on estimation and computation with different strategies with reasonableness, congruent geometric shapes, computational review with multiplication facts through 12, differing complex patterns, interpreting different representations of data with reasonableness, and problem solving using all operations. You will gain a deeper understanding of congruency, computation, and the reasonableness of answers.

Daily Lessons 1 2 3 4 5 6 7 8 9 10 11-12 13 14-15 16 17-19

 

Enduring Understandings are important ideas that students should carry with them years beyond the instruction received this year.

  •  Mathematics is dependent on place value. A sense of number is necessary to communicate the reasoning used in problem solving.

Essential Questions are the most important “big picture” questions students should be able to answer after completing learning activities.

  • In what ways does number sense, including estimations and mental math help solve real-world problems?

  • What makes for a quality solution?

  • What essential components are needed to solve real-world problems?

CSAP Tested Standards  Highest Frequency High Frequency Other Standards and E-Skills

 Highest Frequency = the timing, intensity and level of accountability is extremely high because mastery of these skills will must be demonstrated in multiple test items on CSAP at this grade level.
 High Frequency = the timing, intensity and level of accountability is high because mastery of these skills will be tested at this grade level.
 Other Standards and E-Skills = the timing, intensity, and level of mastery are not urgent. It should be introduced during this time so students can experience the concept and return in future quarters to strive towards mastery.

 

Standard 1: Number Sense (August)
 Read, write and order numbers to hundred thousand
 Recognize and explain different strategies for estimating and computing.
Recognize and explain different strategies for estimating and computing with money.
Standard 4: Geometry (August)
 Identify, describe and give examples of congruent shapes.
Identify, classify and compare 2-dimensional shapes and use vocabulary to describe the attributes (i.e., number of sides, vertices, angles and parallel sides).
Recognize and draw lines of symmetry in a given shape.
Identify a line of symmetry for a given shape.
Standard 5: Measurement (August)
Tell time in hours and minutes, including a.m. and p.m., using analog and digital displays.
Standard 6: Computation (August)
 Review computation without context (addition, subtraction, multiplication, division facts)
 

Everyday Mathematics Resources Math Expressions Resources
Everyday Mathematics requires lesson by lesson presentation to preserve the spiral nature of the instruction. The page links provided on the Unit Chart are for comparison only. Teachers are advised to follow the district-determined EDM pacing calendar.
 Everyday Math Games for Fourth Grade		 Click the following links to find books and games correlated to units of instruction K - 5th grades.

MX Literature Lists

MX Game Lists


 

August  Standards

Everyday Mathematics

Math Expressions

Determining reasonableness using estimation and computation

Multiple pages under Estimation, Rounding, and Problem Solving/estimation

Multiple pages under Estimation, Rounding, and Problem Solving/estimation
Congruent Shapes pp. 275 pp. 177F, 178-179, 181, 183, 192, 224, 397E, 408, 414-417, 427

Computation review

Multiple pages under Addition, Subtraction, Multiplication, Division, and Review and Assessment

Multiple pages under Addition, Subtraction, Multiplication, Division, and Review and Assessment


Resources for Teachers

  • For Scott Foresman and Houghton Mifflin page numbers click here.

  • Mountain Math, Math Their Way, Creative Mathematics (Kim Sutton), Math Solutions (Marilyn Burns), Math Perspectives (Kathy Richardson) (if your building has purchased these resources)

  • Your particular math series (see chart on Unit pages listing page numbers to support standards)

  • Success Maker (ask your LTE)

  • Exemplars (CSAP style problem solving with writing, 4-point rubrics, and sample student papers available on D11 website For Teachers pages)

  • Math Keys (electronic manipulative – ask your LTE)

Assessments
Teacher observation, Hundreds Chart, Calendar Activities, Math Bingo, Manipulative/White Board/Slate assessments, EDM assessment CD’s.
 


Parents

You can support your fourth grader’s math understanding by asking questions about his/her math homework. Asking your student to explain what is happening in the math work helps your child learn to communicate the process and thinking. It also helps transfer the concept from short term to long term memory.
 

