Beginning processes

Beginning processes such as, matching, sorting, comparing, ordering and patterning assist children in recognising attributes, simularities and differences in everyday items. Activities based on these processes assist children in reasoning, problem solving and communication, while they also assist in connecting mathematical ideas. Children are exposed to these processes in their early childhood education through activities that encourage them to match, sort, compare and order objects. It is common for children to identify and describe attributes in a basic manner. For example a child can often identify an object by its colour or size. However, it is important for children to use higher order thinking skills to reason, and develop a deeper understanding of mathematical connections and language. This can be encouraged through questioning, seeking ideas, and creating games that develop these abilities (Irons, 1999).

Matching

Matching objects by their attributes is an important comprehension skill related to success in mathematics. In early childhood, there are three levels of matching activities. These begin with children matching objects that are familiar to them. Once children are able to match with familiar objects they are then likely to adopt a more mathematical vocabulary. This is important, as mathematical language needs to be understood to assist with an intermediate level. At the intermediate level, children learn to match more complex shapes. Then, at the advanced level, children build earlier experiences in order to match patterns. Shape matching activities at these three levels develop skills that can be used in recognising letters, words and numerals. Terms of equivalency is important when teaching matching concepts. 

Vocabulary:

• Same

• Match

• Belong

• Together

• Alike

• Another 

The language above is descriptive language that will assist the students in describing contrasts and differences in the non-matching objects.

Humpty dumpty game

      

Activity:

Domino Drag

Children match dot pictures using dominoes.

Show the dominoes and point out the dot pictures on each end. Demonstrate how to match the dot pictures by placing the matching ends of the dominoes together. Place one domino in the middle of the group. Deal the remaining dominoes and ask the children to place their dominoes facedown. Have one child flip one of their dominoes and decide if it matches either end of the face-up domino. If they find a match, they move their domino to its match. If they do not find a match, the next child has a turn. Continue to play until all dominoes are matched in a straight line, or until no further matches can be made. 

Sorting

Sorting is any process of arranging items in some sequence and/or in different sets, and accordingly, it has two common items of the same kind, class, nature, etc. Students in an early childhood classroom can sort objects within their classroom, they can sort the objects according to colour, size, shape, texture. Examples of the items sorted within the tutorial is used below. These items assisted in demonstrating some examples for the classroom. In addition to sorting objects students can sort their peers according to similar elements such as, height and hair colour. An activity that was created for this purpose is demonstrated below.

Shells

Shapes

Teddy bears in buckets

Sorting activity:

Explain to the students that sorting objects helps people see the similarities and differences between items, and it also helps people locate things in an efficient way.

 Students are given a little activity to give them further practice with sorting. I have a small box full of items that need to be sorted into the right groups or categories.

 Spread out all the items and give children a few minutes to study them. Then, tell them that it will be their job to find a way to sort them. Allow the children to think of as many ways to sort as they can. Put the items into the suggested groupings and then as a class we will discuss why they chose to group the items the way they did.

 I would then ask if anyone came up with a different way to group the items and ask if they would like to share it with the class.

 If there are no questions, we will then move onto show and tell time! After each child has a chance to show and talk about the item they brought in, we will arrange the objects from largest to smallest.

 I will have the child with the biggest object brought in lay their item down first. Then I will have the next biggest item placed down beside it, etc... After sequencing the items largest to smallest we will find the common similarities and differences among the items and discuss how we could arrange them into at least 2 separate groups or categories. Have the class think of these groups and help them if needed.

Examples: size, softness/hardness, shape, use of the objects

Go over how the items were grouped/sorted. Now we will count how many items are in each group and mark them on a table or chart, using an X. Then we will tally up each X and put that number to represent the number of items in the group.

Comparing

Comparing objects is a great way for children to evaluate differences and similarities in objects and numbers. Children can compare elements within objects such as, texture, shape, size, and group them according to these attributes.

Ordering

Ordering is an excellent concept to assist children in recognising number patterns while it encourages them to use higher order thinking when using the right activity within the classroom. There are various activities that students can learn from. One of the activities I did on my practicum is below. The students enjoyed this a lot, and I found they understood the concept quite well.  A number line of cards is also a good introduction to ordering for students that find the concept a little difficult to grasp.

Classroom activity:

Practice by neatening up your friends. Measure their heights, then place them in ascending order of height. Try it again, but use their weights.

Patterning

Pattern definition: A set of shapes or numbers that are repeated in a predictable way. We use different types of patterns to organise our daily lives.

