Differentiated Math Fact Practice

Making Ten

4th Grade Resources

Using Number of the Day to Develop Number Concepts in K - 3

The beginning of the school year is an exciting time. While getting to know our students, we are also establishing routines and procedures to set us up for success. We complete lots of activities together as a class to form relationships and expectations for the year to come. Even with all of the fun chaos those first few weeks bring, we as teachers are constantly observing and assessing our students. It is sometimes difficult to know where to begin with instruction because our students will come to us at different levels. Let's talk about how you can use Number of the Day resources to develop numbers concepts in kindergarten thru third grade and get a peek into your students current level of understanding. 

Developing Number Concepts in Kindergarten

kindergarten Number of the Day will give students the practice they need to develop solid number sense skills
In kindergarten, we are building basic foundational number sense skills.   Developing an understanding of numbers and what they represent is a big part of kindergarten math instruction.  We mainly focus on recognizing and writing numbers through twenty.  Number of the Day is an excellent way to do this.  Through Number of the Day activities, students are provided with opportunities to recognize the number,  write the number and learn to represent the number in a variety of forms.  All of these activities help them develop that foundational understanding of numbers and what they represent. 

It is important to assess your students at the beginning of the school year to see what they already know, where any misunderstandings might be and what instruction is needed.  In kindergarten there are likely to be vast disparities amongst the students in your class.  This initial informal assessment will be your starting guide for your instruction. 

While end of year goals may differ from state to state, there are some consistent math standards you will find for all kindergarten students.  

kindergarten Number of the Day will give students the practice they need to develop solid number sense skills

Skills to Assess:

  • Counting to 20
  • Counting with 1:1 correspondence
  • Write and identify numbers 1-10
  • Add and subtract to five
  • Make 5 with objects
You will be practicing these same skills plus a few more, all year long with the Number of the Day program.  Students will get the repeated practice they need to move their new learning from short term memory to long term memory.

A great way to introduce these new skills is by using a five frame and tally marks. These new skills should be practiced and reinforced daily. It is this repetition that leads to a true understanding of the number concepts.

A great way to implement these strategies is with a number of the day resource. Each day the students will complete these skills in different engaging ways that lead to mastery.  You can find everything you need for Kindergarten Number of the Day in this resource. 

kindergarten Number of the Day will give students the practice they need to develop solid number sense skills

First Grade Beginning of the Year Number Concepts

First graders come to us with some basic number sense concepts.  They should have mastered numbers to 20 on all fronts (identifying, writing, counting and representing). They are ready to move on and start working on numbers to 100.  This is a big jump and it is important that students truly grasp the number patterns in our number system and not just memorize a song or chant for counting to 100.

In kindergarten, students were introduced to the concept of ten plus more to get to twenty.  In first grade they will build on this.  Students should also enter first grade with an understanding of place value ones and tens.  During first grade they will add hundreds to this.  

The first weeks of the year are a great time to review the kindergarten number concepts and see where students are.  Back to School Number of the Day is a great way to do this!
First Grade Number of the Day will give students the practice they need to develop solid number sense skills

Skills to Assess:

  • Count to 100
  • Count by 10 to 100
  • Understanding Numbers Before/After
  • Counting objects to 20
  • Making groups of objects to 10
  • Comparing using one more and one less

Assessing these skills at the beginning of the year gives you solid data you can use to plan your future instruction.  As we continue to develop these important number concepts in first grade, I make Number of the Day a daily part of our routine. 
Throughout first grade, there are many new skills you will be introducing to students. Some of these build on kindergarten skills and others are introduced for the first time.  New skills you will need to address will include counting by 1 and 10, counting and creating groups of 10, and adding within 10.  You can easily introduce these concepts by teaching skip counting, using a 10 frame, and writing number words. All of these skills plus more are included in the First Grade Number of the Day Resource Bundle! 