 

 

Standard: Geometry
 Unit 1: Lessons 1 - 16  
 Subject: Geometry
Grade Level: 4th
Recommended Timeframe or Quarter: 1st and early 2nd quarter
 Instructional Unit Title: Using Geometric Shapes to Solve Problems
Approximate Duration (15 - 17 Days):  (some days will have multiple lesson; final lesson will take multiple days)
Enduring Understanding/s: Geometry builds our world.
 Essential Questions: What is geometry? How do we use geometry in our everyday lives? How does geometry build our world?
 Highest Frequency Standards:
4.2: Identify 2-dimenstional geometric shapes, identify and describe attributes of geometric shapes; identify parallel lines, identify the properties of a given figure, identify geometric shapes given their attributes.
4.3: Determine the area of a rectangle and creating rectangles of a given area; solve problems involving the perimeter of polygons; find perimeter and are of squares and rectangles on a grid.
High Frequency Standards: 5.1: Measuring and determining perimeters of polygons; determining the area of a rectangle on a grid.
Other Standards and E-Skills: 5.1:Choose an appropriate tool to measure a specified attribute; measure accurately. 6.5:Use appropriate operations to solve a problem. Understand the relationship of ratios in scale.

Overview
 In this unit, you are going to find 2-dimensional shapes used in both the classroom and your house, describe them in mathematical terms, learn how to find area and perimeter, discover ration, and then use what you have learned to create a blueprint of our classroom.

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Lesson 1: Scavenger Hunt
 Duration: @ 45 minutes or 1 class period


 Materials: The Greedy Triangle by Marilyn Burns and The Art of Shapes: for Children and Adults by Margaret Steele and Cindy Estes. Assign partners in a way that works best for your class.

Assessment: Lesson 1 checklist: Does student have a minimum of 5 different shapes? Participation in discussion: Can student describe a polygon?
 

Activities

  1. How does geometry build our world? Read the essential question on the board “What is geometry?” Turn to a partner and share your ideas on an answer to the question. When you think you and your partner have an answer, write it on your response board. In 5 minutes we will share answers. See if students arrive at geometry being the study of shapes and relationships of shapes.

  2. Look around the classroom and find as many different 2-dimensional shapes as you can.  Try to find at least 5 different shapes, not different sizes of the same shape. Write or draw them on your paper.

  3. Discuss similarities and differences of the shapes you have found with a partner and be ready to share your findings with the class.

  4. Answer the question with your partner: How do you define (describe) a shape? You will need a paper, clipboard, and pencil for this activity.

  5. Group Discussion: How do you describe a rectangle? A parallelogram? A square? A rhombus? A trapezoid? Can any shape be described using more than one name? Did you find shapes with more than 4 sides? Did you find any with less than 4 sides?

  6. Your homework tonight is to do a scavenger hunt at home to find as many different shapes as possible.
     Lesson 1 Checklist for Geometry Scavenger Hunt

  7. How would you answer the questions on the board? Write down your thoughts in your math log to come back to later in the unit.

  8. Vocabulary: (Create a Frayer model booklet for vocabulary, or Dinah Zyke booklet) polygon, quadrilateral, parallelogram, rhombus, rectangle, square, trapezoid, parallel, perpendicular, intersecting, lines, line segments, right angles, sides, vertices, area, perimeter, scale, ratio. As you introduce vocabulary, have students write it down, or draw a picture and include examples and non-examples.
     Frayer Model for Vocabulary

Differentiation
 Extension: Identify the 3-dimensional objects represented in the classroom. Find the number of faces, edges, and vertices. Describe the 2-dimensional shapes on the faces in terms of their attributes.
Support: If students are having difficulty identifying shapes, a template of shapes or a cutout of each shape can be provided and they can match the shapes in the classroom to the shapes on the template or cutout.

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Lesson 2: Definitions and Descriptions of Polygons
 Duration: @ 45 minutes or 1 class period


Materials: The Greedy Triangle, by Marilyn Burns, straws, twist ties, and scissors, or geoboards and rubber bands, or dot paper.

Assessment: Lesson 2 Checklist: Did students accurately construct polygons?

 

Activities

  1. Come to the carpet and listen to this book, The Greedy Triangle by Marilyn Burns. After we read it, each of you will get straws and twist ties or geoboards and rubber bands to construct your own polygons.

  2. Straws should be used in whole lengths, half lengths, and quarter lengths. You will need 4 straws of each size and 8 twist ties, or 1 geoboard and 4 rubber bands, or dot paper, or go to the MathKeys computer program for geometry, or go to the website http:/nlvm.usu.edu/en/nav/vlibrary.html  for virtual manipulatives for geoboards.

