When we think about mathematics, it is helpful to remember that we explore mathematics through what is called a base-ten number system. Simply put, 10 ones make up 1 ten and 10 tens make up 1 hundred. And so on. We also use place value as a way of describing the value attached to a number. I like to ask students would you rather have five hundred dollars or five dollars? When you say it like that, the choice is easy but that isn’t always the case. As adults, we sometimes take for granted these foundational math skills that our little ones are learning.
When exploring addition and subtraction, a very perplexing situation may occur if your child’s understanding of place value is weak.
Let’s explore it through the eyes of a child first. Your teacher or tutor asks you, “what does 2 take away 8 equal”.
Well, maybe as an adult you jump to negative numbers but for a child, this can be an illogical and impossible question. I’ve seen many creative attempts to solve this question. Most often I get the answer of 6 because they reverse the question 8-2. (Hint: if you model this question with real blocks, they quickly realize their own error).
So what is happening?
Regrouping.
Regrouping occurs in some addition or subtraction questions when they need to compose or decompose the number in the adjacent place-value spot to solve the question. I left a little bit out with my previous example the teacher or tutor was really asking, “what does 42 take away 28 equal”. A child who has a weak understanding of place value will usually answer 26.
When regrouping with addition this looks like, “what does 36 plus 28 equal”. A child who has a weak understanding of place value could answer 514. Thus, mistakenly adding an additional place value column and vastly changing the meaning of the number, even though they did almost all the steps correctly.
When do students start seeing questions like this?
In the Ontario Curriculum, in grade 3 students start to explore the concept of regrouping more explicitly. Some students may dabble in it before then, but you can expect by grade 3 this concept of regrouping will be necessary.
So, how do we teach regrouping at Latch Onto Learning?
1. Have the student solve the question using a learning tool
That learning tool could be counters, a number line or a hundred chart. By presenting the question differently and in a way that does not require decomposing or composing the numbers, the student will be able to see the difference of answer. From there, we have a great student-lead conversation about the two different answers.
2. Teach Place Value
If the error we are seeing in regrouping is caused by a misconception in place value, we need to go back and clarify that foundational skill. This might look like practicing counting ten ones to form one tens rod with base-ten blocks or practicing representing tally marks as a multidigit number. Ultimately, if your child has a foundational gap, it is going to be extremely difficult to solve math questions that require that conceptual understanding.
3. “I do, you do”
If the child is still struggling with regrouping, we model how to solve the question for the child. Sometimes children just need a little extra practice and modelling how to solve the questions. We start by modelling it with manipulatives and then we move progressively towards a more abstract understanding of addition.
How long does it take to learn?
It’s important to remember that every child learns at a different pace. This concept may take 30 minutes, 2 sessions or 8 sessions. Every child learns at their own pace. At Latch Onto Learning, we gear our programming to your child’s learning needs, learning pace and personal interests. Every program is custom built for your child.
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