Different Format for a PYP Maths Planner

I used to be a strong advocate for creating PYP planners for stand alone maths and can still see a lot of merit in them. 

But, lately I feel slightly dissatisfied because with the PYP planner format for maths stand alone because it makes a unit too teacher-driven and this makes inquiry-based maths learning difficult to achieve. For maths stand alone, unless you are willing to go the extra mile and complete all the profiles etc etc, it becomes a mammoth amount of documenting when it shouldn't be for maths.



So, I've been playing around with different ways we could create a PYP planner for maths that is perhaps more practical for teachers to use and more importantly to make maths unit more student driven and inquiry-based. 

The sample below isn't completed as we are still in the midst of our enquiries. 

What I like about it is that it ensures the provocations and pre-assessment wonderings give the students voice in what they will enquire into.  It values the student wonderings and ensures those wonderings drive our unit.

Tapping into student curiosities is the bedrock of inquiry-based classrooms and this should also happen with mathematical learning.  When the children explore what they really want to know rather than what a scope & sequence document dicates what they have to know, the learning instantly becomes authentic, inspiring and meaningful. I like to think those conceptual and skill understandings will have far more longevity in their memories too for when they revisit those maths concepts in later years.



Sample format:

Google doc link to planner

                               Maths Planner Year Level:  6

                              Strand /Topic:  2D Shapes & Measuring Angles      

                                 (Needs to be done post-area unit due need to understand quadrilaterals can be 2 triangles)                          

                               Duration:        3 weeks approximately depending on student-initiated enquiries

                               Links to UOI etc:  Visual Arts- Cubist art making: angles used

              

Central Idea:	PYP Phase 4 Conceptual Understanding:
When angles co-exist, connections and relationships are formed.	Geometric tools and methods can be used to solve problems relating to shape and space.

Provocation/s

Pre-Assessment:

° Which are angles?   Draw types of lines on board:  Discuss which are angles- why/why not? Establish understanding angles are formed when straight lines intercept ° Can an angle exist alone?      Look at an acute and obtuse angle on board.   Write theory on post it note and share with class on continuum establish understanding that angles always co-exist ° Angles hunt at home Students predict the types of angles they would find the most and the least at home.  Home learning: find examples of types of angles in objects at home and draw.  Think why right angles are most commonly found and revolution least. ° Why is a circle 360°? Discussion Establish understanding that 360 was chosen because it has many factors and therefore easy to divide.  What would a 480° circle look like?  A metric circle to align with our base 10 number system?  Students design and share findings. ° Give assorted triangles, quadrilaterals and polygons.   Explore types of angles and connections / relationships found.

° 10 minute open-ended pre-assessment. Record your understandings of angles- What are angles, types of angles and their sizes, angles in shapes etc. ° With partner, draw and discuss the sizes of different angles known (acute? obtuse? right? straight? reflex? revolution?) Observation assessment. ° Ability to measure angles with a protractor Draw 3 lines across an A4 page at different angles vertically and another 3 horizontally to create angles. Observe students ability to measure the angles. Extension: naming the shapes and types of angles created.

Student Wonderings From Provocation/s & Pre-Assessments to Explore:

Student Wonderings During Unit That Were Explored:

° FORM: Are there other types of angles other than acute, obtuse, right, straight, reflex and revolution? ° CAUSATION: Why are right angles the most commonly found? ° FORM: Can an angle be larger than a revolution (360°)? ° CONNECTION: What connections exist between the angles of triangles and quadrilaterals? ° CONNECTION:What patterns exists when we add all the angles of 2D shapes?   ° CONNECTION: What relationships exist between the angles of regular and irregular polygons? ° CONNECTION: When lines or parallel lines intercept, what connections between the angles form? ° CONNECTION: Do relationships and patterns exist between interior and exterior angles?

° Is there a pattern for the exterior angles of polygons? ° Is a 100 sided shape called a centagon? ° If we make one angle in a triangle larger, what effect does it have on the other angles? How do they co-exist? With quadrilaterals? ° What do all the angles of a hectagon equal? ° What do all the angles of 3D shapes equal? Is there a pattern? ° Why are angles of  a triangle 180° and a straight angle also 180°?- Connection? ° What is the connection between quadrilaterals adding to 360° and a circle being 360°? ° If the 3 angles on a corner of a cube equal 270°, will the angles of a pyramid also equal 270? Why or why not?