  3. Lesson 2 Checklist for Polygon Construction

  4. Make plane shapes using your materials. When you have constructed one, raise your hand and I will come check it. Be prepared to name it and tell me why that is its name. Then you may continue to construct other polygons.

Differentiation: Students may check back with the book if they are having difficulty.
 Extension: Strategies for Higher Order Thinking

Support: SIOP Strategies: Eight Components of Sheltered Instruction Observation Protocol


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Lesson 3: Exploration of Lines Using Geometry
 Duration: @ 45 minutes or 1 class period
Materials: Students will need pencils and straightedges for drawing their own lines. Rethink and revise opportunities should be provided for students. Check worksheet as students are finished and give immediate feedback. Lesson 3 Identifying Lines Worksheet
Assessment: Answer this question in your math log: Why is it true that all squares are rhombuses but not all rhombuses are squares?

Activities

  1. Everybody stand up. Put both arms straight in the air above your head. If they are exactly straight up, will they ever cross? This is the definition of parallel lines. Quadrilaterals can be defined in terms of how many pairs of parallel lines they have. Now cross angle your arms toward each other. If two lines are continued on and will eventually cross, they are called intersecting lines. Think of the intersections of streets.  Now keep your left arm straight, but bend your right arm at the elbow and cross it over your left, forming as close to a right angle as you can. We call these perpendicular lines, when intersecting lines form right angles. Now you will identify these lines on the worksheet, and draw your own lines according to the directions. Remember that lines have arrows on each end, showing they extend beyond what is drawn on the paper. Line segments have endpoints, and do not go further than you see on the paper. Lesson 3 Holistic Rubric for Classification Question

  2. Discuss the definitions of parallel lines, perpendicular lines, and right angles, and use them to describe plane figures in terms of attributes. Use the holistic rubric for classification question to assess answer in math log.

Differentiation
Extension: What are all the names a square could have? Why? How do you know?
Support: Show a physical square and rhombus in small group. Discuss right angles, length of sides, and parallel lines to lead students to correctly answer the question.

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Lesson 4: Practice Matching Geometric Figures with Correct Geometric Descriptions
 Duration: @ 45 minutes or 1 class period.  Lessons 4 and 5 may be combined in 1 class period.

Materials: Teachers will need to create a concentration game on cardstock with descriptions and pictures of quadrilaterals. See EDM Math Masters pages 1 and 231 for ideas, or another resource for pictures of geometric figures and descriptions.
Assessment: Include appropriate and varied assessments from the Assessment Blueprint EDM Math Master page 231 (Geometry Matching) for assessment worksheet.

Activities

  1. You will use the concentration cards to match geometric figures with their correct descriptions.

  2. Lesson 4 EDM Geometry Matching

Differentiation
Extension: Strategies for Higher Order Thinking
Support: SIOP Strategies: Eight Components of Sheltered Instruction Observation Protocol

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Lesson 5: Using Quadrilaterals to Construct a Picture
Duration: @ 45 minutes or 1 class period (May be combined with lesson 4 if time allows)

Materials: The Art of Shapes for Children and Adults, pattern blocks or shape blocks, construction paper
Assessment: Go back to your math log from the first day. How did you answer the question “How does geometry build our world?” Would you change your answer? Would you expand it? Continue writing down your thoughts. Teacher observation of appropriate use of materials.

Activities

  1. First, we will read the book The Art of Shapes for Children and Adults. Pay close attention to the shapes you see the artists use. Discuss the use of shapes in architecture. Bring in Matisse prints if possible, or talk to your art teacher.

  2. Then you will use squares, rectangles, trapezoids, parallelograms, and rhombuses to construct your own picture on construction paper.

  3. We will place these around the room and let everyone see how each person created a unique picture using geometric shapes.