Patterns can be shapes, designs or groups of numbers that repeat. Patterns can be seen when investigating items that are around them in their everyday environment. Children can be encouraged to translate patterns and see repeated patterns in objects. Being able to see repeated patterns allows children to identify what is a pattern and whether the pattern is a repeating pattern or not. The core of a pattern is the shortest string of elements that repeats. Patterns can also be extended. Patterns can be labelled by using letters of the alphabet. This assists in the recognition of the pattern. 


Resource suggestion:


Growing patterns challange

Example of repeating patterns:

Example of labelled patterns that do not match:




 

    A                    A                B                 A               A                   B



   A                      B                  A                  B                  A                   B

Early number concepts

Subitising

Definition: Instantly recognizing the number of objects in a small group, without counting.

Subitising is when children are able to recognise an amount by seeing the total without counting. For example, if three flowers are drawn on the board the child that can subitise is able to instantly see three instead of saying “1, 2, 3.” This form of recognition can be encouraged through the use of practise. The teacher may represent varying amounts of an object on the board and see what the children did to figure out the amount. Teachers should ask the students questions to decipher whether they are subitising or counting.

Conceptual subitising:

people are able to recognise a number on an object such as a dice or domino without counting. They often “just know” what the number is (Clements & Douglas, 1999).

Perceptual subitising: recognising a number without using mathematical processes, such as counting (Clement & Douglas, 1999).

 Counting

Hundreds charts can be used to assist children in grasping the concept of counting on and back using counters (Unglaub, 1997).

Koala bear train

Clown counting game

Cardinal numbers are... counting numbers, these can be seen as any number that we can count. Therefore, zero is not included.

Integers are... a set of numbers composed of counting numbers and their negative versions. They are rational numbers, and do not include decimals. For example, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

Whole numbers are... all numbers, but they do not contain fractions.

Ordinal numbers are... place numbers. For example, first, second, third, forth, fifth and so on.

Counting Language


What does number 5 look like? (Have students represent this with counters or unifix cubes)
Which number comes next?
How many more do you need to reach 10?

Frog number line

Website suggestions:

Count us in

learning planet counting

Counting dinosaurs

Number

Addition is...

bringing two or more numbers (or things) together to make a new total.

Here 1 ball is added to 1 ball to make 2 balls:

Using Numbers it is: 1 + 1 = 2

And in words it is: "One plus one equals two"


Resource suggestion for addition:


Minko's milkshake shoppe - addition game

Subtraction is...

taking one number away from another.

If you have 5 apples

and you subtract 2,

you will be left with 3.

This would be written: 

5 - 2 = 3

Division is... splitting into equal parts or groups.

It is the result of "fair sharing".

Example: there are 12 chocolates, and 3 friends want to share them, how do they divide the chocolates?

12 chocolates

12 chocolates divided by 3

Counting on 
These cards assist children with counting on. The children are able to see how many there is my the written number and how many more they are required to count to obtain the total. Counters are encouraged to be used with these cards to demonstrate a concrete example to the students.

   Doubles
Doubling cards such as these lets the student see how the numeral can double to make a total of four. Children that can not subitise the amount instantly can practice this with doubling cards or die.

Near doubles
Domino cards such as these can be used to show near doubles to children. The difference in colour allows the child to see the near double plus one.




Resource suggestion: 

Count me in too 

This site includes various mathematical games that focus on addition, subtraction, division and multiplication number facts. It is a useful resource for children in early childhood and upper primary, as the games can be adapted for both age groups.

             

Mental and written computation

Mental computation is an important mathematical concept for students. Understanding how to incorporate mental computation strategies into the classroom is simple and essential. Strategies to encourage mental computation are getting the students to reflect on their learning and share their experiences with others, so they have a better understanding of how they performed the activity and came to their conclusion (Perry & Dockett, 2002). playing games that allow them to see how an equation results in a specific outcome (number line game). In addition to this the students can play games, such as memory to assist in their recognition of whole digit numbers. 

Algebra

The central ideas promoted in algebra are patterns, functions, relationship and change. Patterns are an introduction to algebraic thinking. Children often investigate patterns each day by seeing patterns in routines, songs, objects etc.  For example, a teacher may share a pattern with a child

“clap, tap, clap, tap, clap, tap.” However, it is essential to encourage children to go beyond demonstrations of patterns. It is important that children recognise, describe, extend and translate patterns. This can be encouraged through problem solving activities that assist children in identifying relationships and making generalisations.  


