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# Mr Barton Maths Podcast - Alison and Charlie

*On 30$^{th}$April 2018, Charlie Gilderdale and Alison Kiddle were interviewed by Craig Barton for his Mr Barton Maths Podcast. On this page, we share the main themes that were discussed, with links to the activities we mentioned, and other useful resources.*

**NRICH is not just for high attainers**

We talked about the challenge level star rating system that we use, from relatively easy (1-star) to very challenging (3-stars), and pointed out that we have many more 1-star and 2-star problems than 3-star problems. Here are some of our favourite 1-star activities which can be used with most Key Stage 3 classes:

Dicey Operations

Add to 200

Dozens

Mixing Lemonade

What's it Worth?

Estimating Angles

**Time pressure - how to fit NRICH tasks into a busy curriculum**

Sometimes, it might feel like there's too much pressure to get through the curriculum, and NRICH tasks are a luxury that there isn't time to include. We discussed ways that NRICH tasks can actually save you time, by making strong connections between different curriculum areas so that students are revising one topic while meeting another for the first time, or bringing together several different mathematical ideas in one task. Here our some of our favourites (which are all either 1-star or 2-star problems):

M, M and M

Isosceles Triangles

Factors and Multiples Puzzle

Up, Down, Flying Around

Perimeter Expressions

Which is Bigger?

Temperature

**The NRICH Pedagogy**

Tilted Squares is one of our favourite examples of a task linked to a curriculum topic (Pythagoras' theorem), where students can explore, make conjectures, and generalise. Watch these video clips showing extracts from a lesson of us working on this problem with a group of 14 year old students.

**Fluency or Problem Solving - a false dichotomy**

We believe that problem solving does not have to be done at the expense of students developing fluency in key mathematical skills. By choosing tasks carefully, teachers can provide opportunities for students to engage in**purposeful practice**.

Mathematical Etudes - article by Colin Foster

Factors and Multiples Game

Completing Quadrilaterals

Charlie's Delightful Machine

Warmsnug Double Glazing

Pair Products

Cyclic Quadrilaterals

In "Adding It Up" Kilpatrick, Stafford and Findell suggested five essential aspects for developing young mathematicians: conceptual understanding; procedural fluency; strategic competence; adaptive reasoning and productive disposition.

The interwoven and interdependent nature of these five essential aspects are powerfully captured by the image of the rope. Many NRICH problems are written with this model in mind.

**Low Threshold High Ceiling tasks to aid with differentiation**

We discussed the use of Low Threshold High Ceiling tasks, which offer the opportunity for different groups of students within the same class to work on the same task but reach different end points. Here are some of our favourite Low Threshold High Ceiling tasks.

Summing Consecutive Numbers

Shifting Times Tables

Odds and Evens

Unequal Averages

Marbles in a Box

Hollow Squares and What's Possible?

Finally, here are some of our**general resources** which we mentioned during the podcast:

What we think and why we think it

Enriching the Secondary Curriculum

Secondary Mapping Document pages

Short Problems

Or search by topic

Age 11 to 18

Challenge Level

We talked about the challenge level star rating system that we use, from relatively easy (1-star) to very challenging (3-stars), and pointed out that we have many more 1-star and 2-star problems than 3-star problems. Here are some of our favourite 1-star activities which can be used with most Key Stage 3 classes:

Dicey Operations

Add to 200

Dozens

Mixing Lemonade

What's it Worth?

Estimating Angles

Sometimes, it might feel like there's too much pressure to get through the curriculum, and NRICH tasks are a luxury that there isn't time to include. We discussed ways that NRICH tasks can actually save you time, by making strong connections between different curriculum areas so that students are revising one topic while meeting another for the first time, or bringing together several different mathematical ideas in one task. Here our some of our favourites (which are all either 1-star or 2-star problems):

M, M and M

Isosceles Triangles

Factors and Multiples Puzzle

Up, Down, Flying Around

Perimeter Expressions

Which is Bigger?

Temperature

Tilted Squares is one of our favourite examples of a task linked to a curriculum topic (Pythagoras' theorem), where students can explore, make conjectures, and generalise. Watch these video clips showing extracts from a lesson of us working on this problem with a group of 14 year old students.

We believe that problem solving does not have to be done at the expense of students developing fluency in key mathematical skills. By choosing tasks carefully, teachers can provide opportunities for students to engage in

Mathematical Etudes - article by Colin Foster

Factors and Multiples Game

Completing Quadrilaterals

Charlie's Delightful Machine

Warmsnug Double Glazing

Pair Products

Cyclic Quadrilaterals

In "Adding It Up" Kilpatrick, Stafford and Findell suggested five essential aspects for developing young mathematicians: conceptual understanding; procedural fluency; strategic competence; adaptive reasoning and productive disposition.

The interwoven and interdependent nature of these five essential aspects are powerfully captured by the image of the rope. Many NRICH problems are written with this model in mind.

We discussed the use of Low Threshold High Ceiling tasks, which offer the opportunity for different groups of students within the same class to work on the same task but reach different end points. Here are some of our favourite Low Threshold High Ceiling tasks.

Summing Consecutive Numbers

Shifting Times Tables

Odds and Evens

Unequal Averages

Marbles in a Box

Hollow Squares and What's Possible?

Finally, here are some of our

What we think and why we think it

Enriching the Secondary Curriculum

Secondary Mapping Document pages

Short Problems