What Numbers Can We Make
 All in a Jumble
 Attractive Tablecloths
 Can They Be Equal
 Charlies Delightful Machine
 Diamond Collector
 Factorising with Multilink
 Factors and Multiples Game
 GOT IT
 Keep it Simple
 Kite in a Square
 M M and M
 Marbles in a Box
 Mixing Lemonade
 Nontransitive Dice
 Number Pyramids
 Odds and Evens
 Olympic Measures
 Olympic Records
 Painted Cube
 Pair Products
 Place Your Orders
 Seven Squares
 Summing Consecutive Numbers
 Temperature
 Tilted Squares
 Warmsnug Double Glazing
 What Numbers Can We Make
 Whats Possible
 Whats it Worth
 Which List is Which
 Which Spinners
Problem, Clue, Solution, Teachers' note
Teaching approach. This lesson idea is about visualising and explaining^{(ta)}.
The collection of NRICH activities are designed to develop students capacity to work as a mathematician. Exploring, questioning, working systematically, visualising, conjecturing, explaining, generalising, justifying, proving are all at the heart of mathematical thinking.
This particular resource has been adapted from an original NRICH resource. NRICH promotes the learning of mathematics through problem solving. NRICH provides engaging problems, linked to the curriculum, with support for teachers in the classroom. Working on these problems will introduce students to key mathematical process skills. They offer students an opportunity to learn by exploring, noticing structure and discussing their insights, which in turn can lead to conjecturing, explaining, generalising, convincing and proof.
The Teachers’ Notes provided focus on the pedagogical implications of teaching a curriculum that aims to provoke mathematical thinking. They assume that teachers will aim to do for students only what they cannot yet do for themselves. As a teacher, consider how this particular lesson idea can provoke mathematical thinking. How can you support students' exploration? How can you support conjecturing, explaining, generalising, convincing and proof?. ^{(edit)}
Resource details  
Title  What Numbers Can We Make? 
Topic  Number 
Teaching approach  
Learning Objectives  Visualising and explaining 
Subject  
Age of students / grade 

Related ORBIT Wiki Resources 

Files and resources to view and download  The following parts are available: Problem, Clue, Solution, Teachers' note. The original problem is available on the NRICH website here. 
Acknowledgement  The NRICH website http://nrich.maths.org publishes free mathematics resources designed to challenge, engage and develop the mathematical thinking of students aged 5 to 19. NRICH also offers support for teachers by publishing Teachers’ Resources for use in the classroom. 
License  CCBy, with kind permission from NRICH. This resource was adapted from an original NRICH resource. 