edx education C13J6NNKtAL Four Color Plastic Base Ten Set User Guide

Mathematics

Base Ten

Activity Guide

Use the Base Ten blocks to teach :

• Place Value

• Number Representation

• Operations (+ – x  ÷ )

• Decimals, Percentages and Fractions

• Measurement

 Written by Dr Paul Swan

Introduction

Use the Base Ten blocks to teach :

• Place Value
• Number Representation
• Operations (+ – x  ÷ )
• Decimals, Percentages and Fractions
• Measurement

Base Ten Blocks are also known as MAB (Multibase Arithmetic Blocks) or Place Value Blocks.

Naming the Pieces

cube                                        flat rod   unit

Relationships

The relationships between the blocks should be emphasized :

• cube is 10 times a flat
• fiat is 10 times a rod
• rod is 10 times a unit
• fiat is 100 times a unit etc

Before Using Base Ten Blocks

Students should use bundling materials such as pop sticks or bundling sticks and experience bundling ten sticks with an elastic band to make one ten.

The 10 x concept is fundamental to the use of Base Ten Blocks. As the name implies each piece in the set is proportional, that is ten times the size of the previous piece.

Representing Number

The Base Ten Blocks may be used to represent four-digit numbers. If a value of one is assigned to the unit, then the rod is worth ten, the flat is worth one hundred and the cube is worth one thousand. Two digits numbers should be represented first. Students can be asked to represent a number like 47. This number would require 4 rods and 7 units. A three-digit number like 254 would look like this :

Once the students have become familiar with representing numbers with the Base Ten Blocks they may be used to help them learn to calculate.

Addition

Addition involves combining two sets. When adding numbers involving regrouping it makes sense to use a place value mat, so that the students’ work is clearly laid out and links to place value are clearly seen. With base ten, you are allowed to keep 9 items in any one place but as soon as ten or more items are put there, for example ten ones (units) must be exchanged (traded) for one ten (rod).

Calculate 87 + 46

Step 1. Lay down 87 on the board (8 rods in the tens place and the 7 units in the ones place). Forty-six is then added to the board (4 rods and 6 units).

hundreds

| tens |

ones

---|---|---
| |

Step 2. Ten of the 13 units are exchanged for one rod and 3 units are left in the ones place. The rod moves to a new place – the tens place. The place value mat would now look like this:

hundreds

| tens |

ones

---|---|---
| |

Step 3. By the same rule, only 9 items allowed in any one place, ten of the 13 rods, would need to be exchanged for a flat, leaving 3 rods and one flat. The one flat would need to move to the hundreds place. The result is 133.

hundreds

| tens |

ones

---|---|---
| |

87 + 46 = 133

Subtraction

When subtracting with Base Ten Blocks, a number is represented on the Place Value Mat and the number to be subtracted is written on sticky note paper and stuck on the Place Value Mat, below the Blocks.

Calculate 74 – 56

Step 1. Lay down 74 on the board (7 rods in the tens place and the 4 units in the ones place). Below these Blocks, write 5 in the tens place and 6 in the ones place.

hundreds

| tens |

ones

---|---|---
|   5|   6

Step 2. It is not possible to take 6 units away from 4 units, so one of the 7 rods must be exchanged for 10 units (that is, one ten = ten ones). Temporarily 14 units are placed on the board and 6 of them are removed, leaving 8 units on the board. The sticky note with 6 is removed at the same time.

hundreds

| tens |

ones

---|---|---
| 5|

Step 3. Five rods are now removed from the board along with the sticky note with 5 written on it.

hundreds

| tens |

ones

---|---|---
| |

74 – 56 = 18

Decimals

If the value of the unit is redefined, then addition and subtraction calculations involving decimals may be performed. If the rod is defined as representing one, then the unit is worth 0.1, and the fiat is worth 10. The number 24.6 would look like this :

hundreds

| tens |

ones

---|---|---
| |

Calculations for addition and subtraction would be performed in a similar way to whole numbers.

Percentages

The flat is an ideal model for depicting percentages as it is made up of 100 squares. To show a percentage such as 15%, 15 squares would need to be covered.

Decimal Fractions

Simple fractions may be added or subtracted using a similar approach. Two tenths and twenty seven hundreds may be added by converting the tenths to hundreds. Twenty squares and twenty seven squares would be covered in all, that is the result is 47/100. Subtractions may be performed in a similar way.

Trading Games

Trading games are used to develop fluency with the trading process.

• A game for 2-6 players (one player takes on the role of banker)
• Each player will need a Place Value Mat
• One set of Base Ten Blocks to share
• Two 6-sided or one 10-sided dice

Rules

• Players take turns to roll the dice and collect that many Base Ten units and put them on the board. Every time more than 9 items are placed on the board, a trade must take place (ten units are traded for one rod).
• The banker supervises all trades – the banker controls the box of Base Ten Blocks and the players must exchange units for rods with the banker.
• The first player to reach one hundred is the winner.

Variations

• Extend the game to 200 or 300, which means 10 rods will need to be exchanged for one flat.
• Start with a fiat and subtract on each turn. The first player to zero wins.

Place Value Mat

hundreds

| tens |

ones

---|---|---
| |

Mathematics

Other related products available from

26102C Place Value Abacus

26023 Place Value Flip Chart (Thousands)

16321C Jumbo Place Value Dice Set

Eco-friendly printing with soy ink on recycled paper

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Printed in Taiwan

References

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