Part 3: Context-Free Calculations & Patterns, Functions and Algebra & Geometrical Space and Shape in Second Grade
The foundation phase is extremely important for future schooling success. We have looked at what developmental milestones should have been reached before starting Grade 1 at Japari. We have seen what students learn in Grade 1 language skills and math (see the links here, here, and here).
We have considered Grade 2 reading and writing. We also looked at their problem solving and other mathematical development.
This article continues to look at milestones in maths for second graders.
Context-Free Calculations
Context-free calculations are those sums done with only the numbers given. For example, 2 + 2 would be a context-free calculation. This is because it is not a matter of being given a word sum.
Here is an example of a calculation that has context. “Billy had two friends, and then made two more. How many friends did Billy now have?” Here the students are seeing how to use mathematics in a “real-life” scenario.
Context-free calculations are important because they focus on the knowledge of the mechanics of maths. Of course, the real-life application is also very important. But the context-free calculations undergird their mathematical development.
Second Grade Context-Free Approaches
Grade 2s learn to employ a few approaches when working out calculations. They can make use of drawing appropriately to work out problems. They also continue to use physical equipment such as beads or other counters. It is also possible for them to refer to number lines to add and subtract.
In second grade, pupils build on what they learnt in Grade 1 math. They continue to break numbers down with better ease and precision. They also become more adept at halving and doubling numbers in their math. Grade twos can practise number bonds to 20. These are the ways to combine or split up numbers. For example, twelve is one ten and a two.
Using appropriate symbols, second grade learners will be able to add up to 99. The appropriate symbols are the plus sign (+), the minus sign (-) and the equals sign (=).They will also be able to subtract from 99.
Grade twos learn to multiply the numbers 1 to 10. They can multiply these numbers by 1,2,3,4, and 5. They know how to use the times symbol (x) properly.
The number concept expands from 20 to 99 in Grade 2. This means they can look at number up to 99 and compare them to other numbers. They will be able to say whether a number is greater or less than another number.
Rapid Recall
A second grader learns to quickly do sums up to 20. They will know subtraction and addition facts up to this figure. This means they won’t have to work sums out. They will know that 11 – 3 = 8. This is building on the understanding of how sums work to allow them to quickly do these computations. For adding or subtracting in multiples of ten, students will be able to do sums up to 100.
Strategies to Sums in Grade Two
Grade twos will be able to employ strategies in solving math problems. They will learn to use the relationships between adding and subtracting to work out sums. For example, consider 12 – 4 = 8. A grade two learns that to get back to twelve, they will need to add four to eight.
The pupils become better and better at what they learnt in Grade 1. They will continue to put the largest number at the beginning in order to count down. Grade 2s will employ halving, doubling and number lines. They will make use of breaking numbers down and building them back up.
Second Graders Begin to Learn and Use Fractions
Grade two is when the learners begin to use fractions. They can understand a diagram of a fraction. They learn particular single (unitary) fractions. These include one half, one quarter, one third and one fifth. They are able to use and name these in familiar contexts.
Patterns in Grade Two
Grade twos have learnt how to copy, extend and describe number patterns in Grade 1. They continue to develop these skills this year. These are patterns that are constructed with physical objects. The learners also get better at working with more complex patterns that have been drawn. The drawings consist of objects, shapes or lines. The students are able to use words to describe the patterns that they can see.
Second graders also learn to create their own patterns. They are able to use both physical objects and can draw them as described above. The students are also able to use words to describe the patterns they make.
The students continue to identify and work with patterns that are all around us. These are from nature, our everyday lives and from each student’s cultural heritage. Grade 2s get better and better at identifying and describing these patterns. They are also able to copy them.
Number sequences in Second Grade
Grade twos can identify and describe simple number sequences. These are up to at least the number 200. They also learn to copy and extend these number sequences. They learn to create their own number patterns. A grade 2 will be able to explain and describe the number patterns they make.
Geometric Positioning in Grade Two
Second graders can recognise and match the different views of everyday objects. This means that they can tell if they are looking at an object from behind or above and so forth. They can also describe where an object is in relation to another.
For example, they will be able to tell whether the cat is under, on top of, behind or in front of the couch.
This will also mean they can follow directions as they move around the classroom.
3-D Objects and Geometry in Grade Two
Grade 2s can recognise 3-D objects in the classroom. They will be able to label them as spheres, prisms and cylinders. They will be able to compare, sort and describe them in terms of those that slide and those that roll. They will also be able to compare them according to size. They will be able to do the same for objects in pictures.
Second graders will also be able to build 3-D objects using concrete materials. These will include 2-D shapes that have been cut out for the purpose. They can also use construction kits, recycling material, building blocks and other 3-D geometric objects.
2-D Shapes and Symmetry in Grade Two Geometry
The students continue working with basic shapes (rectangles, squares, triangles and circles). Second graders develop in their ability to sort and compare 2-D shapes in terms of shape. This builds on their learning of size, round sides and straight sides in comparing shapes.
A grade 2 builds on the recognition of symmetry in their own body. They learn to draw lines of symmetry in both 2-D geometrical shapes, as well as non-geometrical shapes.
Japari’s Grade Two Curriculum is Second to None
At Japari we love to meet the needs of Grade 2s. We strive to make sure that they have all the fundamental lessons mastered as they progress through the year.
We also have expert approaches for any individual child who might be struggling with any particular concept. This ensures that they are ready to progress to success in their schooling as they complete second grade.
It is our passion to equip the children to do well at each milestone. Having a firm grasp at the Grade 2 level is the best way to ensure success in Grade 3. This is true of each year, and we love to see our second graders excelling.
We will conclude the Grade 2 milestones with measurement and data handling in our next article.
Bibliography/Further Reading:
https://www.splashlearn.com/math-vocabulary/fractions/unit-fraction
https://my.nctm.org/blogs/matthew-larson/2018/02/21/why-teach-mathematics
