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Level Two > Number and Algebra

# Place Value Blocks

Keywords:
Purpose:

This unit uses one of the digital learning objects, Place Value Blocks, to support students as they investigate the place value of numbers up to 9999. The numbers are represented using place value blocks.

The knowledge section of the New Zealand Number Framework outlines the important items of knowledge that students should learn as they progress through the strategy stages. This unit of work and the associated learning object are useful for students at stage 5, Early Additive Part-Whole, of the Number Framework.

Specific Learning Outcomes:

know how many ones, tens, hundreds and thousands are in numbers up to 9999.

Description of mathematics:

The learning object allows students to explore how many ones, tens, hundreds and thousands are in numbers up to 9999. Students can rearrange numbers, for example 258 can be represented with 2 hundreds, 5 tens and 8 ones, or as 25 tens and 8 ones.

This unit of work and the associated learning object are useful for students at stage 5, Early Additive Part-Whole, of the Number Framework.  It fits in the grouping/place value domain of the knowledge section.

It can be used by both the teacher to support teaching and independently by students to explore place value concepts.

Required Resource Materials:
Copymasters 1- 4
Activity:

### The learning object

The learning object, Place Value Blocks, can be accessed from the link below.

### Prior to using the Place Value Blocks learning object

Show me the Number helps students to understand place value for tens and ones using two digit numbers and equipment. It would be useful to do this lesson prior to using the Place Value Blocks learning object.

The number strategies unit Modeling Numbers: 3 digit numbers and its associated learning object, Modeling Numbers: 3 digit numbers are also related to this unit.

### Working with the learning object with students (Exploring the learning object)

Show students the learning object and explain that it provides a model for representing numbers using place value equipment.

Use the +1 and -1 buttons under each column to show students how to make a number. Ask the students to make a number with some blocks in each column. Show students the number of blocks in each column is shown above the column, for example 2 hundreds, and the total value of each column is written below, for example 200. Check they understand this by making a number, e.g. 8530 and ask how many tens are in the tens column (3) and what are the 3 tens worth (30). The total of the whole number is shown at the bottom in orange.

Show students the rubbish bin button. Clicking this button clears all the blocks in the column.

Ask the students to use the +1 and -1 buttons to make a number. Show the students the arrow buttons that appear on the boundary lines between the place value columns.

The right arrow appears when there are one or more blocks in a column other than the ones column. Click the right arrow and watch one of the blocks move to the boundary line and then break up into the units of the next column on the right and move into that column. Watch the numbers above and below the columns adjust. Discuss that the yellow total number does not change because nothing has been added or subtracted to the number, it has just been rearranged.

The left arrow appears when there are 10 or more blocks in a column other than the thousands column. Click the left arrow and watch ten blocks move to the boundary line and form the shape of the block in the left column then move into that column. Watch the numbers above and below the column adjust. Again discuss why the yellow total number does not change.

### Working with the learning object with students (Find how many tens, hundreds, thousands in numbers)

The learning object can be used to help students learn how many tens and hundreds are in numbers up to 9999.

Ask the students to make a hundreds number and then use the right arrow between the hundreds and tens column to find the number of tens in the number.   For example, make the number 467 and click the right arrow. Ask the students to explain what is happening. They should notice that each hundred is splitting into 10 tens and moving into the tens column.  Ask the students how many tens are in 467. Look at the yellow total number and reinforce that 1 hundred is made up of 10 tens so in 4 hundred there are 40 tens. There are 6 tens in the tens column so together that is 46 tens.

Ask the students to try more examples using the right arrow to find how many tens are in hundreds, and how many hundreds are in thousands numbers. Once students understand the relationship it is not too hard to find the number of tens in thousands.

### Notes regarding working with place value equipment.

There are a number of ways to explore place value concepts.  The learning object provides a model to help students visualise the place value columns. Students will benefit from exploring place value with a range of equipment including place value blocks, beans and canisters, bundles of sticks,  three bar abacus, and number flip charts.

