| PART A | SENA 1 | STUDENT AGE: 6 | ||
Aspect to be developed | Where are they now? | Where to next? | Outcomes and indicators | How? | Why? |
Level 2 (1-20) Easily identified numbers 1-20. Had problems with numbers 23 and 43, however could recognise other numbers between 1 and 100 | Level 3 (1-100) Work on numbers 1-100, beginning with work on the early decades. | NES1.1 Counts to 30, and orders, reads and represents numbers in the range 0-30 - Recognises numbers in the range 20-30 (adaptation) | Working on tasks that involve naming and recording numbers above 30 Teacher input: Helping to explore numbers above 30 by continuing number sequences and talking about numbers within the different decades Activities: Identifying numbers on a 100’s chart. Using base 10 materials to build understanding of 2-digit numbers. | Students require a sound ability to identify numerals in order to use counting on strategies. They will use these skills to develop good counting strategies that will assist with the development of early arithmetic (NSW Department of Education and Training, 2002). | |
Forward number word sequence
Identifying numbers in a backward sequence gives students the ability to count down to or from a number (NSW Department of Education and Training, 2002). An ability to count back from given numbers will assist students in solving number problems. Counting back assists with early addition and subtraction, and will facilitate an understanding of patterning – an early foundation for multiplication and division strategies (Bobis et al., 2004) | |||||
Subitising
| EmergentHad no difficulties with small numbers, encountered some difficulties with the larger numbers, however was very close to correct answer | PerceptualAnswers to questions 45 & 46 were only off by one number – would not take long to move to conceptual thinking | NES1.1 Counts to 30, and orders, reads and represents numbers in the range 0-30 - Names instantly the numbers represented on a set of dice (adaptation) | Use flash cards representing numbers as dots or objects, in doubles, and numbers to 12 Teacher input: Show students a variety of dot/object arrangements. Help students to see numbers as both wholes and parts (eg double 4 is also 8) Activities: Partner dice games, involving recording number rolled, allowing students to create and record numbers on 10 frames, comparing and discussing number combinations, estimating numbers in randomly selected groups of objects | Subitising can assist with addition and subtraction strategies as it is an essential pre-requisite for establishing part-part-whole number knowledge for the numbers 1 to 10 (Victorian Department of Education and Early Childhood Development). This knowledge can help lay foundations for multiplication and division strategies. Subitising also helps students to develop spatial awareness (Bobis et al., 2004). |
PerceptualHad difficulties when counters were screened. Correctly answered the word problem for addition, main troubles were with subtraction | Perceptual/FigurativeNeeds help with subtraction. More work with both concrete and non-concrete materials is required. | NES1.2 Combines, separates and compares collections of objects, describes using everyday language and records using informal methods - Uses concrete materials to solve simple addition and subtraction problems - Joins two groups of objects states the number altogether - Takes part of a group of objects away and states the number remaining | Demonstrate addition and subtraction using concrete materials, adding and taking away objects. Represent addition and subtraction in different ways Teacher input: Help will be needed with the concept of taking one group away from another (or adding to another), rather than counting on or back using ones Activities: Using Unifix blocks and dice, add or subtract blocks according to number rolled (NSW Department of Education and Training, 2002). Work on partitioning/separating, using one group of concrete materials, and one that is abstract (eg, ‘I have 3 blocks here, if was given 3 more, how many would I have?’) |
New arithmetical strategies need to be regularly learnt in order to encourage more sophisticated number fact knowledge (Bobis et al., 2004). Students need to be able to move from count-by-ones strategies, to counting on. A strong sense of ‘5’ and a strong sense of ‘10’ can help students develop counting on strategies (NSW Department of Education and Training, 2002), and will assist students with instant recall of number facts. More sophisticated strategies will also allow students to develop abstract counting skills (Bobis et al., 2004). A better understanding of place value is also necessary for more complex number problems. | |
Multiplication and division | Unable to form groups. Didn’t understand question, had problems understanding equal groups | Able to form groups Needs work on forming groups before understanding concept of equal groups. Work on sharing would help | NES1.3 Groups, shares and counts collections of objects, describes using everyday language and records using informal language - Uses the term ‘sharing’ to describe the distribution of a collection of objects - Uses concrete materials to solve grouping or sharing problems | Demonstrate the construction of equal groups, and the concept of sharing Teacher input: Ensure that the words equal, part and whole are correctly understood. Establish students understanding of ‘half’ Activities: Interactive sharing games, using concrete materials such as cards, play dough and counters, and a focus on word problems to help understand grouping and sharing. | The ability to think of groups of numbers as both parts and wholes is necessary for skip counting, repeated addition and subtraction, estimation, and derived thinking. And understanding of groups leads to the ability to multiply and divide (Bobis et al., 2004) , and will provide the student with more sophisticated strategies for solving problems and thinking mathematically. |
B – Lesson Ideas
The SENA 1 results reveal that, the student requires some development in backward number word sequencing (BNWS) and forward number word sequencing (FNWS). A strong ability to count in sequence, in both directions, will help to develop more efficient Addition and subtraction strategies. A focus on the numbers in the range 0-30, means that the student can expand upon number sequences he already knows, while being introduced to more complex number inclusions.
