Read intervals on a number line and apply the digit sum operation.
How to interpret spacing on a number line.
Number lines help us visualize math, but sometimes not all numbers are labeled. We can find the value of unknown points by looking at the distance between the numbers we do know.
Number lines must be rendered precisely for students to count tick marks and find intervals.
A clean, professional coordinate-graph showing a horizontal number line with major tick marks labeled 1000 and 2000. A s…
Fill in missing values on a given number line.
Observe the number line where two known labels are 2010 and 2020. There is exactly one unmarked tick between them. First, find the total difference between the known marks: .
Since there is one tick mark between them, there are 2 intervals connecting the two values. Divide the total difference by the number of intervals to find the step size: .
To find the value of the mark immediately to the left of 2010, subtract the step size: . Continuing to the left, the preceding marks are found by subtracting 5 each time: 2000, and then .
Following this pattern, the leftmost position on the sequence is .
Introduce the concept of adding the digits of a number.
Numbers aren't just for counting whole amounts; we can also play with their individual pieces! A digit sum is calculated by taking a number and adding all of its digits together.
Find the smallest number with a specific digit sum.
Problem. What is the smallest number whose digit sum is 14?
Find the largest 5-digit number with a digit sum of 14.
Find the largest 5-digit number whose digit sum is 14.
To make a number as large as possible, fill the highest place values first.
To make the number as large as possible, think about which place value matters the most.
Use the biggest possible digit without making the digit sum more than 14.
Subtract the first digit from 14.
Put the remaining sum as early as possible, then use zeros after that.
Write the final number after arranging the digits.