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Year 4 Mathematics Decimal Fractions Unit overview
Decimal fractions are an integral part of our number system, underpinning money and measurement concepts. It is therefore vitally important to ensure that students understanding and ability to work with decimals is well grounded in sound foundational knowledge. This unit uses a popular game of ten pin bowling to support students understanding of the concept of fractions as parts of a whole, and provides a simple and effective platform for describing results in the game in tenths. Ten pin bowling can utilize visual and auditory processing of fractions which in turn can then be used to develop the concept of fractions along a number line. This unit involves students in playing ten pin bowling over a one week period during which they will engage with the concept and language of fractions to describe the results of each game, record results as fractional notation and progressive scores on a number line.
Curriculum intentWays of working
Identify and describe the mathematical concepts and procedures required to generate solutions.
Evaluate their own thinking and reasoning, using everyday and mathematical language, concrete materials, visual representations and technologies.
Communicate and justify thinking and reasoning, using everyday and mathematical language, concrete materials, visual representations and technologies.
Reflect on learning to identify new understandings and future applications.
Knowledge and understanding
Number:
Whole numbers, simple and decimal fractions and a range of strategies are used to solve problems
Decimal fractions (to at least hundredths), and common and mixed fractions have positions on a number line
Common and mixed fractions involving denominators to tenths can be represented as a collection of objects, or on number lines and as parts of a measure to solve problems
Whole numbers (to thousands) and decimal fractions (to hundredths) can be calculated using addition and subtraction
Assessable elements
Knowledge and understanding
Thinking and reasoning
Communication
ReflectingWhat deep understandings are desired?
The desired result is for learners to understand that:
Values of numbers can be represented, described and recorded as parts of a whole
Fractions or parts of the whole can be added together to equal a whole numbers or whole and part numbers
Number values can be represented on a number line to show whole numbers and fractions that fall between the whole numbers
What essential questions will guide the inquiry?
How many pins are down? How can I describe my results as a score out of ten?
How can I represent my score as a decimal fraction?
If I wanted to record my score on a number line, how would I draw the number line?
In what ways is my number line same/different to a number line with whole numbers?
What happens when I add my next score to the number line? In what way does my progressive score change?
What have you learnt about decimal fractions?
What key knowledge and skills will students acquire as a result of this unit?
Students will know:
Fractions are parts of a whole
Decimal fractions require ten parts to equal a whole
Decimal fractions can be written as a decimal or as a common fraction with a denominator of ten
Decimals can be represented on a number line with numbers less than 1 represented between 0 & 1
Decimals can be represented on a number line with whole numbers and fractions of a whole (eg 1.3)
Adding decimal fractions is a counting pattern in tenths
Students will be able to:
Describe a collection of objects (eg five pins down) as a decimal fraction and common fraction with a denominator of ten
Record their score as a decimal and a common fraction
Record the decimal fraction correctly on a number line
Record additional scores and explain the result as a progressive total
Assessment What evidence of student understanding is needed?
Describe numbers as a decimal fraction and explain what that means
Record values as a decimal and common fraction with a denominator of 10 on a number line
Explain what the values on the number line mean in relation to the whole numbers of 0 & 1
Explain what a mixed number (eg 1.3) represents
Communicate how adding decimal fractions results in whole numbers and fractions
Assessment task outline
The assessment task aims to evaluate students understanding of decimals allowing for students to demonstrate a range of knowledge and understanding from simple recording of scores as fractions through to addition of decimals and recording using a number line. The assessment task also evaluates students reasoning and explanation.
Students will play five games of ten pin bowling and record their scores as a progressive total. They will describe their score for each game as both a decimal fraction and a common fraction, and then record it in written notation on a number line. After each game, they will calculate their progressive total and mark this on their number line.
Literacy demands: Low
Numeracy demands: Making links to other contexts where decimals may be used
Explicit teaching required
Describing and recording collections of objects as fractions. Collections of ten objects should be the focus but should not be the only number of parts in the group thereby developing the understanding of fractions, denominators and numerators
Using correct metalanguage of denominators and numerators, parts of the whole, decimals, and decimal point
Drawing number lines to represent different fractional patterns (eg halves, thirds, quarters, eighths, tenths)
Adding fractions using a number line
Counting in tenths using a number line
Explanation and reflection on thinking
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