The syllabus outcomes and indicators relevant to development within this area are:
Outcomes
NES1.1 Counts to 30, and orders, reads and represents numbers in the range 0-30
MWES1.1 Asks questions that could be explored using mathematics in relation to early Stage 1 content
MWES1.2 Uses objects, imagery, technology and/or trial and error to explore mathematical problems
WMES1.4 Uses concrete materials and/or pictorial representations to support conclusions
Indicators
Counts forward to 30, from a given number
Counts forward from 30, from a given number (adaptation)
Compare, order, read and represent numbers, to at least 20
Continue simple number patterns that increase or decrease
Justifies answers by explaining strategies or processes used
Gives reasons for placing a set of numbers in a particular order
Solves problems using strategies that include using objects, trial and error, and acting it out
Explains why a collection of objects has been sorted in a particular way
Recognises when an error occurs in a pattern and explains why it is wrong
Names the number before and after a given number
Orders a set pf numbers up to 20 from smallest to largest
Activity 1 – Number sequence role play
Resources: Large pieces of card displaying each of the numbers in the range 10-30
10 cards in a sequence (eg 10-20, 15-25, 20-30) are handed to 10 students. The students without cards become the ‘sequence police’. Their role is to help put the card-holding students into the right order. To begin, a card-holder is asked to stand at the front of the class. Class members are to state the number that is being held. Another student is asked to stand, and class must decide which number is bigger, and where the new number should be placed. This process is to be repeated until all the cardholders are standing in the correct sequence. The class should then say aloud all the numbers in sequence.
Teaching input: Card-holders can be called to stand randomly, or the teacher may ask ‘what number comes next?’, or ‘what number comes before?’. The teacher should always ask class to identify each number, and allow students to justify why they are putting the numbers in a particular order. Starting the activity with a number other than 10, 20, or 30 will help students to move away from simply memorising the sequence, and allow them to use other strategies for ordering. Having the teens and the 20’s in a sequence together may help stop common number reversals. At any point in the activity, the teacher can ask students to say aloud the numbers already displayed, and state which numbers are missing.
Working mathematically: Reasoning, questioning
Activity 2 - Number chart and number bingo (adapted from DENS 1)
Resources: Number charts, counters
9 | 10 | 11 | 12 | 13 |
19 | 20 | 21 | 22 | 23 |
13 | 14 | 15 | 16 | 17 |
26 | 27 | 28 | 29 | 30 |
17 | 18 | 19 | 20 | 21 |
This activity is designed for small group work, with students who are in the perceptual/figurative stage. Students are given a number chart with numbers suited to their particular ability. On the squares to the left of the number, students must write the 2 numbers that come before. On the right, they are to write the numbers that come after. Students are then put into pairs (desk pairs are fine) and given a 3 x 3 grid, and asked to select 6 of the numbers from their previous grid. This becomes their bingo card.
16 | 17 | |
28 | 29 | 30 |
19 | 20 | 21 |
Bingo numbers are called out by the teacher who says, for eg, ‘The number that comes after 26’, or the number that comes before ‘13’, and records each number announced. The pair must determine if they have the number, and if so, cover that number with a counter. When all numbers are covered, the pair calls out ‘Bingo’
Teaching input: For the first stage of the activity , the teacher should ensure that students have filled the spaces in correctly, and that they understand the terms ‘before’ and ‘after’. The first number chart can also be used for early addition and subtraction questioning, eg ‘how many more units does 17 have than 15?’.
During Bingo, the teacher should also check that the right numbers are being identified, by asking (every now and then), what the number they should be covering up is.
Activity 3 – Number sequence worksheet (see appendix I)
Students are to complete worksheet, which focuses on numbers before, after, and in sequence, in the range 10-30. This worksheet could be adapted to suit different ability levels by using different numbers. This activity allows students to examine number sequence and number value.
Teaching input: Representing the sequences in both words and numbers is important, as students are shown that a value can be represented in different ways and still mean the same thing. At the completion of the worksheet, which should be done in ability groups, the teacher should discuss each answer with the students to determine how they found their answer. Questions such as ‘ how do you know what number is bigger/smaller?’ ‘Are 21 and ‘’twenty-one’’ the same number?’ ‘How do you know what comes next? And ‘ how much bigger is 22 than 23?’ will encourage students to use reasoning, and help the teacher to identify the strategies used.
Working mathematically: Questioning, communicating, reasoning
Appendix I - Number sequence activity sheet
What number comes next?
16, 17, 18, 19, 20, ...? _______
twenty-five, twenty-six, twenty-seven, _____________________, twenty-nine
What number comes after 12? _______
What number comes before 30? _______
13, 14,…, 15, 16, 17 19, 20, 21, …, 23, 24
Which number is bigger, twelve (12) or twenty-one (21)? _______
Which number is smaller, thirteen (13) or twenty-three (23)? _______