First Grade Number of the Day will give students the practice they need to develop solid number sense skills

Second Grade Number Sense

As students move into second grade, they should have a good understanding of numbers to 100 and possibly a little beyond.  They should understand the basic number patterns and be ready to apply those to numbers beyond 100.  
Second Grade Number of the Day will give students the practice they need to develop solid number sense skills

Second grade brings the addition of fact families and equations. Students will begin to connect the dots with the previous skills they learned in first grade and kindergarten. It is so much fun to watch all of the growth happen!

During the beginning of second grade, it is important to conduct an informal assessment of your new students so that you can see what they have mastered and what, if anything, they are struggling with.  This will help you as you plan out your math instruction and guided math groups.

Skills to Assess:

  • Count forward and backward to 120
  • Count by 2, 5, and 10 to 120
  • 10 more/10 less
  • Place value to 100
  • Ways to make numbers to 30 using models, numbers, and ten frames
  • Fact Families
  • Addition/Subtraction Strategies using models and equations
  • Comparing numbers using place value
There will be lots of new skills to practice along the way like counting/skip counting to 1,000, writing number words to 120, creating models with larger numbers, and adding within 100. By incorporating Second Grade Number of the Day into your math block or morning work routine you can be confident in knowing that your students will get the repetition they need with all of these skills.

Second Grade Number of the Day will give students the practice they need to develop solid number sense skills

3rd Grade Number Concepts

Third Grade Number of the Day will give students the practice they need to develop solid number sense skillsIn third grade, students will move to thousands and beyond.  Up until this time students have been focused primarily on 3 digit numbers.  Students will build on their understanding of place value to move into larger numbers. It is important to make sure students have an understanding of these concepts before moving on.  This is where that informal assessment comes in to play.  You can quickly identify and address any issues that students are having at the beginning of the year.  This will help to ensure that the new concepts have a solid foundation to build on.  

Skills to Assess:

  • Count within 1,000
  • Write number words to 120
  • Build and write 3 digit numbers
  • Place value to 1,000
  • Fluently add/subtract within 20
  • Add/subtract from 100 using different strategies
  • Add/subtract 3 digit numbers
  • Compare 3 digit numbers using place value
Lots of practice will take place building and using arrays, adding within 1,000, and using place value with larger numbers, You will need to introduce area models to build these skills.  And...you guessed it! Number of the Day activities are perfect for this.

Third Grade Number of the Day will give students the practice they need to develop solid number sense skills

Assessment Made Easy

sample anecodtal notes form - grab this free resource
I've done a lot of talking so far about the importance of doing informal assessments at the beginning of the school year.  There is so much information you can learn just by observing and doing some informal checks.  But these informal assessments don't have to be hard or time consuming.  In fact, it can be as easy as jotting down a couple notes for each student.

Teacher Tip: Don't be overwhelmed with all the things that you feel like need to be assessed. You don't need to do them all at once. Take your time and get to know your students!  

For many years I have been using the anecdotal notes as a means of keeping data through informal observation and assessments.  What started out as a notepad has turned into an editable digital page that allows me to quickly document student progress and access data for all my students in one place. 

I start using anecdotal notes at the beginning of the year and continue with them throughout the school year.  They become a key component of my data binder and I refer to these notes often as I plan.  

After gathering all of the beginning of the year information, I use the data to assign small group assignments and make adjustments from there.This helps me to figure out what my students already know and what areas I need to focus on more intensely in both small group and whole group instruction. 

I've put together my anecdotal notes forms for you to use in your classroom!  There's a version for each grade - kindergarten thru third grade and they are ready for you to use with your students. There is also an editable form where you can add any skill or concept you are monitoring.  I've also included the master sheet I use to quickly see each student's level and to assign small groups with ease.

Free anecdotal notes resource for teachers to use in data tracking and informal assessments

Number of the Day Resources

Help your students master these important number sense concepts by incorporating Number of the Day into your daily routine.  I believe in using Number of the Day so strongly that I want you to try it out in your classroom.  There's nothing like the consistent review and reinforcement of skills to help our students master these number sense concepts.

Try Number of the Day for FREE in your classroomJust grab the set that best meets your needs and try them every day for a week.  Use them as morning work or as a math warm-up. They also make a great topic for math talks.  

I hope that after trying Number of the Day you see the benefit for your students and are excited to add them to your math routine.

You can find monthly sets or year long bundles in my store at Teachers Pay Teachers.

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Be sure to save this pin to your favorite math board so you can quickly come back for more tips and ideas for teaching math.

Problem Solving: Comparing Problems

Welcome back to the final post in this problem solving series.  In this post we are going to talk about the last group of addition and subtraction problem solving problem types - the comparing problems.  Before you jump in, I would suggest that you take a few minutes and start at the beginning.  Each post in this series builds upon the last so, while you can absolutely start here, starting at the beginning lays the foundation.  Get ready to take your problem solving instruction to the next level!

What are Comparing Problems?

teach students a variety of different problem types to help them master problem solving
In math, when we hear the word comparing, we automatically jump to comparing numbers with greater than and less than.  Comparing numbers is the foundational skill to the comparing problem solving type.  While we don't use the > and < symbols or the vocabulary "greater than", "less than" or equal to, the math concept is the same.  

However, one main difference between comparing numbers and the comparing problem solving type is that these problems often go one step further.  Instead of just comparing the numbers, these problems add in an addition or subtraction component and ask "how many more" or "how many fewer".

It's this combination of these two skills that make this the most difficult of all the problem solving types.  

Three Types of Comparing Problems

comparing problems are the fourth problem solving type
There are three different types of comparing problems that we need to introduce our students to:

  1. Comparing when the difference is unknown
  2. Comparing when the smaller part is unknown
  3. Comparing when the larger part is unknown

We are going to dive into each of these problem types and how I'd teach them in my classroom.

Comparing When the Difference is Unknown

Comparing with the difference unknown is the most common and most basic of all of the comparing problems.  These problems often introduce students to two groups and ask how many more or how many fewer one of the groups has than the other.  These problems will have students subtracting or counting up to solve the problem.

As you teach this problem type, it is important to focus on what is happening.  As we've talked about throughout this series, it is important that students see the context of the problem.  One main goal when teaching this problem type is that students see the difference between these and the separating problems.  While both will use subtraction concepts, one involves and action of separation and one is merely a comparison of two groups.

Here's a comparing when the difference is unknown problem and some strategies I'd teach my students to use with it.

As you can see, there are many great tools and strategies students can use to solve these problems.  I love teaching my students ALL the different strategies.  Since each student is unique and students have a variety of learning styles, you never know which strategy will be the one that gives them the "ah-ha" lightbulb moment we all love to see. 

Comparing When a Part is Unknown 

This problem solving type introduces students to one group and then provides a clue to how many more or fewer are in the second group.  With these two problem types, I love to make my students math detectives.  I start by explaining what a detective is.  I teach students that detectives look for clues in order to figure out what is happening. Then I explain that sometimes in math, we have to use clues to answer problems.

As I present students with their first sample problem, I model in my best detective ways how I look for clues.  If you want to really peak student interest, then wear your favorite trench coat and a large magnifying glass as you teach this lesson.  I start by reading the problem aloud and then giving my best thinking pose.  Then I start to read again, and after I read the first part of the problem I give a big "Ah-Ha!  I found a clue!"  I write the first clue on the board and have students help me determine what the clue means.  This first clue is often the statement that there are two groups.  I draw two large circles or lines on the board and we label each one with the group name.

Become math detectives as you search for problem solving clues

Next, I keep reading as I look for another clue.  Once again, I use my best award-winning acting skills to make a big deal about finding a clue.  This next clue is often the known group so we draw it in the correct place so that we connect clue 1 and clue 2.  

Finally we find our last clue.  This time, the clue tells how many more or fewer we will find in the next group.  I start by writing this out with just a couple words, like "Black 2 fewer" or "Green Apples 3 more."  Then I focus in on the important word (more, fewer, less) and ask students to think about when we've heard that before.  There might be a some guesses, but usually within just a minute someone will make the connection to addition or subtraction.  Once that connection is made, we go back and write our clue using the addition and subtraction sign.  It might look like: "Black -2" or "Green Apples +3."  

