Following on from my article on place value sliders, I've curated some more ideas for teaching place value - one of the most important building blocks for maths. Place value is important because it helps students understand the meaning of a number as well as the order of numbers.
Place Value Questioning
- Study different arrangements of the same digits. for example 13 and 31. What does each digit represent?
- What is the importance of zero in place value?
- What could be the implications of omitting or increasing the number of zeros (when counting money, for example)?
Packaging showing how objects are grouped: for example, egg boxes, cake trays, chocolate bars, 'vases' with paper flowers to be arranged in them, sets of plastic farm anima ls and fences, plastic money and purses, etc. Structural base apparatus such as Dienes.
Activities, Ideas and Investigations
Games in Different Bases
Devise games in different bases which give practice in grouping and exchanging. When using dice in such games, the dice need to be numbered accordingly
- Base 3 - 1,2,1,2,1,2
- Base 4 - 1,2,3,1,2,3
- Base 5 - 1,2,3,3,4,4....etc.
(Omitting zero eliminates the need to miss a go occasionally.)
Play games with Dienes apparatus
- Build a Cube (3 base). Use a die, and collect the number of units shown on the die. When you have three units, exchange for a long . When you have three longs, exchange for a flat. Three flats make a cube - you win!
- Build a Castle (4 base). Play as for the previous game until the 'keep' is made from a 4x4 cube. Now build four towers from four longs, and four turrets from four units.
- Build a Square (10 base). Play as before. The aim is to make a 10x10 flat square. Lose a hundred (10 base). Start with a 10x10 flat and remove units by d ecomposing.
Use cards numbered 0-9 placed face down. Each player has a grid. and takes a turn to take one of the cards, which are placed on the grid to make the largest number possible. The one who manages to finish with the largest number wins that game. Try varying the rules: for example, have two boards each, and add the combined numbers to obtain a score at the end_
Play People Numbers
This game is played in teams of no more than ten. Give each team a set of identical cards, enough for one per child (0-5 if 6 in the team, 0-9 if 10 in the team, etc). The 'caller calls out a number made from 2/3/4 digits, for example 'Three thousand four hundred and seventy one". The winning team is the first to organise its members who are holding the relevant cards into the right order to show that number.
Animal Numbering Systems
How would spiders count? What about donkeys, or beetles?
Use an Abacus Board
Use an abacus board to reinforce place value principles. Position counters to represent a number, for example 26, on the board. Then move them two places to the left, and read off the number that is shown now, i.e. 2600.
Using five counters on a tens and units abacus board, how many different numbers can be shown? Extend the activity by changing the number of counters.
Research Number Systems
Research number systems from other civilisations, for example, Egyptian, Roman, Sumerian, Gujarati, Hindu. Mayan. How do other systems record large numbers?
This site gives an overview of different numbering systems.
Below is the Egyptian number system:
The Quipu number system used by the Incas relies on knots being tied on pieces of string.
This could be a fun learning activity to explore/reinforce place value.
Devise Your Own Number System
Leading on from experience of games in different bases, try addition in different bases, using base boards. Progress to recording on an abacus, using coloured beads and a pre-arranged scheme. For example, three red beads on the right rod can be exchanged for one green bead on the middle rod, and three greens can be exchanged for one purple bead on the left rod. Practise counting on and counting back (using decomposition).