Number Play

Playing with Numbers

This introductory section invites students to explore numbers beyond their conventional use in counting and arithmetic operations. It encourages curiosity and enjoyment in observing numbers, their properties, and the patterns they form. The chapter begins by presenting students with various number tables and sequences, prompting them to notice interesting features and relationships among numbers. For example, students are asked to look at a number table and identify numbers that stand out due to their size or position. This playful approach helps build a foundation for deeper mathematical thinking by fostering an investigative mindset. The section emphasizes that numbers are not just tools for calculation but also objects of fascination that can reveal surprising patterns and properties when examined carefully. This exploration sets the tone for the rest of the chapter, where students will learn about concepts like place value, number patterns, and special numbers called supercells. The idea is to make learning mathematics engaging and to develop a sense of wonder about numbers. **Table on page 14 (7×8)** | 32 | 32 | 32 | 32 | 32 | 32 | 32 | 32 | | --- | --- | --- | --- | --- | --- | --- | --- | | 32 | 32 | 32 | 32 | 32 | 32 | 32 | 32 | | 32 | 32 | 32 | 32 | 32 | 32 | 32 | 32 | | 32 | 32 | 32 | 32 | 32 | 32 | 32 | 32 | | 64 | 64 | 64 | | | | | 64 | | 64 | 64 | 64 | | | | | 64 | | 64 | 64 | 64 | | | | | 64 | | 64 | 64 | 64 | | | | | 64 | **Table on page 14 (10×5)** | 1 2 5 1 2 5 1 2 5 125 | | | | | | --- | --- | --- | --- | --- | | | 125 2 5 0 2 | | | 5 | | | 1 | | | | | 1 2 125 5 125 | 2 5 | 0 2 5 0 | | 125 5 2 25 1 1 | | | 2 5 0 | 5 0 0 | 2 5 0 | | | | | 5 0 0 1 0 0 0 5 0 0 | | | | | | 5 0 0 | | | | | 2 | 5 0 2 5 | 0 | | | 1 | | | | | | | 5 2 1 0 5 2 5 5 2 | | | | | 1 2 1 2 5 1 2 5 1 2 5 | | | | | **Table on page 14 (5×9)** | | | 15 15 15 | 15 | 35 35 | 25 2 | 25 5 25 | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | 25 25 25 | | 35 3 | 5 35 | 35 | 15 15 | | | | 3 | 5 | 25 25 | 25 1 | 5 25 | 15 1 | 5 15 | 15 3 | 5 | | 35 3 | 35 5 | 15 15 | 35 | 25 15 | 35 | 25 25 | 35 3 | 35 5 | | | 15 15 15 | | 15 3 | 5 35 | 25 | 25 25 25 | | | | | | 25 25 25 | 35 25 | 35 35 | 35 1 15 | 5 15 15 | | | **Table on page 23 (3×9)** | | 96,310 | | 96,301 | | 36,109 | | 39,160 | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 96,103 | | | 13,609 | | 60,319 | | 19,306 | | | 13,906 | | | 10,396 | | 60,193 | | 60,931 | | | 10,369 | | | 10,963 | | 10,936 | | 69,031 | | **Table on page 23 (1×4)** | 2180 | | | 3600 | | --- | --- | --- | --- | | | | | | **Table on page 23 (1×3)** | 8000 | 9000 | 10000 | | --- | --- | --- | | | | 9590 | **Table on page 24 (1×24)** | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 1990 | | | 1995 | | 2000 | | | 2005 | | | 2010 | | | 2015 | | 2 | 020 | | 2025 | | 2030 | | 2035 | **Table on page 24 (1×28)** | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 9993 | | | 9994 | | 9995 | | | 9996 | | | 9997 | | | 9998 | | 9 | 999 | | | 10000 | | | 10001 | | 10002 | | | **Table on page 24 (1×20)** | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 15077 15 | | 15 | 078 | | 15079 | | | 15080 | | 1 | 5081 | | | 15082 | | 15 | 083 | | 15084 | **Table on page 24 (1×21)** | | | | | | | | | | | | | | | | | | | | | | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | 83705 84 | | 84 | 705 | | 85705 | | 8670 | | 5 | | 87705 | | | 88705 | | 8 | 9705 | | | 90705 |

• Numbers can be explored beyond basic arithmetic.
• Observing numbers helps discover interesting patterns.
• Curiosity about numbers builds a strong mathematical foundation.
• Numbers have properties that can be fun to investigate.
• Exploration encourages a playful approach to mathematics.
• 📌 Number: A symbol or group of symbols used to represent a quantity.
• 📌 Pattern: A regular arrangement or sequence that repeats according to a rule.

Supercells in Number Tables

This section introduces the concept of 'supercells' within a number table. A supercell is defined as a cell in a table whose number is greater than all the numbers in its immediate neighboring cells. Neighbors are considered to be the cells immediately to the left, right, top, and bottom of the cell in question. Diagonal neighbors are not considered. The section explains how to identify supercells by comparing a number with its neighbors. For example, if a cell contains the number 8632, and its neighbors are 4580, 8280, 4795, and 1944, since 8632 is greater than all these, it is a supercell. The section provides tables with numbers and asks students to find supercells within them. This activity helps students practice comparison of numbers and understand spatial relationships in tables. It also introduces the idea that some numbers in a table have a special status based on their relative size. The section includes exercises where students fill tables with numbers to create or avoid supercells, encouraging creative thinking and application of the concept. This concept is important as it combines numerical comparison with spatial reasoning and pattern recognition. **Table on page 4 (5×5)** | 8. Fill a table such that the cell having the second largest number is not a supercell. 9. Fill a table such that the cell having the second largest number is not a supercell but the second smallest number is a supercell. Is it possible? 10. Make other variations of this puzzle and challenge your classmates. Let’s do the supercells activity with more rows. Here the neighbouring cells are those that are immediately to the left, right, top and bottom. Table 1 The rule remains the same­: a cell becomes a supercell if the 2430 7500 7350 9870 number in it is greater than all 3115 4795 9124 9230 the numbers in its neighbouring cells. In Table 1, 8632 is greater 4580 8632 8280 3446 than all its neighbours 4580, 8280, 4795 and 1944. 5785 1944 5805 6034 Complete Table 2 with 5-digit numbers whose digits are ‘1’, Table 2 ‘0’, ‘6’, ‘3’, and ‘9’ in some order. Only a coloured cell should 96,301 36,109 have a number greater than all 13,609 60,319 19,306 its neighbours. 60,193 The biggest number in the table | | | | | | --- | --- | --- | --- | --- | | | | 96,301 | 36,109 | | | | | 13,609 | 60,319 | 19,306 | | | | | 60,193 | | | | | | | | | | | 10,963 | | | **Table on page 4 (3×4)** | 2430 | 7500 | 7350 | 9870 | | --- | --- | --- | --- | | 3115 | 4795 | 9124 | 9230 | | 4580 | 8632 | 8280 | 3446 | | 5785 | 1944 | 5805 | 6034 |

• A supercell is a cell with a number greater than all its immediate neighbors.
• Neighbors are the cells directly above, below, left, and right.
• Diagonal cells are not considered neighbors.
• Identifying supercells involves comparing numbers in a table.
• Supercells highlight special numbers based on their position.
• 📌 Supercell: A cell in a number table whose number is greater than all numbers in its immediate neighboring cells.
• 📌 Neighboring cells: Cells immediately to the left, right, top, and bottom of a given cell.