  4. Have a variety of construction paper shapes in various colors for students to glue onto another whole piece of paper.

Differentiation
Extension: Strategies for Higher Order Thinking
Support: SIOP Strategies: Eight Components of Sheltered Instruction Observation Protocol

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Lesson 6: Finding Perimeters of Rectangles and Squares
 Duration: @ 45 minutes or 1 class period
Materials: plain paper, pencils, grid paper, straight edge/ruler, Lesson 6 Perimeter of Rectangles Worksheet
Assessment: See embedded assessment within the lesson. Check student work and give immediate feedback.
Activities

  1. How do we use geometry in our everyday lives? Perimeter is the distance around a closed figure.

  2. When do you think you would need to find the perimeter of something? (Allow students to come up with scenarios-fencing, wallpaper border, etc)

  3. The way we find perimeter is adding all four sides together. You will do activities with perimeter today-one in which you will draw rectangles of a required perimeter, and one in which you find the perimeter of rectangles. Using a transparency of grid paper, model that what students are counting are the individual lines on each square, so they have to count 2 sides of the corner squares to come up with the correct number for the perimeter.

  4. I am going to show you how to find the perimeter first, then you will use grid paper and a straightedge to draw your own rectangles or squares.

  5. You will need to draw rectangles or squares with perimeters of 12, 16, 18, and 24 units. 

  6. Then I will give you a worksheet without gridlines. You will need to use the perimeter formula of P= (2*length) + (2*width) to find the perimeters.

Differentiation
Extension:  Strategies for Higher Order Thinking

Support: Give students more opportunities with shapes on grid paper.


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Lesson 7: Areas of Rectangles and Squares
 Duration: @ 45 minutes or 1 class period
Materials: Grid paper, scissors
Assessment: Lesson 7 Checklist for Equal Area, Use the checklist for a yes/no evaluation, See embedded assessment within the lesson.
Activities

  1. How do we use geometry in our everyday lives?

    2.

  2. Allow students to experiment with different areas, then bring them back and show them the formula, along with the assignment.

  3. Area is the space inside a shape. When do you think you might need to know the area of something? (Students should give examples of carpet or tile in a room, wallpaper on a wall, and sod in a yard) Using grid paper we are going to cut out rectangles and squares. The number of squares inside the shape is the area.

  4. Now that you have tried cutting out different rectangles and squares, what have you learned about finding the area? (Usually someone has figured out that the number of squares across (base or length) multiplied by the number of squares high (width or height) equals the number of squares inside. Use this to explain the formula of length * width or base * height.

  5. Now I want you to use what you know about finding area and cut 1 rectangle AND 1 square that have the same area. You get to choose how large or how small they are, but they MUST have equal areas.

  6. Resources such as EDM 8.5, Student Journal 2 page 246 can be used to reinforce hands-on material. Use the textbook and student pages in place at your school to continue practice of this concept.

Differentiation
Extension: Strategies for Higher Order Thinking
Support: If you are still having trouble figuring out the area, count the squares inside, then check it using the multiplication.

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Lesson 8: Finding Area of Polygons, Parallelograms, and Triangles
Duration: @ 45 minutes or 1 class period

Materials:  transparencies of worksheet and grid paper to model, Lesson 8 Area of Triangles EDM Worksheet
Lesson 8 EDM Area of Parallelograms (additional resource)
Assessment:  Paper and pencil worksheets that are scored and given back to students for revision immediately-Triangle worksheet is from EDM Math Masters page 336.
Activities

  1. Remember that area is the space inside a given shape. Now we will look at parallelograms and triangles specifically. These shapes are not drawn exactly on the gridlines. You will have squares that have diagonal lines through them. How will you count these? (students should know they are divided into halves, and that 2 halves together-even of different squares- equal 1 whole).

  2. Look at EDM Student Math Journal 2 page 239 (or other resource showing polygons drawn on grid paper). Using what you know about area, and by counting the squares within a shape, estimate the area of each of these shapes. There is also the Area of Parallelograms worksheet attached for more practice without grids.

  3. Check student work and give feedback, then continue with lesson.

  4. You know the formula area for rectangles and squares (l*w). With parallelograms, you have to find the width, which is also called the height. How many squares high is the parallelogram in problem 2 (or whatever resource you are using)? (2 squares high)  How long in whole square units is this parallelogram? (5 squares long). We call the length of parallelograms the base. The formula for parallelograms and rhombuses is base * height.

  5. On grid paper, draw a parallelogram or rectangle. Now draw a diagonal line from one upper corner to the opposite lower corner (demonstrated on the overhead with a transparency of grid paper).

