To count up to 100 objects successfully, students need to learn the number names, and to develop systematic methods for accurately counting large collections. These will generally use the base ten structure of the number system.
When extending students’ factual knowledge (the names of numbers), be mindful that as with numbers to 20, the irregularity of English can cause confusion. Some students may confuse ‘teen’ and ‘ty’ number words. For example, when counting aloud by ones from 12 to 20, some students might say: 'twelve, thirty, forty, fifty, sixty, etc'. There may be a slight hesitation before the student says twenty (or thirty, forty etc) and one hundred. Also, students may say: 'ten, eleven-teen, twelve-teen, thirteen' in order to ‘fit’ these number names into the counting by ones pattern.
Also, students who find bridging across decades difficult often follow saying twenty-nine with ‘twenty-ten’. Counting backwards makes these transitions even harder. For example to go from 30 to 29, the student needs to not only think that the twenties come before the thirties, but also to go to 29 rather than just 20.
The teaching challenge is to extend students’ factual knowledge (the names of numbers), conceptual understanding (linking number names to base ten and place value properties) and strategic skills (to plan methods of counting efficiently).
At this level, using the hundreds chart will help students to find relationships between numbers. For example, 42 is the number 10 more than 32, and so 42 is directly below 32 on the hundreds chart. Likewise, the number 33 is next to 32, and it is 1 more than 32.
Assist students to visualise the patterns in the hundreds chart, which will improve their ability to calculate mentally. While initially students may need to see a chart, ultimately they will visualise the patterns and solve problems without reference to the chart.
Provide additional support for those students who do not see the base ten patterns underlying the hundreds chart. These students will attempt to count by ones. For example, when asked the number that is ten more than 23 they touch or say each number until they get to 33. Research has shown that persisting with counting by ones to add and subtract is a characteristic of students who need more support to make adequate progress in mathematics.
Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line (VCMNA087)
VCAA Sample Program: A set of sample programs covering the Victorian Curriculum Mathematics.
VCAA Mathematics glossary: A glossary compiled from subject-specific terminology found within the content descriptions of the Victorian Curriculum Mathematics.
Students count to and from 100 and locate these numbers on a number line. They partition numbers using place value and carry out simple additions and subtractions, using counting strategies.
Students recognise Australian coins according to their value. They identify representations of one half.
Students describe number sequences resulting from skip counting by 2s, 5s and 10s. They continue simple patterns involving numbers and objects with and without the use of digital technology.
- Counting out aloud
- Using hundreds charts and number tracks
- ‘What’s missing?’
- More efficient strategies for counting
Counting out aloud
Take every opportunity for counting with the whole class both out loud and silently, with and without moving or touching objects; with and without writing numbers.
Learning the number names to 100 is done in conjunction with developing base ten knowledge (place value). Students will first learn to count and read two digit numbers (in the teens, twenties and possibly beyond) without explicit attention given to the grouping into tens. For example, when young children see 24, they see it only as ‘twenty four’ and probably as the number after twenty three, but initially not as 2 tens and 4 ones. Later the base ten understanding begins as they learn to count by tens (ten, twenty, thirty, etc) and then to ‘fill in’ the numbers between.
Using hundreds charts and number tracks
Reading and writing numerals is developed simultaneously with the higher verbal sequence. A hundreds chart is a very flexible visual aid to support verbal work. It is particularly useful because the numbers are arranged in groups of ten, so the base ten patterns are evident.
It is also important to use different formats of the hundreds chart in order to highlight different patterns to students. There are many charts that can be downloaded from mathematics websites.
A lineal tool, such as a number track could also be used, particularly for assisting students bridging the decades for example, from 59 to 60.
‘What’s missing?’ is an activity that can be used for many counting tasks. A hundreds chart on the wall or made with tiles on a frame, provides the number sequence in order. Ask the student to look away while you turn one number face down/hide it/turn tile over. Ask the student to say what number they think is missing then let them check. This can be extended to hide adjacent sets of numbers, rows of numbers, etc.
There are many patterns on the hundreds chart that support these activities.
Using downloaded versions of hundreds charts, cut them up along some lines to make a jigsaw piece. Ask students to reassemble the chart from the pieces and discuss strategies.
Once students can put a complete chart together, prepare a chart with some numbers missing. Cut the chart into ‘jigsaw’ pieces. You could use jigsaw pieces with only one number showing for the students to complete the missing numbers. For example what numbers are missing in the boxes shown? Always, students should describe how they obtain answers in terms of adding or subtracting 10 (moving vertically) or 1 (moving horizontally).
When students are confident completing the chart with one given number on each jigsaw piece you can ask more open-ended questions.
For example: The number 43 is covered by pieces like these shown below. What other numbers might be covered?
More efficient strategies for counting
Students need plenty of practice to develop efficient strategies to count large numbers of objects. There is much more involved than counting smaller collections.
Place a large number of Unifix blocks on a table. Students estimate how many blocks there are altogether. Then ask students to count them. Initially they count, or attempt to count the number of Unifix by ones. However, soon students realise they can join ten Unifix together and then count by tens rather than by ones. This is more efficient and more likely to be correct, and easier to check.
Initially the estimates will be guesses, but with practice students will become quite proficient at estimating the number of Unifix. They develop a better idea of the quantity of larger amounts.
Students need to learn to group into tens in many contexts. For example, if counting a large number of objects, students must learn to group in tens. This will commonly occur with coins. An efficient strategy is to make piles of ten, then count the number of piles, then include the remaining objects not in a pile. This enables easy checking and calculating.