Odd integers

Odd integers Three consecutive odd integers are such that, the sum of the first and second is 31 less than three times the third. Find the integers:

Solution;

Let the 1st odd integer be letter a,

The 2nd odd integer will be, a+2,

The third odd integer will be, a+4,

This is because the difference between consecutive odd integers is 2. Hence, we take the 1st odd integer to be an unknown value.

1st+2nd=3(3rd)-31

a+ (a+2)=3(a+4)-31

2a+2=3a+12-31

2a+2=3a-19

2+19=3a-2a

21=a

a=21,

Therefore the integers are: 21, 21+2,21+4

21, 23, 25

To proof this;

21+23=3(25)-31

44=75-31

44=44

Hence 21, 23 and 25 are the consecutive odd integers.

Patterns and Algebra

Algebraic study guides ones thinking ability to; generalize, replicate, describe, complete, continue and create repeated patterns and number patterns that either increase or decrease. The number patterns are formed through skip or rhythmic counting. Repeated patterns can be formed through; shapes actions, pictures, sounds or any other material. Pupils can be encouraged to create a wide variety of such repeating patterns and describe and also label them using numbers for example; in repeating patterns, they can be described using numbers indicating the elements that are repeating. I.e. B, C, D, B, C, D… hence it has three elements that are repeating and can be said to be a ‘three’ pattern, because there is a flow of sequence of repeating elements. More so, the ability to identify and use number relationships and make conclusions about number relationships is a very important aspect of algebraic thinking.

Tipps, M. explains that, pupils in primary level rush for conclusions whenever they undergo patterns and algebra test, in his case of series, he argues that; some students examine only the first two terms in a series, where, they try to calculate and determine subsequent terms in the series, without considering the other terms that follows it, this approach can only work if all terms shows the same increase or decrease in the series set. However, consider the pattern; 1, 3, 6, 10, 15… the difference between the first consecutive terms is +2 and is not the difference for subsequent terms. A pupil who chose to use +2 rule from the first two consecutive terms would mistakenly predict that, the next immediate term in this series is (15+2) which is 17, hence it is not the case.

Illustration 2

Students being taught should be of grades; k-2, it should consist of a setting of small groups, the objective should be to allow students to demonstrate five different representations of a pattern, the materials should include, sentence strips and symbol patterns. Begin with displaying or a display of geometric shapes cut from one color of poster board, read the pattern with the children uniformly for example; square, triangle, circle, square, triangle, circle,. At this point, ask the children to name the shapes in the pattern, let them explain the number of shapes in one sequence and where the sequence begins and ends, evaluate the sharpness of the students by asking them if the alphabetical letters could be used to illustrate the sequence, have them suggest the different alphabetical letters combination such as E-F-G, explain to them to choose any letter combination of their choice.

Figure 2: Source author 

Conclusion;

Students can have various benefits from patterns and algebra in the following ways; they get to know how to check solutions to continuing a pattern and repetition of the process i.e. they can apply this in strategic reasoning, also, they can use these skills to make coherent connections between counting and repeating patterns, lastly, they can use the skills to create a repeating pattern through use of simple computer graphics.