# Place value, estimation and rounding

Core concept 1.1 covers the structure of our place-value system (particularly as it relates to decimals) and rounding numbers to a required number of decimal places or significant figures.

### Place Value

1.1.1.1   Understand place value in integers

1.1.1.2   Understand place value in decimals, including recognising exponent and fractional representations of the column headings

1.1.1.3   Understand place value in the context of measure

1.1.1.4   Order and compare numbers and measures using <, >, =

## Base Blocks - Dienes Blocks from base -10 to 10

1.1.1.1   Understand place value in integers

Understand the multiplicative relationships between columns in the place value structure by exploring place value in different bases.  See Number to Algebra with Base Blocks

secmm-cc-theme-1-key-idea-1 (4).pptx

### 1.1.1.2 Understand place value in decimals, including recognising exponent and fractional representations of the column headings

Know and understand powers of ten

Interpret powers of ten written using index notation

Connect different representations of column headings

Understand the multiplicative relationships between columns in the place value structure

Click here to see more on place value in different bases and introducing algebra tiles through Base Blocks

## Gattegno Tens Chart - MathsBot

### Rounding

1.1.2.1   Round numbers to up to three decimal places

1.1.2.2   Round numbers to any number of decimal places

## Decimals - multiple representations of decimals to 3d.p. between 0 and 1

Change the sliders to change the area model, number line and bar model.  Compare the three representations.

Is 0.632 closer to 0.63 or 0.64?

Is  0.637 closer to 0.63 or 0.64?

Is 0.635 closer to 0.63 or 0.64?

The top number line is set to 2 dp, the middle to nearest whole number and the bottom to 1 decimal place.  Move the top slider and see when the bottom sliders move.

### Significant Figures

1.1.3.1   Understand the concept of significant figures

1.1.3.2*  Round integers to a required number of significant figures

1.1.3.3   Round decimals to a required number of significant figures

secmm-cc-theme-1-key-idea-2.pptx

### 1.1.3.2 Round integers to a required number of significant figures

Understand the value of the ones digit and how it impacts on rounding.

Appreciate that the value of the first digit needs to be reflected in the size of the final answer.

Extend understanding to round to more than one significant figure.

Understand ‘what is the same’ and ‘what is different’ when rounding to the nearest 10, to the nearest 100 and to one significant figure.

Understand the importance of place value and maintaining size when rounding.

Explore the significance of zero digits when rounding to significant figures.

Consider real-life applications of rounding and its limitations.

Solve problems where there is more than one answer and there are elements of experimentation, investigation, checking, reasoning, proof, etc.

### Estimation

1.1.4.1   Understand what is meant by a sensible degree of accuracy

1.1.4.2*   Estimate numerical calculations

1.1.4.3   Estimate and check if solutions to problems are of the correct magnitude

1.1.4.4   Determine whether calculations using rounding will give an underestimate or overestimate

1.1.4.5   Understand the impact of rounding errors when using a calculator, and the way that these can be compounded to result in large inaccuracies

1.1.4.6   Calculate possible errors expressed using inequality notation a < x ≤ b

secmm-cc-theme-1-key-idea-3.pptx

### 1.1.4.2 Estimate numerical calculations

Understand what estimation is and how it is useful.

Understand how to estimate answers to numerical calculations.

Understand how to apply estimation to problems in a given context.

Understand how to use and apply estimation in problem-solving situations.