# Decompose Numbers to 10 Worksheets

Decomposing numbers is simply taking a value and breaking it into equivalent parts. For example, if we had the number 10, it could be decomposed into any of these two quantities: 1 + 9, 2 + 8, 3 + 7, 4 + 6, or 5 + 5. There is a natural progression here, the more parts that students can break these values into provides for a better learning outcome. So the goal is to eventually get students to look at 10 as 1 + 2 + 3 + 4. Having the ability to do this with ease can really help students when it is time to learn all the various mathematical operations. We want to our Kindergarteners to learn to be confident with their 5s and 10s. This leads them toward a better understanding of the decimal system and place value. These worksheets and lessons help students learn that whole numbers can be the sum of multiple numbers with the goal of being to write addition sentences.

### Aligned Standard: Kindergarten - K.OA.3

- Decomposing Numbers Step-by-step Lesson- Start with visual blocks than transition to actual digits.
- Decomposing Numbers Guided Lesson - I covered the skill from top to bottom. These four problems sum it all up for you.
- Decomposing Numbers Guided Lesson Explanation-The explanation is a bit lengthy because students sometimes get lost with this skill.
- Butterflies and Addition Sentences Worksheet - Color the butterflies based on the sum they are flying towards.
- What Does The Picture Say? (Addition Sentences) - I use friendly pictures to push forward on this skill. What problems do the pictures represent?
- Addition Sentence Match Worksheet - Note that there are multiple answers per box.
- Making the Number 10 Worksheet - In this case the top section is where you draw the box. The bottom section is where write the numbers that the boxes represent.

- Answer Keys - These are for all the unlocked materials above.
- Count Backward Worksheet- A very interesting way to learn this skill. If you can do something forward and backward, you have mastered.
- Addition Sentence Equal to Model Worksheet- This is very challenging for students at this level. Proceed knowing that they might not have much success with it.
- Picture Addition Worksheet - A little picture addition to give them a jolt to their confidence.
- Addition Sentence Match Worksheet- Remember that there are multiple answers needed here.
- Composing and Decomposing Numbers Guided Lesson- You are asked to find the sum that makes a total of 8.
- Composing Numbers Worksheet- See if you can make these numbers from the pieces and parts that you are given.
- How to Make Numbers Guided Lesson- This is slight advanced for the skill level. More for your upper learners.
- Parts of Whole to Totals Numbers Step by Step Lesson- A perfect lead into to fractions.
- Putting Together Visuals in Sentences Lesson- You are given a model and need to find an equation that matches it.
- Your Own Addition Sentence Guided Lesson Explanation- Yes, this is guided but there are pretty much an infinite number of possible choices.

### How to Decompose Numbers

Breaking numbers into two separate numbers is not difficult at all. It is a critical skill towards developing a solid number sense. You just have to determine what makes the entire number altogether. The bigger the number the longer the process can take for an individual to determine the breaks. In this section we are focused on just getting to 10. It is important to help students determine the maximum number of slices you can make of a number with other whole numbers. Let's take a look at a problem that includes this and walk you through the steps to solving it:

**Problem:** What is the maximum number of parts you can break 9 into with whole numbers?

**Solution:** Start with lowest whole number available (1) and keep add the next largest until you run over the number.

1 + 2 + 3 + 4 – This sum is 10 and runs over our needed value (9). This means that we need to knock off the last digits (3 + 4) because those are the values that make us spill over. We are left with 1 + 2 and the need to find what value when added to those numbers would make our needed value (9). So it would look like: 1 + 2 + __ = 9. The value would be 6.

This simple skill really accelerates in future grade levels and is applicable to a great volume of material. Having the ability to decompose values will become second nature and students will learn to adapt this to much larger values. For example, if you have a number 12,345, then it can be broken down based on the numbers you see at each place value. Like, 12340 + 5, 1230 + 45, 12000 + 345, 10000 + 2345.

As students advance, they will be to work this skill seamlessly into their everyday. The other way of determining how the number is to be broken into two parts is by dividing the number by 2. This will ensure that the number be divided into two equal parts such as: 28/2 = 14 | 14/2 = 7 | 100/2 = 50.

While this skill may seem like busy work it has a hug impact on their ability with future material in math. It is a real foundational skill to help them understand the whole-part relationship of numbers. You can help students progress to mastering this skill by starting to explain that numbers are not just composed of 1s such as 4 is 4- 1s. That value (4) can be composed of 4- 1s or 2- 2s or a 3 and a 1. I find that hands-on manipulatives can really help students learn this quickly.