To introduce multiplication, I usually start with our math bears. You can use any type of small object that is easy for your child to manipulate. Once the child seems to understand the concept, I will use the multiplication chart using beans. Since the spaces on the chart are uniformly spaced, the child can see the relationship between the various products they will create. For example, the array s/he creates for 2×3 will be much smaller than the array created for 4×5. While this seems like common sense to us, a child’s mathematical reasoning is developing. They need to see this!
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Multiplication With Math Bears
1. Select multiplication facts with small numbers for factors. Put the multiplication facts in a pile for your child to use.
2. Pick the top card and show your child the multiplication fact. Tell your child that just like we have symbols that tell us to add or subtract ( +, -) the “x” on the card tells us to multiply. The numbers on the card give us information too; the the first number tells us how many groups we have and the second number tells us how many items are in each group.
3. Using 2×3 as an example, explain that the we know that there are two groups and each group has three items in it. Demonstrate this with the math bears. Take out three math bears and line them up together. I would talk out loud as I am working, “We have one group, but we need two. So, I need to get three more bears to make two groups of three”. Line up the second group under the first. “Now I have two groups of three. If I count them, then I will know what 2×3 equals.” You can count them or ask your child to. S/he may announce the answer before you even do this!
4. Choose another card and walk your child through the process again, but this time let your child manipulate the bears. You can still verbalize what to do at each step.
5. Once your child seems to be able to do this easily with your help, have him or her try one on his or her own without you directing each step.
Not sure if your child is ready to multiply? It’s helpful to understand psychologist Lev Vygotsky’s Zone of Proximal Development (ZPD) and it’s role in teaching.
The graphic above shows three concentric circles. The center circle represents everything your child can do by him or herself with no help needed. The next circle represents the area where your child can do something (such as multiplying) with help or guidance from an adult. This is the Zone of Proximal Development. The outer circle represents things that your child cannot do, even if you are helping (like calculus). When working on this activity, take a moment to see where your child’s understanding of multiplication falls. Can your child accomplish the task at hand with your assistance? If so, that’s good! You are working in the ZPD, which is where you want to be for your child to learn something new. With enough practice and guidance your child’s multiplying ability will move from the ZPD into the center circle of things he or she can do independently.
However, if your child is looking at you like you have three heads when you are working on multiplying and seems totally confused no matter how much you try to help, your child’s understanding may fall in the outer circle. This means that your child may not be ready for this task. S/he may need to work on skills that lead up to multiplication. Practice more addition, demonstrate multiplication informally in play situations, talk about groups, read books about multiplication (see additional resources at the end), practice skip counting, etc.
Activity 1–Solving Problems:
1. Present your child with the materials as pictured above.
2. Show your child how we can use the beans to solve the multiplication problems just as we did with the math bears. This time however, we can use the chart to place the beans in an orderly fashion.
3. For example, if the card says 2×3, we know that we need to make two groups of three. Demonstrate this by placing the beans on the chart one group at a time.
4. Have your child count how many beans there are on the chart. This is your answer.
5. Repeat the process with more multiplication facts.
Keep this chart on hand to help with homework. Your child can use this as a tool to solve multiplication problems independently.
Activity 2–Filling in the chart:
Once your child understands the concept, you can encourage your child to fill in the chart. I usually wait to fill it in so that the child is not memorizing the facts at first.
1. Follow the same procedure as above to solve multiplication facts.
2. This time, when your child gets the result have him or her record their answer directly on the chart. For example, if the child solved 2×3, s/he would count the beans (left to right, top to bottom) and write the answer in the square of the final bean. Naturally, this will be in the lower right hand corner of the array where the two factors meet.
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