In the previous article, we covered Pre-K and Kindergarten. This article covers 1st and 2nd grades.
1. 1st Grade
In first grade, the priority shifts from number sense to arithmetic. Your child should have grasped number sense by the end of kindergarten.
Your child’s success in math will be largely defined by how well your child studies math in the latter half of kindergarten and first grade. Many challenges await your child in later elementary school and afterward. However, if your child can establish confidence in math by the end of first grade, your child will be able to overcome those challenges with relative ease. On the other hand, if your child is not able to build solid skills and confidence in first grade, the future will be very difficult for your child, as it is nearly impossible to keep up with the pace of classes. Also, it is almost impossible to catch up on math in school if your child’s progress is delayed.
By the end of first grade, your child needs to be very proficient in multi-digit addition with carryover and multi-digit subtraction with regrouping. The first goal is to perfectly memorize 45 single-digit addition combinations. If you follow the steps described above, your child is ready to memorize the combinations, as he or she already understood carryover addition in kindergarten.
If your child is not familiar enough with carryover addition, please take extra time to ensure that your child perfectly understands the process and can perform the proper calculations, as opposed to using counting. It is possible for children to memorize combinations without fully understanding the carryover process, but without a full understanding of this process, your child will struggle with multi-digit carryover addition.
The steps you need to take are as follows:
1) Ensure that your child can calculate single-digit sums less than ten
2) Ensure that your child understands and has memorized the combinations of single-digit numbers that add up to 10
3) Ensure that your child understands that a carryover process essentially creates 10
8 + 7 = (5 + 3) + 7 = 5 + (3 + 7) = 5 + 10 = 15
4) Memorize all 45 combinations and ensure that your child can immediately answer to all of them without making an error
5) Teach the process and have your child practice multi-digit addition with carryover using a vertical format (if your child has succeeded in the above steps, this should be easy)
Subtraction is a reflection of addition, so it is best to practice it in tandem with your child’s mastery of benchmarks in addition. For instance, once your child has mastered single-digit addition, you can introduce single-digit subtraction within the same range. You may do both simultaneously, but my recommendation is that you first wait for your child to fully understand addition. You can start asking your child questions, such as “4 plus something equals 7. What is that something?” The other format, e.g. “What is 7 minus 4?” comes later.
Once your child fully understands carryover addition and is familiar with it, please explain subtraction with regrouping.
Many children are good at addition, but not subtraction. It is ideal to practice subtraction with regrouping to ensure proficiency. Proficiency in subtraction helps your child immensely in understanding division later on. The same proficiency mantra applies to subtraction: Your child should be able to apply subtraction with regrouping immediately, without thinking, counting, or making mistakes.
1.2 Number Sense
The number line and rounding are two major topics in first grade. If you follow the aforementioned recommendations, your child will have already gained familiarity with the number line in kindergarten. Revisit number line questions to ensure that your child first checks the unit size and then reads the number line.
Once your child understands the number line, he or she is ready for rounding. A solid number sense and visualization of the number line will make learning to round a piece of cake for your child.
The difficulty with rounding is that the same number yields multiple solutions, based on the digit being rounded to. For example, take 1647. 1650 is the answer when rounding to the nearest ten, 1600 is the answer when rounding to the nearest hundred, 2000 is the answer when rounding to the nearest thousand, and 0 is the answer when rounding to the nearest ten thousand. This is where solid number sense comes into play – the combination of answers will be complicated for your child if he or she does not have a solid number sense.
If your child has good number sense and proficiency in addition described above, it will be relatively easy for your child to understanding how to read minutes. The concepts of carryover and regrouping apply to the calculation of time. So, ensuring a solid number sense and arithmetic skills will certainly help your child in reading and understanding time.
2. 2nd Grade
If your child clears the goals described above, math will be easy in second grade. Your child is ready to master multiplication. Arithmetic is still a priority in second grade.
First, ensure that your child has memorized the 45 combinations of addition patterns. Then, practice multi-digit addition with carryover and subtraction with regrouping. Once your child finds this practice too easy, it is time to start memorizing a multiplication table.
Memorize the table column by column. Once your child has memorized the table, focus on improving proficiency. Many students have a weakness when it comes to products that have multiplicands between 6 and 9 and multipliers between 6 and 9. Do not leave any weaknesses unexplored. We use various matrixes to measure the speed and accuracy of calculations.
In two weeks, the majority of students can achieve the desired level of proficiency with perfect accuracy per matrix.
If you follow the recommendations in this article, you do not worry about geometry in second grade. Review the names of shapes, keywords (e.g. side, right angle, vertices), and knowledge related to angles.
You may think that memorizing addition combinations is too much, or that we place too much emphasis on proficiency, but these methods are simply required in order to build a strong foundation in math.
1) Start early and allow substantial time to play with carefully selected toys to nurture number sense, figurative reasoning, and spatial reasoning.
2) Be patient and provide positive feedback with a big smile, though sometimes difficult. Never use negative words or show frustration.
3) Ensure that your child understands number sense.
4) Ensure that your child achieves very high proficiency with perfect accuracy after your child fully understands the process. With the proper method, the majority of children can reach this level of proficiency in two weeks.