This unit supports students learning to understand the structure of two-digit numbers and how to operate with them.
Specific Learning Outcomes Session One
Session Two
Session Three
Session Four
Session Five
Description of Mathematics Our number system is very sophisticated though it may not look it. While numbers are all around us in the environment the meaning of digits in those numbers and the quantities they represent are challenging to understand. Our number system is based on groupings of ten. So, of all the ways we could collect single objects into groups, we choose ten as our preferred group. Using ten is so common around the world because humans have ten fingers. In fact the part of our brain that controls our fingers is also associated with counting. To represent all the numbers we could ever want we use just ten digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The word for digits also comes from our fingers. We don’t need a new number to represent ten because we think of it as one hand, one group of ten. When we write 10 for ten we are using place value for the first time. So the place of the digit 1 tells us the size of the quantity it represents 1 ten. Zero has two uses in the number system, as the number for ‘none of something’ and as a place holder. That means it occupies a place or places so the reader knows the values represented by of the other digits. In 10 zero is acting as a place holder in the ones place. Place value means that both the position of a digit as well as the value of that digit indicate what quantity it represents. In the number 73 the position of the 7 is in the tens column which means that it represents 7 units of ten, 70. Renaming a number flexibly is important. In particular it is vital that students understand that when ten ones are created they form a unit of ten. For example, the answer to 25 + 35 is 6 tens since 5 ones and 5 ones combine to form another ten. Similarly when a unit of ten is ‘decomposed’ into ones the number looks different but still represents the same quantity. For example, 42 can be viewed as 4 tens and 2 ones, or 3 tens and 12 ones, or 2 tens and 22 ones, etc. Decomposing is used in subtraction problems such as 72 – 48 = □ where it is helpful to view 72 as 6 tens and 12 ones.
Opportunities for Adaptation and Differentiation This unit can be differentiated by varying the scaffolding of the tasks or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:
Some of the activities in this unit can be adapted to use contexts and materials that are familiar and engaging for students. For example:
Required Resource Materials
Prior Experience This unit is targeted at Level 2 so students are expected to have experience at Level 1 including:
Session OneIn this session the students explore how groupings of ten can be used to aid counting and to perform calculations. They also create the sets of countable objects that will be used in later lessons. Acknowledgment: The game 60 second challenge was created by Ann Downton from Monash University, Melbourne.
Session Two In this session students learn to match quantities with two-digit numbers and vice versa. Part One
Part Two
Session Three In this session students investigate how 100 can be partitioned to form ‘number buddies’ like 20 + 80 and 1 + 99. Part One
Part Two
Session Four In this session the students explore different names for the same two-digit number. Part One In the last lesson the class explored how 100 can be renamed in lots of ways. Now is time to do the same thing with other numbers.
Part Two
Session Five In this session students apply the place value structure of two-digit numbers to change a given number into a different number either mentally or with support of materials. Part One
Part Two
Hello parents and caregivers, Our next mathematics unit is based on Place Value. So we will be working a lot with two-digit numbers like 26 and 79. We will be using materials grouped in tens so we can make sense of the quantities that the numbers represent. For example, 62 means 6 tens and 2 ones and is said as “Sixty-two.” We will also rename the two-digit numbers in flexible ways so that we can apply renaming to the operations, particularly addition and subtraction. |