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Types of Angles Part 2 Quiz - Turtle Diary

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For example: Consider the clock shown below. Observe that the angle formed between the hands of the clock is more than 0°, but less than 90°. So,

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Photomath cool tool for introducing algebra concepts

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Photomath cool tool for introducing algebra concepts

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Math Superpowers for Every Student

Award-winning Photomath app makes math easy to understand and master

Scan. Solve. Learn.

Math can be a daunting task when you don't have the right support. Photomath is the #1 app to learn math, to take the frustration out of math and to bring more peace to your daily student life.

Whether you are a mathlete or math challenged, Photomath will help you interpret problems with comprehensive math content from arithmetic to calculus to drive learning and understanding of fundamental math concepts.

App Downloads

100M+

Math problems solved and explained

1,234,054,453

monthly

What Else Can Photomath Do?

Smart Calculator

Enter or edit scanned math problems using an intuitive math keyboard. Experiment with changes to get a deeper understanding of math problems.

Graphs

Use graphs to visualize math problems. You can not only explore graph details such as the root, the domain, etc. but also use graphs to interpret solutions of equations and system of equations.

What Do Users Think about Photomath?

Incredible, in-depth explanation.

This is a fantastic app. The text recognition is near perfect, even with my sloppy handwriting. The solution, no matter how complicated, is accompanied with steps which go in detail to explain the problem and it's properties. I use this app mostly to check my work and see exactly where I went wrong in solving. I use this on all of my homework and practice notes. Five out five stars, hands down.

This gave my son his confidence in math

Since my son started middle school his math has gotten significantly more difficult than elementary school. This overhelmed him and he felt ashamed because he didn't "get it" right away like he always had. I tried to help but that didn't work out too well. Photomath was able to show him how to get to the correct answer and the light bulb came on. The joy he felt when he actually understood the problem he was looking at was amazing. He now doesn't feel hopeless and has a sense of accomplishment. Thank you!

The most awesome math app ever!!

Two snaps and a twist. Yes, I tech kids math. I love math but on occasions, no matter how much you show your students how to do long division they just can't get it. This app works. The animated explanations are the best. All of my students have this app and I am seeing an improvement with their comprehension and understanding of basic and complicated math facts. Well done to the creators of this app.

Because Math Is Even More Important Today

- Be the expert your child can depend on

Photomath can help review math concepts and fend off math anxiety that can take a big bite out of a student's performance.

- Amplify your math teaching

Photomath has improved student performance in a wide range of classrooms and schools worldwide. Implement Photomath to elevate your teaching and accelerate student learning.

Awards

Since its launch, Photomath has topped App Store & Google Play Store education charts. Being trusted by millions is one of our proudest achievements to date.

Photomath is a proud winner of 4YFN competition in Barcelona, the world's largest startup competition on mobile technologies and business models.

Photomath also received a Netexplo Forum Award for its work in educational technology.

Supporting a Wide Range of Math Problems

Photomath can explain anything from simple addition to more complex calculus problems.

Download Photomath for Free

Photomath is the ultimate educational tool for a smartphone or tablet. The core of Photomath is free for you to download. With over 100 million downloads, Photomath is one of the most popular educational apps of all times. Join students across the globe learning math effortlessly.

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Photomath is the #1 app for math learning; it can read and solve problems ranging from arithmetic to calculus instantly by using the camera on your mobile device. With Photomath, learn how to approach math problems through animated steps and detailed instructions or check your homework for any printed or handwritten problem.

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Join a game of kahoot here. Kahoot! is a free game-based learning platform that makes it fun to learn - any subject, in any language, on any device, for all ages!

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Download Explain Everything Interactive Whiteboard from the Apple App Store or Google Play Store!

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Teaching Tools | Resources for Teachers from Scholastic

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Factions game

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Woot Math is an adaptive online curriculum that focuses on fractions, ratios, and decimals. It includes narrated tutorials and targeted practice. Teachers set up student accounts (with student names, usernames, and passwords) and students log in using this info and a teacher code. Woot Math Polls is part of Woot Math and is a standards-aligned tool that can be used to create warm-ups, exit tickets, quizzes, and formative assessments.

