What Grade 6 Maths milestones are scholars required to master? We continue our overview of the mathematical skills Grade 6s acquire during this year of their schooling. In our last Grade 6 Maths milestones article we considered numbers, operations and relationships. This article will consider how number sentences are used to build the foundation of algebra.
Remedial Learners Can Thrive in Maths
Japari is a proudly remedial school. Each of our staff members has the necessary training to assist remedial students from Grades 1 – 7. Our students learn the mathematics skills, which will serve them in good stead for the rest of their schooling. Our results show that we have an outstanding track record in preparing our remedial learners to function and even thrive at conventional high schools – not only in Maths, but in all primary school subjects.
To do this, Grade 1 – 7 remedial learners need an effective remedial learning environment. It is here that they learn to succeed in their subjects. A solid foundation in mathematics will serve them well in various areas of their lives to come, well beyond the completion of their schooling.
Sixth Grade: Number Sentences
Grade 6 is the year that introduces algebraic functions to the learners. This happens under the broader category of patterns, functions, and algebra. Students are first shown algebraic concepts using number sentences. Number sentences form the crux of mathematics from the earliest grades and beyond high school.
Number Sentences
“Number sentences” is another term for “sums” or “Math problems.” From the earliest school years, pupils have been working with word sums and performing the necessary calculations.
So, to make it very simple, consider the following number sentence:
5 + 17 = 22
That is a straightforward number sentence. Grade 6 learners have been working with them since early in their academic school careers and are used to working with number sentences by now.
These can be expressed in English with examples, such as when Bobby invites five friends to his party. He then invites seventeen more. How many friends come to his party?
5 + 17 = How many friends were at Bobby’s party
This means that: 5 + 17 = 22. Bobby had 22 friends at his party.
An understanding of this simple method is really the foundation of algebra. Although one might not realise it at first, the question has algebra built into it. To show students that this is what they have been doing for many years already up to this point in Grade 6, it is possible to phrase the question like so:
5 + 17 = x
This means that: x = 22.
Pupils can then consider:
5 + x = 22
And then solve for x: x = 22 – 5
Therefore x = 17
This is one of the ways that number sentences are used to introduce the concepts and ideas of algebra.
These steps are not complex. However, these simple steps can be used to introduce sixth graders to the ideas of algebra. They can also see the real-world application of finding solutions to mathematical problems that arise in everyday life. They are shown how “solving for x” has practical uses.
This is the platform that teachers will build upon to venture into concepts that are more involved.
Number Sentences and Problem Situations
As learners have been using number sentences to solve problem situations from the earliest grades, these problems have slowly been building in complexity.
The example above about Bobby’s friends and his birthday illustrates how students approach the content. They have been taught to think through a scenario and discern the mathematical task that is in the premise.
This is the springboard to formulating algebraic equations in Grade 6.
Number Sentences and Other Forms of Representation
There are questions that are posed to students only as a number sentence. However, it is more common for learners to work with number sentences in conjunction with other mathematical forms of representation.
This means that most often students will not simply be given the numbers to be calculated. Rather they are asked Math questions in different ways. These include word problems as the above examples illustrate. The information is also given in various visual formats.
The visual formats include charts and diagrams. The information from these visual representations must be reduced to number sentences to solve Math problems.
Throughout the year, different examples are specified and solved at appropriate moments, on the Math’s curriculum calendar.
Equivalence and Number Sentences
Many people, even adults, might not at first grasp that number sentences show equivalence. This is often over-looked, in our day-to-day interactions while doing Math problems.
What this means is that on either side of the equals sign, both formulas or numbers are really always the same.
So: 3 + 2 = 5
3 + 2 = 4 + 1
3 + 2 = 9 – 4
5 = 9 – 4 Or any myriad of equivalent number sentences.
When phrased in this way, it is obvious that what is on the left side is equivalent to the side on the right of the equals sign. Grade 6 learners will be trained to see this equivalence. They will also learn to utilise this fact in their problem solving. The algebraic problems they will be interacting with from now on will make more sense when they see the equivalence that is found in all equations.
Using the patterns of number sentences in Grade 6
Grade 6 learners will use the patterns that emerge from number sentences to address various topics. Using these patterns, the learners can make sense of a variety of Maths problems.
As examples, there are the commutative, associative, and distributive properties with whole numbers. These are used to break down and build numbers we are using in calculations.
Commutative property: This means that in addition and multiplication number sentences, the numbers can be moved into any order without the result being affected.
Associative property: This is similar to the communicative property, but focuses on how the numbers are grouped without changing the end result in addition and multiplication problems.
Distributive property: In multiplication, if you were to multiply each of the numbers together, you would get the same result if you multiplied each of the numbers individually by a number, and then added up each of the answers one by one.
Learners don’t necessarily need to know these terms, but they do need to know how to work with each number or variable, and in what order to tackle each part of the problem. In follow-up Maths milestones articles, we will further explore what and how sixth graders learn about the subject.
Grade 6 Remedial Learners and Maths
Maths is a language. This means that it requires constant practice. It is also necessary for learners to understand the steps to take to solve the problems.
Japari is the proudly remedial school that can assist your remedial child to thrive with Maths. We are a school for those children who find that they have not flourished in a mainstream education environment. At Japari our learners receive needed support. Often, this support is not offered to remedial learners in most mainstream schools. This is a key difference in addressing the needs of learners with particular learning requirements.
We also will take the time to build the foundations upon which Maths proficiency rests. Our small classes and specialist teachers are here to help your remedial child realise their academic potential. This lays the foundation for them to do well in a mainstream high school.
As time progresses, we will continue to explore what Grade 6s learn in Maths. We will also always be available to help you with your child’s remedial Maths needs. Call us today to see how Japari can help your child flourish in whatever Grade they are in, in sixth Grade and beyond.
Bibliography/Further Reading
https://www.thoughtco.com/why-mathematics-is-a-language-4158142
https://www.splashlearn.com/math-vocabulary/addition/commutative-property
https://www.splashlearn.com/math-vocabulary/addition/associative-property
https://www.splashlearn.com/math-vocabulary/algebra/distributive-property