  6. What two shapes do you have now? (2 triangles). This is why the formula for the area of triangles is ½ base time height. A triangle is half of a rectangle or parallelogram, so the area must be half also.

  7. Now do the worksheet on area of triangles.

Differentiation
Extension: Strategies for Higher Order Thinking
Support: Have a transparency of grid paper ready to use for modeling for students who are struggling. See note within lesson also. Use whatever textbook resource you have for area of triangles, if your school does not use Everyday Math.

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Lesson 9: Practicing Perimeter and Area of Quadrilaterals and Triangles
Duration: @ 45 minutes or 1 class period, NOTE: Lessons 9 and 10 may be combined in 1 class period.
Materials: Grid paper and straightedges, graphic organizer of a table labeled similarities and differences.
 Lesson 9 Analytic Rubric for Similarities and Differences Table
Lesson 9 EDM Tennis Court Extension
Lesson 9 Table for Similarities and Differences of Rectangles
Assessment:  Check to see if students are using mathematical language to describe the similarities and differences.
Activities

  1. Take grid paper and construct at least three rectangles that have a perimeter of 24 squares and at least 3 rectangles that have an area of 24 squares.

  2. How are they the same? How are they different?

  3. Fill out the table noting the similarities and differences. Also, complete the worksheet for the area and perimeter of triangles.

  4. Discuss the similarities and differences as a class.

  5. Model using mathematical language to describe shapes in terms of parallel lines, right angles, and units.

Differentiation
Extension: Find all the possible combinations for an area and perimeter of 24. Graph the perimeters and areas by laying the rectangles on the X axis, making a point where it ends, and then laying it on the Y axis and making a point. EDM Math Master page 333, “The Tennis Court."
Support: Small group works together to complete the table, instead of individually.

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Lesson 10: Finding Perimeter and Area within the Classroom
Duration: @ 45 minutes or 1 class period (May be combined with Lesson 9 if time allows)

Materials: Paper, pencil, clipboard, rulers and meter sticks, Lesson 10 Rubric for Area and Perimeter Measurement
Assessment: Analytic Rubric
Activities

  1. Remember when you explored the classroom and found different geometric shapes.

  2. Now I want you to explore again, but this time you are looking for rectangles, squares, parallelograms (if there are any), and triangles.

  3. Once you find them, measure them in centimeters using your ruler or a meter stick, and find the area and perimeter.

  4. Write the name on your paper, along with a description of where the item is, and draw and label the shape, showing the measurements on your paper.

  5. Let me give you an example: I will draw the top of my bulletin board pin box. It is a square with 8 cm on each side. The area = 64 sq. cm., and the perimeter is 32 cm around.

Differentiation
Extension: Strategies for Higher Order Thinking
Support: Measure the top of something on your desk, describe its location in words i.e. the pushpin box on the left side of my desk, and draw it on the overhead with measurements per side. Then find the area and perimeter of the box using the formulas the class has learned

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Lessons 11 & 12: Scale vs. Sketch Drawings
Duration: @ 90minutes or 2 class periods
Materials: paper, pencils, Students will need the similarities and differences page for Lesson 11.
 Lesson 11 Rubric for Area and Perimeter (sketches)
Lesson 11 Table for Similarities and Differences of Sketches
Assessment: Math log questions: What are the ways in which our classrooms are the same and how are they different? Why is the kindergarten classroom different from ours?
Activities

  1. How does geometry build our world?

  2. How do we use geometry in our everyday lives?

  3. Pretend you are looking at our classroom from the ceiling (a bird’s-eye view) and sketch the perimeter of the classroom, then draw in the desks, bookcases etc. Use rectangles, squares, and other plane figures to represent each object in our classroom. Don’t include students. Then we will post them side by side and compare the similarities and differences gallery walk.