Students access a progression of adaptive lessons through units organized by topic and presented as notebooks, and they view their progress through units. Student home pages show 12 lessons (which look like sticky notes) per screen: Completed ones are shaded, future ones have locks. Each lesson begins with a short (1-2 minutes) narrated example, followed by a series of practice questions, sometimes with further tutorials and more questions. At the end of the lesson (each of which are about 10 questions long), a student earns 1-3 stars depending on quantity correct, and the next lesson is unlocked (it's now gray, with a "new" sash). The site's adaptiveness makes it so that the "next" lesson may or may not be sequentially next -- sometimes it's a review of content that needs some extra attention, and sometimes it skips ahead to a more complex concept. At any time, previous lessons may be redone; new problems are provided, and the adaptive feature still works. Students can also earn pens, badges, and trophies.

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Woot Math is an adaptive online curriculum that focuses on fractions, ratios, and decimals. It includes narrated tutorials and targeted practice. Teachers set up student accounts (with student names, usernames, and passwords) and students log in using this info and a teacher code.

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This video shows an alternative to long division. Many of my students find this method easier than remembering when to divide, multiply, and subtract during "traditional" long division. I usually start teaching this to my 4th graders later in the year. Please let me know what you think!

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PROJECT STRUGGLE: My own modified version of numberless word problems

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PROJECT STRUGGLE: My own modified version of numberless word problems

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PROJECT STRUGGLE: numberless word problems

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PROJECT STRUGGLE: numberless word problems

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Something Amy suggested I want to try.

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Harvard study

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June 12, 2014, Driving Question: What Does Critical Thinking Look and Sound Like in an Elementary Classroom? Volume 1, Issue 5, No. 8
The other day, I walked into one of our primary multi-aged classroom communities. I noticed many wonderful things. It was clear the students were engaged in what they were doing.

These young students were working on an inquiry unit related to force and motion. Students were engaged in reading paperback books, articles and e-books individually and/or with partners. Other students were using their iPads to view videos related to force and motion. Many of the students were recording notes on their iPads or on paper while watching the videos or reading. A few students were experimenting with different materials such as ramps, matchbox cars, marbles, etc. to experiment and learn about force and motion.

Later, students met in small groups and engaged in discussions related to what they learned or discovered through these activities. Their conversations led the students to synthesize their new learning, reflect on the learning experiences they had, and make connections to how this new information relates to the essential question of their current inquiry unit.

It is clear that these students were working on thinking critically.

For us, critical thinking happens when students analyze and evaluate evidence, arguments, claims and beliefs. They can then learn how to make judgments and decisions based on others' points of view, interpret information and draw conclusions.

Fostering Critical Thinking
Four main approaches have made the biggest impact on our children's critical thinking:

Inquiry
"One way we try to foster critical thinking skills in our classroom is by allowing our students to be creative and to inquire about topics that are of interest to them." Katie Hart, Professional Educator

We incorporate cross-curricular inquiry to foster deep learning. The students work through the phases of immersion, investigation, coalescence and demonstration of learning. Throughout these phases the students are able to wonder, build background knowledge, develop questions, search for new information, synthesize information, demonstrate an understanding and share their new learning with others. Throughout inquiry, the students tie everything together through an essential question which helps them probe for deeper meaning. These questions are open-ended, encourage collaboration and foster the development of critical thinking skills.

Questioning
"We push students to dig deeper in their learning by asking guiding questions and providing a variety of resources for students to independently find answers. Throughout their learning, we encourage students to ask and answer their own questions through small group discussions, conferring, working on their Personalized Learning Plans and using graphic organizers." Elizabeth Hatab and Sarah Suesskind, Professional Educators

Questioning plays a critical role in cultivating critical thinking skills and deep learning. Questioning models for students how they should think. Our professional educators use open-ended questions to encourage discussion and active learning. We also incorporate questioning into our everyday discussions with students.

Problem Solving
"In the 4K/5K classrooms, we don't just give students answers to issues or problems they are having. Instead, we turn the problem onto them and ask how could they solve this problem. This allows the child opportunities to solve their problems independently." Teresa Lutzen, Professional Educator

Problem solving extends our inquiry work. It is important that our students think for themselves. In problem solving they apply the critical thinking strategies they have learned.

Collaboration
"Integrating meaningful learning experiences that promote critical thinking skills is essential in cultivating a classroom of 21st Century learners. One way we do this is by actively involving the students in their learning through collaborative work. This helps the students take ownership of the learning and think critically about issues." Patti Kaisler and Rebecca O-Grosky, Professional Educators.

Our student-centered learning environments are varied and flexible to accommodate the needs of learners and provide ongoing opportunities to build a collaborative community of students and staff. Our environments promote collaborative, individual, small and large group learning.
Students learn in collaborative flexible groups based on need. When students collaborate together they learn how to communicate with others effectively, work as a team, practice self-discipline, and improve social and interpersonal skills. Through collaboration, students are able to have a better understanding of what they are learning and improve critical thinking skills.

And Beyond
There are many other ways that we foster critical thinking among our learners, but these are the four that have made the biggest impact for us. Critical thinking is a key skill that our students need to have in order to become life-long learners and self-advocates for themselves.

Stacey Lange is an Academic Dean at Walker Elementary School and is part of the instructional services team for the West Allis-West Milwaukee School District. Her district, West Allis-West Milwaukee, is part of the Next Generation Learning Initiative, an effort that involves all teachers working to transform learning for all students. Her school is a P21 Exemplar. @LangeStacey

Up Next: Project Zero Thinks on the Critical Side

Make it Happen
A Transfer Protocol

At the end of each week, facilitate your transfer of the key ideas into practice. Take a few minutes to share your ideas from want you to takeaway about this week's posts.
Share your favorite blog posts to your friends and colleagues.
Click here to download writable pdf

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Strategies To Promote Critical Thinking in the Elementary Classroom

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June 12, 2014, Driving Question: What Does Critical Thinking Look and Sound Like in an Elementary Classroom? Volume 1, Issue 5, No. 8 The other day, I walked into one of our primary multi-aged classroom communities. I noticed many wonderful things. It was clear the students were engaged in what they were doing.

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Teaching Tools | Resources for Teachers from Scholastic

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Zearn Math | Top-rated Math Learning Platform

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Learning with Zearn helps math make sense. Students explore math through pictures, visual models, and real-life examples. Log in to your Zearn account.

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Page 7: Data-Based Decisions

Data-based decision making is the process of using data (e.g., progress monitoring data) to make instructional decisions, such as which students are struggling with mathematics and which level of instructional support would best meet those students' academic needs. After evaluating a student's rate of growth or performance level, the teacher or team of teachers use this information to make informed instructional decisions. School personnel need to use a standard procedure to determine whether to initiate or discontinue additional instructional supports.

Initiating Instructional Supports

The process of initiating instructional supports often begins with a universal screening. At each subsequent level of instruction, progress monitoring data is collected to determine the progress of struggling students. The graphic below illustrates the decision-making process for initiating instructional supports.

Discontinuing Instructional Supports

The same progress monitoring data can also be used to determine whether the teacher needs to make an instructional change: discontinuing a given level of instruction, receiving another round of intervention, or receiving more intensive instruction. The graphic below illustrates the decision-making process for discontinuing instructional supports.

Teachers should continue progress monitoring even after a student discontinues an intervention. In this way, teachers can catch a student who is beginning to fall behind before the next universal screening, and a decision can be made about providing additional support either at the primary or secondary levels.

When teachers implement the discontinuation process, it is important that they ensure that instructional support is not ended prematurely because the student appears to have acquired the necessary skills. In other words, school personnel need to be sure that a student has mastered and can maintain the skills acquired during intervention before that intervention is discontinued. Discontinuing any level of support too soon can result in students bouncing back and forth between levels (i.e., "ping-ponging"). For example, a student who discontinues Tier 2 intervention without mastering requisite skills will soon begin to fall behind when receiving core instruction only. This, in turn, will result in the student's again needing Tier 2 supports.

For Your Information

If a student does not respond adequately to Tier 2 intervention and if Tier 3 intervention at that school is provided through special education, the student must go through the special education eligibility determination process. If a student responds adequately to Tier 3 intervention and it is determined that the student no longer needs these services, an individualized education program (IEP) meeting must be held to discontinue those services.

In the case of a student who is receiving intensive, individualized intervention and whose progress monitoring data indicate that she is not sufficiently responding to the current intervention, the teacher needs to determine:

Why is the student not responding?

What type of change needs to be made to the intervention?

To determine a student's specific instructional needs and to make intervention adaptations that align with those needs, the teacher can use a diagnostic assessment-a tool that teachers can use to collect information about a student's strengths and weaknesses in a skill area. These assessments can be formal (e.g., standardized achievement test) or informal (e.g., work samples).