Functions can assist with recognising, describing, extending and translating patterns. For example, children can view patterns in pictures and objects and identify the change they see in the pictures or objects. This is a concept in algebraic thinking called change. The understanding that most things change over time, that such changes can be described mathematically, and that changes are predictable helps lay a foundation for applying mathematics.  We must encourage young children to notice and describe many different changes. There are two algebraically oriented types of change: qualitative and quantitative (Willoughby, 1997).

 What do you see when you look at this picture?










       What do you see when you look at this picture?












Asking children questions to seek their translation abilities encourages the students to describe and identify different attributes between the two pictures. Once the students have described attributes they are beginning to translate a pattern (Willoughby, 1997).




Algebra Activity:

Required materials: counters, matchsticks 

Here are two patterns, one made with matchsticks and the other made with counters. You should choose one to work with and your partner should choose the other (demonstrate two different patterns to the students).

Now try this with your pattern! 

1. Make the next three terms of the pattern. 

2. By counting the matches or counters, write down a number 

sequence that describes your pattern. 

3. How many matches or counters will be in the tenth term? Check by 

making the tenth term. 

4. Swap and read each other’s answers. What is the same? What is 

different? Have you both used the same pattern? Discuss your 

ideas with your partner and write a sentence about what you 

found. 

Measurement

Measurement is an essential area of mathematical development for children. There are various concepts that children need to understand in order to convert units, calculate perimeters, area and volume. As shown within the video below, there are various opportunities to develop lessons based on measurement concepts. This assists students in working out distances and conversion. Whether they need to determine how many millimeters, centimeters etc the Bee-bot or chosen object needs to travel. This is also effective with Lego robots for students in higher grades, as circumference and diameter can also be incorporated to develop higher order thinking skills to do with measurement.

Non standard units of measurements assist in measuring areas or objects that are smaller than a standard unit, while using non standard units of measurement also assist in obtaining a close estimate of the length or width of an item. Non standard units include, feet, arm span and even height, hands, straws etc. Non standard units should be introduced to students prior to standard units so they grasp the concept of measurement and build their understanding of larger units such as, metres, millilitres, litres, kilograms etc.

Standard units of measurement are an exact measurement of an object or area. Standard units are represented with tape measures, rulers, measuring cups etc on the metric scale.


Resource suggestion:
Snakes measurement game

Geo-board - students can calculate perimeter & area

Non standard unit

Geo-board

Length

Village and Bee-bot

Circumference

What You Need:

• Paper clips or a tape measure
• 1 sheet of graph paper per person
• Two small bowls
• Lima or red beans
• 1 glass jar with a wide mouth
• Water
• Permanent marker or masking tape
• Blank paper for recordingPencil or markers

What to Do:

1. Show students the measurement tools you've assembled and explain how they are going to measure their hand in 4 different ways.
2. Get the students to write a heading on the blank paper: “My Hand Size”. This will be the recording sheet. Divide the sheet into 4 sections and label them length, area, capacity, and volume.
3. Measuring length: Use the paper clips to make a paper clip chain or use the tape measure to measure the length of your right hand. Start at the wrist and end at the tip of the longest finger. Count the number of paper clips or centimetres if using the measuring tape. Record the information on the recording sheet.
4. Measuring Area: Use the graph paper for this portion of the activity. Help students place their right hand on the sheet of graph paper with their palm down and fingers closed. Tell them to trace around their closed hand with a pencil. Help the students count the number of squares their hand covers. Discuss a method for counting the partial squares. For example, if most of a square is covered does it count as one? Or can you combine 2 half squares to make one whole square? Record the information on the recording sheet.
5. Measuring Capacity: Fill one small bowl with beans. Tell the students to pick up a handful of beans and see how many they can hold in their right hand without dropping any. Have the students empty the beans into the empty bowl and count them to find out their hand's capacity, or how many beans can they hold in their right hand. Record the information on the recording sheet.
6. Measuring Volume: Place some water in the glass jar and mark the water line with a piece of masking tape. Tell the students to use their right hand to make a fist. Have them submerge their fist into the water up to their wrist and record the new water line with masking tape. The amount of water between the two lines is a measure of the volume of their fist. Try pouring this amount into a measuring cup to see the volume of your students' fist. Record the information on the recording sheet.
7. Encourage the students to reflect on the activity by writing down their observations on a sheet of paper after making the four measurements of their hand.

For a challenge, the students can measure their left hand and make comparisons. Are the measurements the same for both hands? You can also encourage students in higher grades to do this at home with a family member. Then they can compare the results. Did their family member have a larger, smaller, bigger hand size capacity to them?