  4. Day 2: We will go to our kindergarten buddies’ classroom and sketch their classroom.

Assessment: Math log: If you were to do this drawing of our classroom again, how would you improve it? What would you do differently? Go back to the essential question “How does geometry build our world?” from the first day? Do you have anything to add to your thoughts?
Use the Lesson 12 Holistic Rubric to check student math logs for complete answers and justification of reasoning. Lesson 12 Holistic Rubric for Changes in Sketches Question
Read student math logs to gauge student understanding of differences between kindergarten needs and 5th grade needs, and their ability to self-assess and improve.
Differentiation
Extension: Strategies for Higher Order Thinking
Support: SIOP Strategies: Eight Components of Sheltered Instruction Observation Protocol

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Lesson 13: Scale and Ratio (map activity)
 Duration: @ 45 minutes 1 class period

Materials: pattern blocks, response boards, chalk or dry erase marker,
Assessment: Response board answers, Lesson 13 Checklist for Pattern Block Ratio
Checklist for pattern block ratio; Accurate answers on maps worksheet.
Activities

  1. A ratio is a relationship between numbers. For instance, take out your pattern blocks. For each yellow hexagon, you can fit 2 red trapezoids in the same space. This would be a ratio of 2 trapezoids to 1 hexagon. Find the ratio of blue rhombuses to yellow hexagons, and from green triangle to red trapezoids. Write them on your response boards.

  2. Check response boards for accurate answers. Reteach as necessary, modeling on the overhead if needed.

  3. Using what you found out about ratios, how can you look at a map, and know how far it is from one city to the next?  (Students should respond “by reading the map key or legend). Each inch equals a certain number of miles. The number of miles to an inch is a ratio. Look at the distances between cities.

  4. Using your ruler, measure the distance in inches, and then calculate the number of miles. You can use a T chart to help you.

  5. Find a class set of maps with a distance key. Often Scholastic News or other classroom publications will have them. If you can’t find one, you can always copy a portion of a road map. You will need to create your own questions sheet based on the map you have chosen.

Differentiation
Extension: Strategies for Higher Order Thinking
Support: SIOP Strategies: Eight Components of Sheltered Instruction Observation Protocol

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Lessons 14-15: Desktop Design
 Duration: @ 90 minutes or 2 class periods
   
Materials: Ruler, grid paper, questionnaire for taking notes, pencil
Transparency from yesterday is on overhead for reminder purposes.
Assessment:  Measurements and drawings are accurate and area and perimeter has been accurately calculated. Rubric is used for the actual desk design on grid paper.
Activities

  1. I will have already measured the most standard items- the desk, a 24-count box of crayons, a 6” X 8” pencil box, a 4” X 12” name tag and 3” X 3” coaster. Using the questionnaire sheet, check for accurate measurement first, then look at the designs using the rubric. *You may need to change the criteria on the analytic rubric depending on the size of your desks. Ours are 20 X 24, so that give us 480 sq. in. with which to work.

  2. Day 1: We are going to design the best way to arrange objects on our desks so we have the maximum amount of work space. You may have out your coaster for your water bottle, your crayons, and your pencil box. We don’t want to cover up the name tag, so it must have its own space also. First we each need to measure the desk, then your crayon box, pencil box, coaster, and name tag to the nearest inch.  Fill out the questionnaire showing the measurement of each object. Once you have measured each item, we are going to use ratio and scale to make a drawing of the items on the desks. Look at the transparency on the overhead. Each square will equal 2 inches of desk space. If the desk is 20 inches long and 24 inches wide, then I will draw a rectangle that is 10 squares long and 12 squares wide. What will I do if an object is an odd number of inches? (allow students to come up with the answer of using half a square). Continue until all objects have a representation drawn on the overhead transparency, but not necessarily in the best way for optimum work space.
    Lesson 14 Analytic Rubric for Desk Design
    Lesson 14 Questionnaire for Desk Measurements

  3. Day 2:  Now, going back to the activity we did yesterday, you are going to arrange the objects on your desk so you have the most work space as you can. Try to find at least 350 square inches (if desktop is 20 X 24 inches).*see teacher note. Remember, you cannot cover up your nametag, nor can you put the crayon box on top of the pencil box. Once you have arranged the items so you have the maximum amount of workspace, get the grid paper and draw in your nametag, water bottle coaster, crayon box, and pencil box according to the scale that each square equals 2 inches. Once you have all the objects in place, you will need to calculate the area you have left in which to work.

Differentiation
Extensions: Strategies for Higher Order Thinking
Support: Students may make cutouts instead of drawing them on the grid paper.

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Lesson 16: Comparing and Evaluating Desk Designs
 Duration: @ 45 minutes or 1 class period
Materials: Lesson 15 Holistic Rubric for Evaluation (Desk Design)
Assessment:  Use the Lesson 15 Holistic Rubric to check math log for complete answers to questions and justification of reasoning.
Activities

  1. We will put the desk designs around the classroom and take a gallery walk, looking at which ones met the criteria for the most workspace.