Outcomes:

Lines of Inquiry & Learning Experiences:

° Describe, measure and construct types of angles: obtuse, acute, straight, reflex, right ° Understand that geometric ideas and relationships can be used to solve problems in other areas of mathematics and real life. identifying and naming right-angled triangles • manipulating, identifying and naming isosceles, equilateral and scalene triangles • comparing and describing side properties of isosceles, equilateral and scalene triangles • exploring by measurement angle properties of isosceles,equilateral and scalene triangles by measuring • exploring by measurement angle properties of squares, rectangles, parallelograms and rhombuses

° FORM: Are there other types of angles other than acute, obtuse, right, straight, reflex and revolution? Some students discovered angle connections such as complimentary angles exist ° CAUSATION: Why are right angles the most commonly found? Discussion after home learning investigation Discovered that right angles provide strength in objects compared to other objects. Used books to support theories ° FORM: Can an angle be larger than a revolution (360°)? Group used a clock to enquire into types of angles and discovered angles larger than 360° can exist. ° CONNECTION: What connections exist between the angles of triangles and quadrilaterals? Some groups enquired into relationships of interior and exterior angles of shapes Discovering connection between triangle adding to 180° and a straight angle being 180° Discovering connection between quadrilaterals adding to 360° and a circle being 360° Can every quadrilateral be divided into two triangles? When we split a quadrilateral into two triangles, what is the relationship with the angles? Used this Nrich activity to help with enquiry You might decide to try this activity. The circles are printed for you. A straight angle is 180° and all the angles of a triangle are 180°.  Why does this connection exist? A circle is 360° and all the angles of a quadrilateral are 360°. Why does this connection exist?      Going further: - Can we use this new understanding with pentagons or hexagons etc?                     ° CONNECTION:What patterns exists when we add all the angles of 2D shapes?   Discovery that all the triangles add up to 180° and that all the angles of a quadrilateral add up to 360°.   Some created a theory of the number pattern that might continue with pentagons, hexagons etc.   Tested theory & changed  theory as needed.  NOTED:  The shapes do NOT have to be regular polygons.                      ° CONNECTION: What relationships exist between the angles of regular and irregular polygons? Some groups discovered number pattern between regular and irregular polygons’ interior and exterior angles ° CONNECTION: When lines or parallel lines intercept, what connections between the angles form?      Some groups discovered complimentary angles and how intersecting lines create a 360° circle What connections exist with the angles? How can we find the size of the angles without using a protector for all of them?                 ° CONNECTION: Do relationships and patterns exist between interior and exterior angles? What can you discover?  Is there a number pattern with exterior angles of regular and irregular polygons?  Why or why not?

Summative Assessment:

PYP Learner Profile or Attitudes used to Assess Maths Learning

Students continually reflect throughout the unit about their new discoveries and understandings of our central idea. Reflection on learning:

Teacher & Self Reflection Feedback Criteria: ° Thinker / Reflective: Connecting learning experiences to deepened understanding of our central idea ° Communicator: Effectively explaining understandings visually and /or in writing ° Curiosity: Takes learning further by asking questions to enquire into ° Committed: Making good use of learning time, participating actively in discussions, showing evidence of taking learning further

Resources:

Reflection: What worked well for next time? What didn’t work well for next time? Ways to improve how to differentiate for next time?

Book: What’s Your Angle Pythagoras? studyladder protractor activities to display on data screen           Lower/mid group: large printed copies of triangles, quadrilaterals and regular polygons for enquiries

° Maintaining wonder wall of questions helped raise curiosity and allowed for easier student-owned investigations ° Not leading students to cut angles off triangles to find connection with straight angle and ditto for quadrilaterals with circle at own pace of discovery made it more authentic and meaningful for those students ° open enquiry into the central idea- amazing! ° doing studyladder protractor on data screen helped a lot in showing how to use a protractor for those who didn’t know!

What do you think?

Is it missing something?

Should some sections be moved around?

I'd love to hear your thoughts so please do post below: