Number Changes
About This Worksheet
This worksheet helps students identify the operation and power of ten that changed one number into another. Instead of being told what to multiply or divide by, students study the starting and ending values and work backward. For example, 6.25 becomes 625 by multiplying by 100. This activity strengthens number sense because students must recognize how the digits moved and then name the correct operation.
Curriculum and Grade Alignment
This fifth-grade worksheet supports CCSS.MATH.CONTENT.5.NBT.A.2 by asking students to reason about place-value changes caused by powers of ten. Students should already know how multiplying and dividing by 10, 100, and 1,000 affect digits. The next step is solving missing-operation problems and using powers of ten more flexibly in equations. This page helps students move from following a rule to recognizing and explaining the rule on their own.
Student Tasks
On this worksheet, students will study ten number transformations and identify what caused each change. They decide whether the original number was multiplied or divided and determine the correct power of ten. The examples include both whole numbers and decimals, so students must carefully compare place values. At the bottom, they complete a rule describing when a number becomes larger or smaller.
Common Challenges
Students may notice that a number changed but choose the wrong operation. Another common mistake is identifying the correct direction but using 10 instead of 100 or 1,000. Decimal examples can be especially confusing because children may count visible zeros rather than actual place-value shifts. Teachers can help by having students choose one digit and trace where that digit moved from the first number to the second.
Teaching Tips
This worksheet works well after students are comfortable solving regular multiplication and division problems with powers of ten. Teachers can model the example at the top and talk through how the place-value change reveals the operation. At home, parents can ask children whether the number became larger or smaller before asking them to name the power of ten. That simple first step makes the reasoning process much easier to follow.
Worksheet Features
The worksheet includes ten transformations that require students to work backward from a starting value and an ending value. Both multiplication and division are included, along with whole numbers and decimals. An example at the top shows students how to record the operation clearly. The final transformation rule gives students a chance to summarize the relationship between powers of ten and number size.