### Students working independently with the learning object.

Once students are familiar with how the learning object works they can work with the learning object independently. Here are some types of activities that students could do:

Worksheet 1 (see copymaster). Types of questions:

1. Use the learning object to make a hundreds number in two different ways. For example 572 can be made with 5 hundreds, 7 tens and 2 ones, or with 47 tens and 2 ones.
2. How many tens are in hundreds numbers? Use the learning object then try without it.
3. How many hundreds are in thousands numbers? Use the learning object then try without it.
4. How many tens are in thousands numbers? Try without using the learning object.

Worksheet 2 (see copymaster).    Types of questions:

1. What is the total of 14 tens?   Students use the learning object then answer questions without it.
2. Make these numbers with the learning object: 243 = 0 hundreds + ___ tens + ___ones.
3. What is the total number? For example, 3 hundreds + 12 tens + 4 ones = ____.
4. What is the total number of tens in these numbers.   For example 253 = ___tens.
Students use the learning object, then try more questions without the learning object.
5. What is the total number? For example 65 tens = ____.
Students work without the learning object.

Worksheet 3 (see copymaster).    Students use the learning object then work without it.  Types of questions:

1. Place value strategies for addition. For example, 43 + 15 = ____ + _____ = _____
2. Place value strategies for addition. For example, 37 + 24 = ____ + _____ = _____
3. Place value strategies for subtraction. For example, 58 + 12 = ____ + _____ = _____

Worksheet 4 (see copymaster).   Students use the learning object then work without it.
Types of questions:

1. Tidy number strategy for addition. For example, solve 137 + 6 by 137 + 10 - 7 = ____.
2. Tidy number strategy for subtraction. For example, solve 142 - 8 by 142 - 10 + 2 = ____.
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worksheet1.doc54 KB
worksheet1.pdf59.34 KB
worksheet2.doc27 KB
worksheet2.pdf54.61 KB
worksheet3.doc31 KB
worksheet3.pdf81.55 KB
worksheet4.doc27 KB
worksheet4.pdf66.67 KB

## Place value with whole numbers and decimals

The purpose of this unit of sequenced lessons is to build on the students’ understanding of place value with three digit numbers and with one thousand. It supports the students as they generalise their 3 and 4-digit conceptual place value understanding across our numeration system.

This unit supports the teaching and learning activities in the Student e-ako Place Value 5, 6, 7 and 8 and complements lessons found in Book 5, Teaching Addition, Subtraction and Place Value.

This is the seventh and final unit in a series of units developing place value concepts.

This unit builds on the previous units of work:

## Building with tens and hundreds

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of place value in three digit numbers and one thousand. It is also to enable students to generalize from known two-digit facts, apply patterns associated with these to three digit numbers to 999, and to introduce 1000.

A number of existing related teaching resources are relatively procedural in their nature. Therefore the purpose of this series of lessons is to deepen students’ conceptual understanding of the structure and patterning within our numeration system.

This unit supports the teaching and learning activities in Student e-ako Place Value 3 and 4 and complements lessons found in Book 5, Teaching Addition, Subtraction and Place Value.

This is the sixth in a series of units developing place value concepts. This unit builds on these previous units of work:

The unit that follows is:

## Building with tens

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of the place value of two-digit numbers. The purpose is also to be able to generalize from known single digit facts and apply patterns associated with these to two digit numbers to 100.

The teaching and learning activities support Student e-ako Place Value 1, p17-33 and Student e-ako Place Value 2. They also complement Book 5, Teaching Addition, Subtraction and Place Value.

This is the fifth in a series of units developing place value concepts. This unit builds on the previous units of work:

## Teen numbers (building with ten)

The purpose of this unit of sequenced lessons is to develop knowledge and understanding of the place value structure of the numbers from ten to twenty.

These teaching and learning activities support Student e-ako Place Value 1, pages 6-15 and to complement the learning activities found in Book 5, Teaching Addition, Subtraction and Place Value.

This is the fourth of a series of units developing place value concepts. This unit builds on the previous units of work: