Reasons why Students Struggle with Place Value and What you Can do to Support Across the Math Progression:

Hey Teachers, did you know that a key foundation in students' mathematical learning is place value? Without a strong understanding, students will have difficulty in many other mathematical concepts and skills such as adding and subtracting multi-digit numbers. In addition, regrouping and decomposing numbers. (all based on place value) are critical to moving students toward fact fluency. Multiplication and division strategies also become too complex when students lack the foundation of place value to support their understanding of concepts and skills such as using the area model.

The decimal system, which is based on place value, is used in a wide range of mathematical concepts, including fractions, decimals, and percents. Using manipulatives to support conceptual understanding of decimals builds a foundation for visualizing each place value. In this video Dr. D demonstrates how you can go from the concrete to the representational to the abstract (CRA Model) and build fluency with decimals through the process of building, speaking, writing, and representing decimal values. In addition, consider using virtual manipulatives for the exploration of decimals as shown here with the Math Learning Center.

Here are several reasons why students may struggle with place value:

1. Conceptual understanding: Place value is a complex concept that requires a deep understanding of the relationships between digits and their place in a number. Students may have difficulty understanding the role that each digit plays in a number and how the position of a digit affects its value.

2. Lack of practice: Practice is key when it comes to mastering place value. Students need repeated opportunities to work with numbers and see the relationship between the digits and their place in the number.

3. Lack of visualization: Place value can be difficult to visualize, especially for students who struggle with spatial reasoning. Some students may have trouble visualizing what the numbers look like and how they change based on their place value.

4. Memorization-based approach: If students rely solely on memorization to understand place value, they may struggle when they encounter new and more complex problems.

5. Misconceptions: Students may develop misconceptions about place value due to their prior experiences or misunderstandings. For example, they may think that a number like "7" is the same as "70."

6. Limited experience with larger numbers: Students who have limited experience with larger numbers may struggle with the concept of place value and the relative sizes of numbers.

Overall, place value is a complex concept that requires a deep understanding, repeated practice, and a clear visualization of the relationships between digits and their place in a number. Teachers can support students in their understanding of place value by providing opportunities for hands-on learning, visual aids, and direct instruction that addresses common misconceptions.

Here are 7 Ways to improve students' understanding of place value:

1. Hands-on Activities: Provide students with hands-on activities that help them understand the concept of place value. For example, students can use base-10 blocks to build numbers and understand the relationship between the blocks and the digits in the numbers.

2. Visual Representations: Use visual representations, such as place value charts and number lines, to help students see the relationship between the digits in a number and their place value.

3. Real-world Applications: Connect the concept of place value to real-world situations, such as money and measurements, to help students see the relevance and importance of understanding place value.

4. Practice and Repetition: Regular practice and repetition are essential for students to internalize the concept of place value. Provide students with a variety of problems and activities to work on and encourage them to self-check their work.

5. Emphasize patterns: Show students how patterns can help them identify place values, such as noticing that the place value of a digit increases as you move from right to left.

6. Use estimation strategies: Encouraging students to use estimation strategies, such as rounding numbers to the nearest ten or hundred, can help them understand the relative size of numbers and place value. Additionally, by estimating, students can check their answers and avoid making careless mistakes.

7. Technology Tools: Students can engage in problem-solving with virtual manipulatives to build a number and solve problems with digital tools. Using virtual number lines, base ten blocks, and recording tools can help you see where students' gaps are and how they are making sense of the concepts and skills you are teaching.

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Harnessing the Power of Technology for Real-World Math Connections

Throughout the Common Core Mathematics State Standards, students should be making sense of mathematics in the real world.  In fact, the word ‘“real-world” appears across the math domains from “solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem (5.NF.B.6) to “solve real-life and mathematical problems using numerical and algebraic expressions and equations (7.EE.B.4)”.   Real-world connections are rooted in the experiences we’ve had whether shopping at a store and calculating the discount price, to planning a road trip and determining the time, distance, and cost given a budget.  Experiences make us mathematize in ways a traditional textbook problem does not.  Moreover, doing the math is driven by our needs and interests, and that is what makes the utility of math something of value. 

This approach to teaching and learning math can be as simple as using a Data Talk (see below) at the onset of instruction to engage your students in math discourse or creating a real world problem for your students to grapple with over a series of days or weeks!

Think about how engaged you were when planning a holiday party and having to scale up or down a recipe online or applying for a loan and determining the monthly cost given your interest rate.  Of course, in these situations attending to precision really matters. Seldomly do we need to be reminded to “check your answer” when math is personal. Creating that kind of interest, excitement, and perseverance in the classroom, will take more than just presenting our students with problems involving a real-world situations, or asking “ Would You Rather” questions.  As teachers, we need to provide our students with an opportunity to put themselves into the experience (aka immersive math).

Here is a video clip of me working with a group of sixth graders introducing the project of building a house.  https://youtu.be/M45VT4UHzcI

Build a house project on Google Slides for Reuse: https://bit.ly/3u2LN8Z

What kids lack in context we can provide with digital projects.  Digital projects allow us the teacher, to build an experience that will drive our students’ passion for doing math.  Students can share their interests, passion, and creativity in a real-world digital project.  For example, building on my second-grade students’ love of the Roblox game, Adopt Me, and their passion for animals,  I crafted a second-grade digital project in which students pick a pet to adopt, shop for items, and create their own animal.  This became an immersive experience similar to a video game, while students were adding and subtracting money, building three-digit numbers with base-ten blocks, and ordering and comparing costs of pets on a number line.

To further students' confidence in this skill have your students create short videos explaining their thinking and how they solve the problem. Check out this video of a student engaged in a digital math project where she reads, writes, and compares three-digit numbers https://youtu.be/GNBM4f2HjPY

Digital projects work across grade spans and allow students to see connections across math domains and other subjects. They can give our students an opportunity to use the academic language of a concept and have students explain their thinking through video, or text as shown in the above video. 

But best of all with digital projects we can hyperlink to awesome tools that allow our students to really connect math concepts to the real world.  For example in the “Plan A Holiday Party” I created for my sixth graders, they were selecting recipes from the site “All Recipes” for their holiday meal and had to scale up or down the recipe given the number of people they invited. 

In the digital project “Plan a Camping Trip” students not only were tasked with exploring a campsite in California but, calculating the mileage for their trip by looking up the gas mileage for a car they selected.   When given this situation, the mathematizing started to happen from students comparing the poor gas mileage between a Lambrogini versus a Hummer to determining the electrical charge they would need if they decided to drive a Tesla instead.  The beauty of mathematics appeared when students were allowed to be creative and explore possibilities which is what makes a good math project.

 Students can efficiently model with mathematics using digital tools and connect big ideas in math across important concepts.  In fact, the 2022 California Framework will require teaching “big ideas” as a way to support students in seeing how concepts are connected and deeply exploring fundamental ideas.  As teaching math continues to evolve towards are more student-centered and less teacher-directed approach, digital projects provide you with an opportunity to approach instruction with an emphasis on connections and ideas.  Projects give your students the time to link multiple practice and content standards in a comprehensive way with real-world connections.  Want to see my thinking process and “must-haves” for Digital projects check out this video in which I walk you through what I consider before creating a digital project and what are must-haves for project success.  

How to create a digital math project: https://youtu.be/ZkdWH_2mndE

 

Technology holds much promise for the future of math and certainly will prepare students for college and career readiness.  Collaboration, critical thinking, creativity, and communication are part of students' experience in working on a digital project.  The 4 C’s are 21st Century skills that have been in education for quite some time, as a staple for the future workforce.   As teachers however we are challenged to bring in the fifth C of compassion in our work with students as well. With compassion everything is possible and we can reimagine our world and our children’s future.  

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6 Fun Ways to Go Digital with Number Talks

One of the cornerstones of a solid elementary math block are activities that support students in developing numerical literacy. Developing numerical literacy in the elementary classroom will support students in being confident problem solvers, and engage in mathematical discussions at a higher level.  Number talks are one such activity that builds students numerical literacy and are taking place in classrooms on a daily basis.  

If you are not familiar with number talks here is the gist of it.  The goal of a number talk is to give your students an opportunity to use mental math strategies to solve a problem.  That's right no paper, whiteboards or pens, just solve the problem in your head.  

The conversation that occurs after the number talk is teacher facilitated with students sharing answers and their strategy.  This process supports students learning from each other and teachers assessing students thinking and what strategies they use naturally.

       Teacher says: How can you solve this problem by doing it in your head? Give me a thumbs up when you have a solution!

One thing I love about a Number Talk is students are provided with a problem that can be solved in a variety of ways.  This allows students to be flexible in their thinking and develop a variety of strategies that will support them when they are faced with cognitively demanding math tasks.   

       Get these slides here

One thing that is a struggle with this process is number talks can be incredibly time-consuming if you are in a class with 30 plus students who all want to share how they found their answer.   As a teacher, I want to honor all of my students' voices and give them an opportunity to express what they know, but logistically this is not always possible.   

This is where technology can come in to support you in making number talks accessible to all students and useful as a formative assessment tool to see where all your students are at and give them a chance to share their thinking.  

Here are 6 Fun Ways To Go Digital with Number Talks: 

1. Google Slides: During a synchronous meeting with your students share this slide deck in edit mode for students to record their solution to a number talk problem.  Students can drag the icon to indicate they would like to explain their thinking or to show agreement with another student's explanation.

Slide Template

2. Google Voice: For asynchronous collaboration post an image and/or your question in a Google Doc.  Students can work with a partner or independently to share their strategy. All you need to do is create a Google Doc and Share with your students.  Then have your students go to the Tools Menu in the Document and click Voice Typing

                                       click here to get this document

If you want to see how quick and easy this process is just check out my 8 year old son demonstrate how to use Google Voice Typing.

                                   


3. Padlet: Post your question on a padlet board.  Students can access the board with a URL and automatically post their response by sharing a picture, text or video.  Try this out by responding to my number talk wall below with your response.  If you have fun doing it imagine what you kids will say! 

4. Google Drawing: teachers can illustrate student responses using Google Drawing either on their IPAD or computer.  The Scribble tool is a quick way to make illustrations and the student can also illustrate their response using this web based tool .  Google Drawing can also be used inside Google Document and it even features math symbols as images.  

                          Click here to view in Google Drawing

5. Flip Grid: Create a video word problem with a student response system that records students thinking in an instant.  This process can ensure that students voices are heard and recorded. You can also leave feedback for your students with this process.  The videos below were created shared on Youtube

6. Shadow Puppet: This tool can be used by you to make video number talks or by the student to share their response. Students can illustrate their work with paper and pencil then take a picture with an ipad or iphone.  Then they can audio narrate their response.  This can be a center activity that students complete and provide feedback and comments to their peers.   This is an app and not accessible on a computer 

If you are an elementary teacher looking to improve your students number sense than number talks are a must.  This process instinctively allows me to see where my kids are at, who has grasped the concept and who needs some extra nudging and support.  With number talks the nudging and support does not necessarily come from me it can be found in how their peers respond and with web tools I have the power to capture their answers.  

Want a book that can put it all together for you with over 100 digital resources and tools then check out my book on Amazon

Check out these digital number talk images I have collected and be sure to share yours with me. 

How much for one (unit rate)? How much for 13?

Join our Facebook Group for more conversations, freebies and best practices: https://www.facebook.com/groups/mathconnects/

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Ratios and Insert Learning

Math Warm Up: Which One Doesn't Belong? 

Look at the Graphic below and decide "which one doesn't belong" 

What justification could you use to say that 8 doesn’t belong?

What justification could Student B say that 64 doesn't belong?

What other justifications could student A have used to decide that 27 does not belong?

How can students A, B, and C all be correct even though they each chose different values?

Today's Lesson: Ratios

Ratios are used to compare values. They tell us how much of one thing there is compared to another. For example, ratios can be used to compare the number of cars to motorcycles on the road. If we have a total of 12 cars on the road, where two are motorcycles and ten are cars, we can write that in ratio form as 2:12 (motorcycles:cars). We can also write it in factor form as 2/12. To compare the number of cars to motorcycles, we can simply rewrite our ratio with the number of cars first as 12:2 (cars:motorcycles ) or 12/2.

3 Acts Math Task: World Fastest Dog

What do you notice and What do you wonder?

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