Year level: 6

Classroom teacher: Alannah Christie Underwood (Elsewhere Primary School)

Background information about classroom context

There are 25 learners in the Year 6 class. The learning environment includes flexible furniture (see image 1) with a classroom culture that allows students to use concrete materials and representations (language, diagrams, & mathematical symbols) to demonstrate their mathematical thinking whilst working in small, flexible groups on purposefully selected and implemented mathematical tasks. As like many classrooms in Australia, the students in Ms. Underwood’s class are from diverse language, cultural, and religious backgrounds.

Five students are learning English as an Additional Language or Dialect (EAL/D) with two of those students working ‘above expected’ level, one working ‘at expected’ level, and the two remaining students are ‘on the way to expected’ level. Two students are identified as gifted learners and one student has a Attention Deficit Hyperactivity Disorder diagnosis. There are five other students that are ‘on the way to expected’ level, whilst most of the students are working ‘at expected’ level.

To cater for the learner diversity, the learning is differentiated by using open-ended tasks, mathematical games, and activities with a mixture of student- centred structured inquiry and active mathematics teaching (Sullivan et al., 2021) using the lesson structure of Launch, Explore, Summarise (most times). Teaching is differentiated by: using enabling and extending prompts, encouraging the use of concrete materials (when appropriate) and representations (language, diagrams, & mathematical symbols), using explicit questions that enable and extend student thinking, and employing strategic grouping of students that is mostly mixed-achievement settings with the occasional use of strategic ‘small pull-out group’. This is done to support and extend students’ thinking through a form of explicit teaching called active mathematics teaching (Sullivan et al., 2021). Mathematics concrete materials (see images 2 and 3), representations (language, diagrams, & mathematical symbols) and technologies (mostly tablets & apps) are embedded in most mathematics lessons. The students in Ms. Underwood’s class are free to use those materials at any time, but students are asked to justify why they are choosing to use them and explain how the materials support their mathematical thinking.

The Gradual Release of Responsibility (GRR) model is not used by Ms. Underwood because she understands that it is a literacy education approach best used when teaching reading and writing. Ms. Underwood uses a flipped version of “I do, we do, you do” where she expects her students to work on the mathematical task by themselves first for a duration of time (~10 minutes). This is when Ms. Underwood carefully and strategically observes and listens to her students, checking in with how they are connecting with the mathematics that underpins the task. She then gathers the students to discuss their strategies, questions, and mathematical thinking as a group where she invites carefully selected students to share their initial thinking about the task. Ms. Underwood highlights appropriate ways of thinking with the students and then she might give the enabling prompts for those students who are not yet connecting with the mathematics, or the task demands. She also provides the extending prompts for those students whose learning is ready to be challenged and extended. Towards the end of the lesson (Summarise), Ms. Underwood carefully selects three or four students to share their solutions and strategies, and she often records their thinking by creating anchor charts. Those charts are then summarised by Ms. Underwood, and she makes the mathematics concepts and ways of working mathematically explicit to students in the final minutes of the lesson. The anchor charts are then displayed in the learning space and referred to during following mathematics lessons.

Photograph of the learning environment

Image 1: The classroom | Image source: Link

Image 2: Mathematics concrete materials | Image source: Link

Image 3: Mathematics concrete materials | Image source: Link

Term 3 Mathematics Scope and Sequence

This is Ms. Underwood’s plan for Term 3 in relation to topics and content descriptors that will inform her planning (AC:M v.9).

Weeks 1 – 3

Weeks 4 – 6

Weeks 7 – 8

Week 9

Week 10

Geometry

Fractions and Decimals

Probability and Statistics

Algebra

Revision

Recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate (AC9M63P03)

First time taught: focusing on use of fractions to describe rotations and reflections (e.g., three-quarter turn)

Apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order (AC9M6N03) Consolidating from

Term 1

Recognise that probabilities lie on numerical scales of 0 – 1 or 0% – 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals (AC9M6P01)

First time taught: using fractions and decimal fractions to measure the probability of specific events within chance experiments

Recognise and use rules that generate visually growing patterns and number patterns involving rational numbers (AC9M6A01) Consolidating work on growing patterns with a focus on fractions and decimal fractions

Revision of Term 3 topics where data suggests further consolidation is required

Solve problems that require finding a familiar fraction, decimal or percentage of a quantity, including percentage discounts, choosing efficient calculation strategies, and using digital tools where appropriate (AC9M6N07)

First time taught: making links between fractions and decimal

fractions

Assessment purpose and strategy

Rational Number Assessment (diagnostic):

Ms. Underwood administered the diagnostic assessment (RNI) at the end of Week 3 with selection of students.

The data was analysed and used to inform learning and teaching in Weeks 4 – 6.

Rational Number Word Wheel (formative assessment):

Ms. Underwood administered the formative assessment at the end of Week 3.

The data was analysed and used to inform learning and teaching in Weeks 4 – 6.

Work Samples from open-ended tasks (formative assessment):

Ms. Underwood gathered work samples produced by the students during the lessons in Weeks 4 and 5 as a way of knowing what learning gains were made

The assessment data was utilised as formative assessment and analysed to inform learning and teaching in Week 6.

My Thoughts about my Learning about Rational Numbers (affective assessment):

Ms. Underwood administered the affective assessment in Week 6 to gain some insights into how the students were feeling about their rational number learning.