Make a ten to find the total. 4. 5 + 8 = 13 8 + 4 = 12 5 + 6 = 5. Stretch Your Thinking Draw a Math Mountain that only uses two different numbers. Explain why.
The Correct Answer and Explanation is:
Let’s begin by finishing the last equation:
5 + 6 = 11
Now, for the “Stretch Your Thinking” section involving the Math Mountain:
Suppose we create a Math Mountain using only two different numbers: 6 and 4. The peak of the mountain, which is the total, would then be 10, since 6 + 4 = 10.
The Math Mountain diagram would place the number 10 at the top, and the numbers 6 and 4 at the two lower corners. It looks like a triangle, where the two bottom corners represent the parts (addends), and the top represents the total (sum).
Why Use Only Two Different Numbers?
Using just two different numbers strengthens a student’s understanding of number relationships. By working with a consistent pair, students can focus entirely on the connection between addition and subtraction without distractions. This strategy solidifies the idea that numbers can be broken into parts and recombined, which is a foundational concept in mathematics. For example, from the Math Mountain showing 6 and 4, children not only recognize that 6 + 4 = 10, but also that 10 – 6 = 4 and 10 – 4 = 6. These interrelated facts promote fluency in both operations.
The simplicity of using two different numbers also makes patterns easier to spot. As students explore various combinations, they begin to recognize families of facts and the symmetry between them. This visualization helps young learners build a mental math toolbox, making future problems less intimidating and more intuitive.
Math Mountains, by their structure, promote flexible thinking. Whether it’s understanding that ten can be split in multiple ways or that addition has an inverse, this exercise plants seeds that grow into strong arithmetic skills.
