# TEACHING AND PROFESSIONAL LEARNING RESOURCES

The Teaching and Professional Learning Resources at A Learning Place A Teaching Place develop deep understanding of concepts and relationships between concepts in **both students and teachers.**

The banners and blog explain the research behind the resources.

The Teaching and Professional Learning Resources may look a little different to what you’re used to, so we have come up with:

Go to Teaching Resources, select Teach by Grade, select a grade, select a concept, watch the Video for a segment, read through the segment of the Teaching Plan, read through the Investigation linked to the segment, read through the problem liked to the segment, teach the segment and have students investigate and problem solve.

Go to Teaching Resources, select Teach by Grade, select a grade, select the Scope and Sequence, select 2 concepts to teach simultaneously, watch the Video for a segment of each concept, read through each concept’s segment of the Teaching Plan, read through the Investigation linked to the segment, read through the problem liked to the segment, teach the segments and have students investigate and problem solve.

Teaching maths for deep understanding **may look a little different to the way you currently teach maths**, and so the resources may be a little over-whelming at first – especially because they cover every concept and every level of every concept from Kindergarten/Prep/Reception to Year 6!

Don’t wait until you are an ‘expert’ before you begin teaching! The research into 21st century / future focused learning (accessed via the banner or blog) explains that in the knowledge age, no one can be the font of all knowledge!

Learning maths for deep understanding **may look a little different to the way your students currently learn maths**.

Students in lower grades will adapt to learning maths for deep understanding and will develop their understanding and capacity to explain concepts and the relationships between concepts quite naturally!

Students in older grades may not have deep understanding of essential prior levels of concepts, and so may not be ready to investigate concepts at grade level.

**So what can we do?**

Let’s initially **set goals as ‘floors’ for our students’ understanding**!

A minimum goal for students in older grades could be to understand and explain **two-digit place value** (Place Value level 11), and to **add and subtract single-digit numbers to and from two-digit numbers using place value** (Addition and Subtraction 6 and 7). This understanding will then allow them to **add and subtract two-digit and higher numbers using an algorithm** with understanding.

Students who understand and explain higher levels of Place Value may add and subtract using this understanding, before reverting to an algorithm for higher numbers. The ‘Teach by Concept‘ pages allow you to see which levels of the concept are prior learning for levels of related concepts.

For example, students who understand and explain **place value of three-digit numbers** (Place Value 15) may **add and subtract tens and two-digit numbers using place value** (Addition and Subtraction 13 – 18) then revert to an **algorithm for adding and subtracting three-digit- and higher numbers** with understanding.

Students who understand and explain **place value of four-digit numbers** (Place Value 17) may **add and subtract three- and four-digit numbers using place value** (Addition and Subtraction 21) then revert to an **algorithm for adding and subtracting five-digit- and higher numbers** with understanding.

A minimum goal for students in older grades could be to understand and explain **multiplying and dividing by single-digit numbers (tables) using the distributive property and the relationship between division and fractions** (Multiplication and Division 9 – 17, Patterns and Algebra 18) before reverting to an **algorithm for higher numbers**.

Students in lower grades may also be differentiated by setting minimum goals as ‘floors’.

As Dylan William explains (accessed via banner ‘Assessment’) teacher judgment is paramount!

**How can we assess current student understanding?**

If students are used to using playing cards to generate numbers that they are ready to investigate place value, addition and subtraction, and multiplication and division, you may use the size of the numbers they generate to determine their current level of understanding.

If students are not yet used to using playing cards to generate numbers to investigate place value, select from the sample levels below.

For example, to assess current understanding of Place Value, you may include the following levels by recording them in different colour on the board: Each student selects the highest number that they are able to:

– explain using standard and non-standard place value,

– partition using standard, non-standard and non-place value,

– count forwards and backwards by 10 from,

– place on a number line with other numbers.

If students are not yet used to using playing cards to generate numbers to investigate addition and subtraction, select from the sample levels below.

For example, to assess current understanding of Addition and Subtraction, you may include the following levels by recording them in different colour on the board: Each student selects the highest numbers that they are able to:

– add using place value

– subtract using place value

Students may demonstrate understanding of addition and subtraction at different levels!

If students are not yet used to using playing cards to generate numbers to investigate addition and subtraction, select from the sample levels below.

For example, to assess current understanding of Multiplication and Division, you may include the following levels by recording them in different colour on the board: Each student selects the highest numbers that they are able to:

– multiply using the distributive property

– divide and find a fraction of

Students may demonstrate understanding of multiplication and division at different levels!

From each student’s work, you can identify their level of understanding by looking at the level descriptions on the ‘Teach by Concept‘ pages.

**Now that we have an idea of students’ current levels of understanding, how can we differentiate our teaching and the students’ learning to ensure each student is learning at their leading edge? **