Year level: 7

Strand: Number

Lesson length: 60 mins

In this lesson, students draw on prior knowledge of rounding whole numbers to develop their understanding and fluency when rounding decimals and are encouraged to reason and problem-solve through a variety of contextual activities. Students will also develop an appreciation of the role of estimation in mathematics and science.

Achievement standard

Students use all 4 operations in calculations involving positive decimals, choosing efficient calculation strategies.

Students use mathematical modelling to solve practical problems involving rational numbers in financial and other applied contexts, justifying choices of representation.

Content descriptions

Students round decimals to a given accuracy appropriate to the context and use of appropriate rounding and estimation to check the reasonableness of solutions. AC9M7N05

Students use the four operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies. AC9M7N06

Students use mathematical modelling to solve practical problems, involving rational numbers including financial contexts; formulate problems, choosing representations and efficient calculation strategies, using digital tools as appropriate; interpret and communicate solutions in terms of the situation, justifying choices made about the representation. AC9M7N09

General capabilities

Numeracy Progression:

Critical and Creative Thinking:

• Drawing conclusions and provide reasons Level 5
• Evaluate actions and outcomes Level 5

Related content: Science AC9S7I03

This lesson uses a short list of questions reviewing the key concepts as a formative assessment opportunity. You can also access these questions in slide 13 of the teacher's slides.

Short formative assessment

• Write 90.56 in words.
• Round 125.65 to the nearest tenth.
• When rounded to the nearest tenth, what numbers might round to 10.6?
• What might be a reasonable estimate for the number of pens you use each year? Tell us your estimate, how you calculated it, and explain why you think it is reasonable.
• Why are estimating and rounding important?
• Give an example of where you use estimating and rounding in everyday life.

Differentiation:

• Vary the complexity of exit ticket questions by changing the values given for different classes or students.
• Support students’ affective needs by allowing them to report on how well they felt they understood how to round decimals (for example, drawing a 😀 😑 😟 face at the bottom of their exit ticket answers).

Some students may:

• believe that the longer decimal always means a larger value
• believe that the shorter decimal always means a larger value
• evaluate the wrong key digits when rounding
• believe that trailing zeros on decimal values change the numbers value
• believe that multiplying always makes a number bigger
• struggle to name decimals with internal zeros, or trailing zeros
• struggle to rename decimals (for example, twenty-hundredths as the same as two-tenths)
• struggle to name decimals using correct place-value language (for example, 0.23 is twenty-three-hundredths, rather than oh-point-two-three)
• believe that decimals are rounded by truncation
• believe that the decimal point itself rather than the integer sitting in the ‘ones’ column, defines how we treat decimals. This may lead students to believe mistakenly in the existence of a ‘oneths’ column after the decimal point, rather than a ‘tenths’ column.

Students:

• use strategies for rounding whole numbers (for example, the rule of 5: that 5 or more rounds up, and less than 5 rounds down)
• recognise place value (to thousandths)
• understand decimal multiplication (with or without technology)
• convert between cents and dollars (with or without technology).

The meaning of the terms rounding, estimate, approximate, reasonableness are found on the Version 9 mathematics glossary.

In this lesson, an emphasis is placed on describing decimals using language descriptively, such as, tenths, hundredths and thousandths. This is purposeful so that students can make deeper connections between how decimals are rounded with respect to place value. For instance, the number 11.65 usually spoken as 'eleven point six five' is rather less meaningful than saying 'eleven and sixty-five hundredths'.

What you need:

• Lesson plan (Word)

• Teacher's slides (PowerPoint)

• Reasoned rounding decimals game (Word)

• Rounding reference sheet (Word

• I have, who has game (Word)

• Ten-sided dice labelled 0–9 (enough for one between two students)