Showing posts with label subtraction. Show all posts
Showing posts with label subtraction. Show all posts

A Path to Ensuring Mastery in Addition and Subtraction for Math Success

Do you happen to know how many standards students have to master to be able to solve basic multiplication and division equations?

I went looking and it’s more than 15!

I’m talking about place value, counting, and solving addition and subtraction facts fluently.

These skills are the foundations and need to be taught to mastery!

Do you need help getting your students to master place value or counting skills or addition and subtraction fluency?

If so, you're in luck! In this blog post, we will discuss how to teach these skills and ways to teach these concepts. 

The first way is drill and kill practice. This is a traditional approach that many teachers use. The second way is with place-value games. Games are a great way to engage students and help them learn in a fun way. Finally, the third way is to give students time to demonstrate mastery in a variety of different ways. 

Why Worry about it??

First–if you don't, who will!! Passing the buck doesn’t help anyone and when they get to 3rd grade your students will drown and the teacher who has them will give up.

Thank you for being part of my soap box.

Mastering multiplication and division requires a strong foundation in several basic mathematical skills, notably place value, counting, and addition & subtraction. Each of these skills plays a crucial role in understanding and performing multiplication and division effectively.

Place Value

Place value is fundamental in mathematics as it helps in understanding the significance of digits in a number based on their position. 

This product is filled with task cards and games that are perfect for interventions or small groups to work on place value from ones to hundreds. It's super easy to differentiate and personalize for your learners in any group. 

These cards are always part of my math groups even as a warm-up. Students always benefit from the remembers--especially once you get to regrouping. 

Place value starts in kindergarten with understanding numbers to 20 aka the 1s and 10s places. First graders, continue building this information by comparing 2-digit numbers and can compose and decompose numbers to 20. In second grade, understanding numbers to the hundreds place. This information is needed because when students move from single-digit math to double or multi-digit operation if they don't understand how those places work students won't understand how to complete any complex math. 

This product has 4 easy to differentiate activities that can be added to any center, small group, or intervention to help students reach independence or practice place value. 

The stronger student's place value is the easier moving into complex math will be!

In multiplication and division, recognizing the place value of digits allows one to:

Break Down Numbers: Multiplication and division often involve breaking down larger numbers into smaller, more manageable parts. For example, understanding that 234 is 200 + 30 + 4 allows for easier mental multiplication and division using distributive properties.

Align Numbers Properly: When multiplying or dividing multi-digit numbers, place value ensures that digits are aligned correctly, which is crucial for obtaining accurate results. Misalignment can lead to significant errors.


Counting

Think for a second, can you students count by 1s past 50 without starting at 1. Or can they skip count by 5s starting at 65. Or counting by 100s starting at 200?

Counting is a foundational skill that underpins many mathematical concepts, including multiplication and division.

Counting is one of those skills that starts in preschool and gets more complex as students move through the grades. But it is also a standard that we think students have mastered or understand and walk away from before there is data to show they can count. 

In Kindergarten, students are to count to 100 in both 1s and 10s. First grade, students are extending the counting sequence 120. Not to mention plus 10s or minus 10s. In Second grade students need to count by 100s and skip count by 5s, 10s, and 100s.

Students don't get counting or skip counting with calendar math. They need more. They need to count everything. Not just by 1s starting at zero or one but starting at 14 or 46 or 98. 

Do you have students that don't know what number comes after 100 or 110? 

You need this! 

In this product, you will find student worksheets to get students working on counting by 1s, 5s, 10s, and writing numbers passed 100. And like all my activities--progress monitoring to support interventions and the RTI process.

Understanding Multiples: Multiplication can be viewed as repeated addition. For instance, 4 x 3 can be thought of as 4 counted three times (4 + 4 + 4). Similarly, division involves understanding how many times a number can be subtracted from another number, essentially counting in reverse.

Skip Counting: Skip counting (counting by 2s, 3s, 4s, etc.) is a direct application of counting that helps in learning multiplication tables and understanding the concept of grouping in division.

Patterns Recognition: Counting aids in recognizing numerical patterns, which is essential for mastering multiplication tables and identifying factors and multiples.

Addition & Subtraction 

I started this blog post with a soapbox. It comes from listening to classroom teachers complain about students being fluent in their addition and subtraction facts. 

I think as a special education teacher, we forget just like classroom teachers that these skills have to be practiced first, then mastered, and then the fluency comes. Just like learning to read or ride a bike. 

Most state standards, like Common Core or your state standards--students have roughly 2 years to get these skills mastered and be fluent. 

The standards start in Kindergarten with working within 10. But mastery is within 5. First grade is working of within 20. Working fluently within 10. Second grade is working within 20 using mental strategies. And by the end of the year from memory all sums of two one-digit numbers. 

I talk a lot about mastery. Like a lot a lot. 

Merriam-Webster's Dictionary defines Mastery as "the possession or display of great skill or technique".

The standards don't define mastery. 

So, who does???

Well, you do, or your team or grade level or building level. 

But ... that also means you have to hold all students to that same standard or benchmark. 

My Addition, Subtraction, and Multiplication fluency products have what my building has agreed to. This means that students who are timed are held to the fluency benchmark. This means you can create interventions and support them in RTI.

This means you also need something more than drill and kill to build students' accuracy and independent practice. 

These three products will help give students more independent practice, and more differentiated practice within small target groups without making it harder for you to support them.

Addition and subtraction are the building blocks of multiplication and division:

In second grade there is a tiny standard that where multiplication starts. It's 2.OA.C--students start to learn about arrays and start using skip counting to solve multiplication facts of 2s, 5s, and 10s. This set of activities will help you build students capacity in using games and number talks.  

Foundation of Multiplication: Multiplication is essentially repeated addition. For example, 5 x 4 can be seen as adding 5 four times (5 + 5 + 5 + 5). A solid grasp of addition makes this concept more intuitive.

Division as Repeated Subtraction: Division can be conceptualized as repeated subtraction. For example, 20 divided by 4 can be understood by subtracting 4 from 20 repeatedly until reaching zero, counting the number of subtractions made.

Handling Remainders: Division often results in remainders. Proficiency in subtraction is necessary to understand and calculate what is left over after dividing.


Interconnectedness of Skills

The interconnectedness of place value, counting, and addition & subtraction with multiplication and division highlights the importance of these basic skills. Mastering them provides a strong mathematical foundation, enabling students to tackle more complex problems with confidence. Understanding place value ensures accurate computation, counting fosters an intuitive grasp of numerical relationships, and addition & subtraction form the operational basis for both multiplication and division.

BUNDLE

Want it all???
I have you covered with a growing bundle. All these products are bundled together in my store, so you can start the year off strong and build those necessary skills to ensure your students master all the skills they need to understand multiplication.

Chat soon-





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Welcome to my all thing special education blog. I empower busy elementary special education teachers to use best practice strategies to achieve a data and evidence driven classroom community by sharing easy to use, engaging, unique approaches to small group reading and math. Thanks for Hopping By.
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