This process, while it might seem repetitive to us as teachers, is what helps build the bridge in the minds of our students.  And it is this that is so much more important than just teaching keywords.  By going through this process we are really teaching our students how to visualize the problem and identify the context.  This visualization is so much more important than knowing keywords.  When students can see what is happening, they can use their reasoning skills to solve the problem no matter what words are used.  But when students are taught only keywords, they get easily stumped when a problem is worded in a different way.

Larger Part Unknown

Students can learn to understand abstract problems by drawing what is happening

In these problems, the small group is known and students will be determining the size of the larger group using addition or counting on.  Here's an example of some strategies I use in my instruction.

Smaller Part Unknown

bar models are a great problem solving strategy to help students visualize

In this problem type, students are provided with the larger group and asked to determine how many fewer are in the other group.  Here, students will use subtraction concepts to find the answer.  However, setting the problem up as a subtraction equation is just one of many strategies.  Check out the strategies I use with my students in this short video.

One benefit to teaching the different solving strategies that I've shown here is that many times, a student struggling with addition or subtraction concepts makes the connection to these strategies and is able to help them with basic equations too!  That's a win-win!

Practice Comparing Problems

Using a variety of problem solving strategies helps students better understand problem context.
If you've been through the series then you know I follow the same practice procedures any time I introduce a new skill or concept.  With our young learners, it is important to always start with hands-on manipulatives that help make the abstract concepts of math more concrete.  Hands-on learning also helps students to develop that important skill of visualizing what is happening.  

From there, we move to paper practice using a variety of different strategies.  These two can also be combined in centers where students start with hands-on building and then transfer what they built to paper using drawing and/or words.  

My go-to practice for problem solving is Mega Math Practice because it includes a variety of practice activities using all the strategies I've taught here and more!  It's a great way to expose students to lots of different problem solving methods without adding more time or work to your schedule.  We all know there's very few teachers who have time for that!

Here are the Comparing Problem practice sets I use in my math classroom.

Mega Math Practice problem solving bundle will help you provide your students with quality problem solving practice and save you time!

Mega Math Practice problem solving bundle will help you provide your students with quality problem solving practice and save you time!

Mega Math Practice problem solving bundle will help you provide your students with quality problem solving practice and save you time!

You can try these comparing problems practice activities with your students by grabbing this FREE Resource!  It will give you a look at all the great practice your students will get from Mega Math Practice.

Grab this free problem solving resource for your classroom.

Wrapping Up . . .

After 5 weeks, I can't believe that we have come to the end of our problem solving journey.  I have loved digging in with you and helping unpack the ins and outs of addition and subtraction problem solving types.  I hope that these posts and videos have provided you with some new ideas that you can add to your problem solving toolbox. 

Here's a few of the most important concepts to remember when teaching your young students problem solving:
  • Teach students to VISUALIZE what is happening
  • Provide students with a variety of STRATEGIES to use when solving
  • Celebrate that we can solve problems in DIFFERENT ways and still get the same answer
  • Focus on the CONTEXT
  • PRACTICE, practice, practice by starting with concrete, hands-on opportunities and slowly moving more abstract.
And . . . if you want to save some time and fill your toolbox with ready to use practice problems for all 11 problem then grab the Mega Math Practice Problem Solving Bundle from Teachers Pay Teachers.

Mega Math Practice problem solving bundle will help you provide your students with quality problem solving practice and save you time!

The Problem Solving Series

I want to make sure that you can quickly and easily access any of the posts from this problem solving series.  While I feel starting from the beginning is best in order to get the foundation, you can also jump right to the post that will help with your current teaching needs.  And . . . don't forget to grab the freebie in each post!

Save these Problem Solving Tips and Strategies

Problem solving is something you teach year after year.  And while we can use some of the same strategies you never know when you'll need to pull something new from your teacher toolbox.  Pin this to your favorite classroom Pinterest board so you can quickly come back for tips, ideas and problem solving strategies. 

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