Grade 6 Number and Algebra
Journal problem 4: Section A – Number and Place Value
Regrouping with decimals
Complete Blast activities A5‐A7 before beginning this problem. Introduction: This focuses on teaching students about place value in the hundredths column, and that the tenths and hundredths can be included in non‐standard groupings across the decimal point (e.g. 652438 hundredths). You may wish to start with just tens, ones and tenths. Be aware that you do need to progress to six digit numbers with thousandths at some point. Leading questions: See Journal problem 2 as well.  If you were just making 524 in different ways, how could
you do it? Do you always have to be limited to having no more than 10 ones? So now how can you apply this to include tenths in this number? How about the hundredths?  If I was considering the number 0.9, how many tenths are
there? How about if I add one more to get 1.0, how many are there now? So how can you use this to come up with different groupings for the tenths in the number above? How many hundredths would there be in 1.0?  In the number 1.0 there should be 10 tenths right? So
what about the number 1.1? How many tenths are there in that number? We are talking about how many tenths there are altogether, not just how many there are in the tenths column. How many hundredths would there be in that number?  If you have to do much more than this you are really just
telling students the patterns. Misconceptions to watch out for: (1) Decimals just separate numbers of the same size.  Tenths are the same size as
ones, hundredths are bigger, and thousandths are bigger again.  Tenths means tens because
they sound the same. (2) Decimals and all fractions are made by cutting in twos.  Decimals are any type of
fraction (e.g. think that 3/5 is the same as 3.5)  Decimals area base‐two
system and are made by cutting into halves (half, quarter, eighth etc.) (3) Decimals mean numbers less than zero (negative numbers)  Be aware that many students
think that numbers after the decimal point are less than zero, not between whole numbers. Teaching Tips:  Students often think that the decimal point is a full‐stop and that numbers cannot be regrouped
over the decimal point.  Try making a decimal number with MAB to see whether students realise that 23.4 is between 23
and 24. Some students make 23 then make 4 and just put them apart from each other.  Try using photocopies of MAB and cutting them up to make tenths and hundredths (e.g. a 1cm2
square sliced into 10 or 100 slivers). These can then be used in a similar way to Journal problem 1. Draw lines to show adding the tenths onto the ‘ones’ and ‘tens’.
 Try not to ask students ‘how many tenths are there altogether’ because previous NAPLAN tests
have just asked for how many tenths. Instead refer to ‘how many tenths’ and ‘how many in the
tenths column’ for variation. Similarly, do not ask students ‘how many hundredths altogether’
but ask ‘how many hundredths’ or ‘how many hundredths just in the hundredths column’.
 To go backwards, give students the names of regrouped numbers to put back into decimal
format (e.g. what is the number ‘three hundred and twenty‐seven hundredths’ in decimal
format?).
© Kennedy Press
For use by 2016 licence holders only
Grade 6 Number and Algebra
Section A – Number and Place Value
Follow up ideas: Choose any other 4 digit number with hundredths (no internal zeroes) to regroup. Use time trials to encourage students to come up with as many different names as possible in 2 minutes. Work in groups as appropriate. Complete Blast activities A8‐A11 © Kennedy Press
For use by 2016 licence holders only
Grade 6 Number and Algebra
Section A – Number and Place Value
Problem 4: Regrouping with Decimals
Complete Blast activities A5-A7 before beginning this task
What different ways can the number 524.398 be made? Write
as many as you can think of. You might like to record them
in a place value chart.
Write them here:
Feeling stuck?
• Try regrouping
• Try using fractions
for the tenths etc.
• Imagine if you only
had 3 ones…
what could you do
instead?
© Kennedy Press
For use by 2016 licence holders only
Grade 6 Number and Algebra
Section A – Number and Place Value
Check your communicating:
Make sure that your answers clearly show how you made the numbers. If you need to, add
captions or describe here how you did it:
Understanding:
What pattern or strategy did you use? Make sure that you refer to
the base ten system.
Teacher initials:
Date:
Problem solving / T&R:
o Problem solved with minimal or
non-mathematical prompting
o Some leading questions were used
to prompt thinking
o Solved after explanation
o Did not work out solution
o N/A- not a novel problem
Are you sure that you have found all the possible ways to make the number? Explain your
answer:
Reasoning / Comm.:
(verbal, written, working and
equations, or visual
representations)
o Clearly and logically reasoned
o Easily understood
o Understood with some
interpretation needed
o Some gaps but on topic
o Minimal or off topic
Manipulation problems:
Regroup and rename 402.027:
Understanding / Reflect:
o Connected manipulation problems
to previous questions and answered
easily
o Connected manipulation problems
to previous questions with some
prompting, and answered correctly
o Answered once the similarities to
previous questions had been
pointed out
o Had some problems in answers but
was on the right track
o Did not answer appropriately
o Student not observed
© Kennedy Press
For use by 2016 licence holders only