  2. Math log: What would you do differently now that you have seen other people’s drawings? Could you improve on your own?

Differentiation
Extension: Graph the workspace area from least amount to greatest amount. Find minimum, maximum, range, mode, and median.
Support: Emphasize positive feedback to others, and stress that improvement doesn’t mean their first attempt was “bad”.  Look for those that have the most workspace and point how the way in which they chose to arrange their items allowed them to have that much space. Maybe have a prize for the one with the most space.

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Lesson 17-19: Blueprint for the Classroom-Performance Unit Evaluation
 Duration: @ 135 minutes, or 3 class periods (another day may be needed)
Materials: Each group will need pencil, paper, and yard stick or tape measure, bring in house blueprints if you can as a real-world example.
Assessment:  Final Product Analytic Rubric; Holistic Rubric for Math log questions, Appropriate Assessment Samples: See assessment blueprint and individual documents included.
 Assessment Blueprint
 Lesson 16 Holistic Rubric for Evaluation of Unit
Lesson 16 Final Product Analytic Rubric

Lesson 17 Activities

  1. Discuss the house blueprints with the students and determine what scale works best for your classroom. Once that is established, model using a transparency how to draw the perimeter of the classroom, and model the size of one student desk. At this point, students should receive their own graph paper and begin the basic outline, and start cutting out the models for desks, bookcases, filing cabinets, etc. The teacher will need to have the list of measurements gathered by the students listed somewhere prominent in the classroom so everyone can see. If too many students are not finished by the end of day 3, this may need to be extended.
    Add as many additional lessons as necessary to complete this unit.
    Instructional Bulletin Board Ideas: architecture pictures of shapes, geometric bulletin board kits, blueprints

  2. How does geometry build our world? How do we use geometry in our everyday lives?

  3. You are going to use everything you have learned to create an accurate blueprint, to scale, of our classroom. You know how the sketches differed from the actual objects, and how some items were much larger or smaller than they should have been. That’s because we didn’t take the time to accurately measure the classroom, the desks, the tables, the bookcases, and the sink area the way we did when we created our desk arrangements.

  4. Today we are going to begin this process, then we will decide together what scale to use. After that, you will be on your own to create a blueprint showing where each major item is in the classroom, in an accurate relationship to the other objects.

  5. Make sure we have enough room for me to walk between the desks, and we must have room for the exit lane in case of fire or other emergency.

  6. We will begin today by measuring the perimeter of our classroom and the area of the major objects in the classroom to the nearest half inch. I will split you into 7 groups of 4, and each group will have a responsibility to complete their task accurately. Four groups will take the walls, one per group. Two groups will measure the teacher desks, filing cabinets, bookcases, tables, and sink area, one group working on the west side and one working on the east side. One group will measure a student desk and multiply it by the number of desks in the room.

  7. Each group should measure their assigned wall twice, buy different pairs of people, then compare and make sure you have accurate measurements.  If you don’t get the same answer (to the nearest half inch), go back and measure again.

  8. When all measurements are complete, and everyone in your group has agreed that you have the most accurate measurement possible, we will meet back together as a group and compile the measurements.

Lesson 18-19 Activities

  1. Now we know the measurements we have for our classroom. If we want to make an accurate model, we have to come up with our scale. For instance, on wall in our classroom is 29 feet, 6 inches long. If we have graph paper that has one-fourth inch squares, what would be a reasonable scale for our blueprint? After we decide on a scale, I will show you what the outline would look like on this transparency, and also how big a student desk would be. You may either use graph paper to actually cut out the number of desks, filing cabinets, tables, and other objects, and then place them on your outline, or you may draw them in. Either way, you will have the rest of today’s math time and tomorrow to finish this.

  2. When everyone is finished, we will hang the designs and take a gallery walk. We can look at the different ideas and vote on which way we think would be the best way to set up the class.

  3. Math log: What is the difference between scale drawings and sketch drawings? Which is harder? What part of this unit did you like the best? Which part was the most difficult for you?

Differentiation
Extension: Strategies for Higher Order Thinking
Support: SIOP Strategies: Eight Components of Sheltered Instruction Observation Protocol

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