Year Four - What is a Decimal?
Home - What is a Decimal Map
About this Big Idea
In this Big Idea students explore numbers smaller than one and build an understanding of what a decimal is and what they are used for. Students investigate the relationship between each decimal place to the right of the decimal point and see how this reflects the scale of the relationship to the left of it. Students develop an understanding of why 0.2 is larger than 0.16. Students expand their understanding of the four operations by using these with decimals.
Understanding Goals:
Students will understand:
- what a decimal is
- that one thousandth is ten times smaller than one hundredth, which is ten times smaller than one tenth
- why 0.2 is larger than 0.16
Background:
By the end of Stage 2, students ask questions and use efficient mental and written strategies with increasing fluency to solve problems. Students model, compare and represent decimals of up to two decimal places. Students use appropriate terminology to describe and link mathematical ideas, check statements for accuracy and explain their reasoning. It is important that students apply and extend their repertoire of mental strategies for the four operations. Comparing their own method of solution with the methods of other students will lead to the identification of efficient mental and written strategies. One problem may have several acceptable methods of solution.
Core Content from the Syllabus:
Working Mathematically
Whole Number
- apply an understanding of place value and the role of zero to read, write and order numbers
Fractions & Decimals
- recognise that the place value system can be extended to tenths and hundredths
- state the place value of digits in decimal numbers of up to two decimal places
- place decimals of up to two decimal places on a number line
- model, compare and represent decimals of up to two decimal places
Addition & Subtraction
- apply known single-digit addition and subtraction facts to mental strategies for addition and subtraction of two-, three- and four-digit numbers
- choose and apply efficient strategies for addition and subtraction (Problem Solving)
- discuss and compare different methods of addition and subtraction (Communicating)
Multiplication & Division
- uses mental and informal written strategies for multiplication and division
- use mental strategies to multiply a one-digit number by a multiple of 10
- apply the inverse relationship of multiplication and division to justify answers
Language:
- decimal, decimal point, digit, place value, round to, decimal places, plus, add, addition, minus, subtract, subtraction, equals, is the same as, multiply, multiplied by, multiplication, double, shared between, divide, divided by, division, strategy.
Connected to:
Mindset Mathematics Learning Activities
Visualise
Students begin their exploration of decimals by constructing visual proofs to determine which store has the better deal on friendship bracelets. Students use their understanding of money to support their thinking about decimal numbers. - See page 226
Questions for reflection:
- Is the group's reasoning convincing?
- Is the visual proof convincing? Why or why not?
- What model or models do you think are most useful for representing decimals? Why?
Play
Decimals on a Line provides students a chance to make connections between whole numbers, the operation of division, and how decimal numbers represent numbers between whole numbers. - See page 234
Questions for reflection:
- What strategies helped you pick your numbers to make a fraction?
- Did you need the calculator all the time? When did it help you? When did you decide you didn't need it?
- What strategies did you use to put the decimal numbers on the number line?
- Which is greater 0.4 or 0.12? Give a picture or an argument to justify your answer.
Investigate
This investigation opens the door to thinking about how decimal numbers fit together to make whole numbers. Students investigate how to write number sentences to find the values 1 through 20, using both whole and decimal numbers. - See Page 218
- Are there any numbers you used more than others? Why?
- What is the number that was used the least? Why?
- What operations were used the most? The least?
- Are there any values still missing? Do you think they are possible? Why or Why not?
- What number was the most challenging number for you to find? What strategies did you use to find that number?
Credit:
Boaler, Munson & Williams (2018) - Mindset Mathematics: Visualizing and investigating big ideas Grade 5
NESA - Mathematics K-10 - 2012
