Ali Elliott's List: M405

• • Working Mathematically:
    
    Measure the area, deciding on the best measuring tools for the job.
    Compute the area of the space provided.
    Problem solving - what items can we comfortably fit in the area, how many.
    Using scale to draw the plans.
    Working out the cost - how much can we spend?
    
    This is an authentic lesson plan which incorporates many KLAs.

• • This YouTube clip includes the following mathematical lesson ideas:
    
    Making a Mud Cake
    Measuring, estimating
    
    Tree faces
    Symmetrical / asymmetrical
    
    Sand Sculptures
    Volume, area, perimeter, problem solving and estimation (as you only have the one lot of sand to create all three sculptures).
    
    Water Clock
    Problem solving skills.

• When reminded to check their solutions,   pupils often limit their checking to the execution of the algorithms to   ensure the attainment of a correct answer to the given word problem.   They seldom apply their common sense knowledge and make realistic   consideration about the problem context.
• Only 23% of the students were   able to proceed to deduce that the number of buses required is 32. Most   students gave an answer (e.g., 31 remainder 12 or 31 ) that did not    make sense when the problem statements were taken seriously. Schoenfeld   (1991) describes these students as engaging in suspension of   sense-making. They fail to see that the solution does not make sense in   relation to the given problem statements.
• Apparently, children   engage in suspension of sense-making irrespective of age and cultural   settings. Greer's study involved 13- and 14-year old Irish students   while Verschaffel et als.' study involved 10- and 11-year old Belgium   children.
• A realistic word problem is   one in which pupil needs to take into consideration the realities of   the context of the problem statements. Correct application of   arithmetic operation(s) does not often lead to the correct solution to   such context-dependent word problem.
• The importance of making connections between school mathematics and   real world has been recognized but, as shown in this study, we cannot   expect pupils to make these connections spontaneously. Pupils must be   shown how school mathematics can be applied to real world situations,   they need to be encouraged to avoid surface processing of information   given in problem text. They have to be exposed to different types of   word problems in school, in particular, the so-called context problems   that invite and sometime force them to use their real-world knowledge   and personal experience to analyse and solve the problems. Pupils would   be more interested in mathematics if they can see how mathematics is   used in their daily life. Lots of problems found in the textbooks are   unreal. These problems would not motivate pupils to solve problems,   they only confirm what the pupils belief that mathematics has nothing   to do with the real world. To change this belief, greater attention   must be given to establish the links between school mathematics and the   real-world settings
• teaching problem solving should also include teaching   pupils to recognize the assumptions and constraints underlying   different problem situations and use reasonable judgment to obtain   reasonable solutions. In addition, pupils should be given opportunities   to talk about the problems and their solutions.
• These problems should not be meant only   for the 'better' pupils. They should be interspersed among the standard   word problems with no special symbols to set them apart as the problems   to be done by more able pupils when they want to think.

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• PDF document.
• Mathematician's Tool Shed
• In other words, across the world, all students can be learning to work like a mathematician in best practice classroooms. There is no reason for mathematics to be taught the way it always has been.
• Strategy Tool Shed. The visual nature of the presentation will add meaning for many students, and the addition of the multiple intelligences checklist will appeal to many teachers.

• Maths Charter
   WORKING MATHEMATICALLY

   

  STATEMENT

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• As part of our geometry unit, the students work in pairs to create geometric solid mobiles. They build their geometric solids from paper nets that they cut, fold, and glue. We attach the nets to wire coat hangers with yarn.
• Our geometric solid mobiles hang in the window.

• we talked about the angles of a triangle and also the three different kinds of triangles.  Instead of them just doing a worksheet, we had them build them with pretzels.
• They LOVED it!

• • Lyrics:
    
    Leg, Leg, Isosceles, parallel lines.
    Ray, ray, point, point, line segment, midpoint
    Bisect, congruent segments.
    
    Acute, right, obtuse, straight
    Diameter of a circle
    Radius, circumference
    Minor arc, major arc, arc of a circle
    
    Tangent to a circle, point of tangency
    Right triangle, right triangle
    This is the hypotenuse
    Trapezoid, pentagon, hexagon, square
    Rhombus, rectangle, parallelogram uh!
    
    Positive slope, negative slope, parallel lines
    Skew lines never touch uh!
    
    Perpendicular, perpendicular
    Undefined, zero slope
    Undefined, zero slope
    Vertical angles are congruent, are congruent.
    This is congruent, this is congruent, this is congruent.
    
    Adjacent angles, adjacent angles
    Linear pairs are supplementary.
    Angle bisector.
    Dilation, dilation, rotation, rotation, reflection, reflection,
    translate right, translate left, translate up, translate down.
    Line of symmetry, symmetry, symmetry, symmetry.
    Geometry, geometry, geometry, geometry.

  • Remember to download clip for class instead of showing on IWB direct on YouTube - due to occassional inappropriate comments below video clip.

• vertical, horizontal, perpendicular, parallel, converge, diverge, diagonal,  perimeter, area.

• find ways to reach all learners
• multiple intelligences
• Provide the visual learners in your classroom with colorful illustrations and graphics while they are learning fractions. Differentiate a lesson on comparing fractions by allowing these students to select from colored pencils or crayons to shade in fraction strips. Use lots of visual aids when working with these types of learners. Sandwich bags filled with colorful candy, snap cubes and counting bears are all useful manipulatives to keep on-hand.
• Help the auditory learners in your class to develop poems and chants that can aid in their understanding of third grade fraction concepts. Be prepared to give oral directions to these types of students and encourage them to verbalize their steps as they complete tasks such as identifying equivalent fractions. Auditory learners may particularly benefit from working in pairs or in small groups where they can speak and interact with classmates.
• hands-on activities like cutting out fraction strips for comparing, adding and subtracting fractions. Allow time for them to physically demonstrate parts of a group using their own bodies. Give them the chance to get up and move in between assignments. Fraction games that involve using manipulatives are great for your kinesthetic learners.
• individual personalities and interests of the students in mind when teaching fractions to your third graders
• students who are into sports may enjoy learning about fractions that involve soccer balls, footballs and basketballs. Students who like cooking activities may catch on to a fraction concept by actually dividing up a pizza or a batch of fresh-baked cookies

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• • Select difficulty level and time limit as per class/student abilities.

• Nine color-coded 3-1/2" quiet, soft foam fraction circles numbered with fractions. Set includes: 1,-1/2, 1/3,-1/4, 1/5, 1/6, 1/8, 1/10 and 1/12