To learn more about how to use assessment data to intensify instruction, view the following IRIS Module:

The following examples demonstrate how to use progress monitoring data to make informed instructional decisions. In this case, the criteria that indicate adequate response to intervention are:

Performance Level = 21 Slope = .5

This graph is titled Student 1. The x-axis is labeled "Weeks of Instruction" and each week from 0 to 18 is labeled on the axis. The y-axis is labeled "Problems Correct." This axis is labeled from 0 to 30, with 10, 20, and 30, delineated numerically with five tick marks between each label, representing 2 digits correct each. The graph itself is divided into two portions by a dashed black line between weeks 6 and 7. The first portion of the graph is labeled "Core Instruction" and the second portion is labeled "Supplemental Intervention." There is a separate red line graph in each portion of the graph. In the Core Instruction portion, six points are plotted all around 11 to 12 digits correct. In the Supplemental Intervention portion, eleven points are plotted from around 17 to 23 digits correct. This graphic is more variable, with steep up and down slopes, than the graph in the Core Instruction portion. The last plotted point in the Supplemental Intervention portion of the graph is Week 17.

Student 1's data indicate that he has exceeded criteria for performance level and slope, therefore the team decides the student needs to:

Discontinue supplemental intervention

Receive core instruction only

Performance Level = 15.5 Slope = .6

This graph is titled Student 2. The x-axis is labeled "Weeks of Instruction" and each week from 0 to 18 is labeled on the axis. The y-axis is labeled "Problems Correct." This axis is labeled from 0 to 30, with 10, 20, and 30, delineated numerically with five tick marks between each label, representing 2 digits correct each. The graph itself is divided into two portions by a dashed black line between weeks 6 and 7. The first portion of the graph is labeled "Core Instruction" and the second portion is labeled "Supplemental Intervention." There is a separate red line graph in each portion of the graph. In the Core Instruction portion, six points are plotted all around 6 to 8 digits correct. In the Supplemental Intervention portion, eleven points are plotted from around 8 to 17 digits correct. This graphic is more variable, with steep up and down slopes, than the graph in the Core Instruction portion. The last plotted point in the Supplemental Intervention portion of the graph is Week 17.

Student 2's data indicate that he has not met the criteria for performance level but has exceeded the criteria for slope, therefore the team decides the student needs to:

Receive another round of Tier 2 intervention to allow the student to increase his performance level*

*Note: According to the dual discrepancy approach, this student is responding adequately to intervention. The team in some schools might decide that he can discontinue Tier 2 intervention and receive Tier 1 instruction only. However, the team at this school decides that he would benefit from another round of Tier 2 intervention to increase his performance level.
Activity

Imagine you are providing Tier 2 intervention to a small group of students. In the demonstration above, Student 1 and Student 2's progress monitoring data were examined and instructional decisions were made. Following the same procedures, make instructional decisions for the remaining students in your group. Click on each to make an instructional decision for that student.

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Data-based decision making is the process of using data (e.g., progress monitoring data) to make instructional decisions, such as which students are struggling with mathematics and which level of instructional support would best meet those students' academic needs. After evaluating a student's rate of growth or performance level, the teacher or team of teachers use this information to make informed instructional decisions.

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IRIS

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IPAD game for teaching Fractions

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How Can Teachers Use It?

Fruity Fractions works best if each student has his or her own device. However, there should be frequent opportunities for students to stop and share what they've discovered. In many problems, there's more than one right answer; give kids a chance to pause and organically learn from each other's thinking. It will also help them see that equal shares of identical wholes don't always have the same shape.

Earlier levels are reading-heavy, so pair less-strong readers with a stronger reader to get started. Once they make it past the first 6 levels, the text instructions become less important. The text is pretty small, so it works better on a larger device like an iPad. In the Grown-ups menu, teachers can turn off sound,turn off the locks to let kids skip ahead, and turn off hints for students who rely too heavily on their guidance.

What's It Like?

Fruity Fractions teaches basic fractions concepts to kids in first through third grade. Students divide up circles, triangles, squares, rectangles, and irregular shapes into equal parts. Without knowing it, kids use the concept of the unit fraction to build an understanding of whole-part relationships. Instruction and practice are interwoven, empowering kids to move from simple to complex seamlessly. Kids move through 50 levels, each of which appears as a single screen with a puzzle to solve. Students learn about what a fraction is by separating fruit into equal parts and describing it with a numerator and denominator. Fruity Fractions emphasizes multiple representations, too: Kids create both the numerical fraction and the corresponding shape model.

There's excellent Common Core State Standards alignment built right in: Kids drag and drop to partition shapes into equal parts, meeting all fractions standards for first and second grade and most of them for third grade. The only drawback is that kids don't learn how to represent fractions on a number line or learn specifically about equivalent fractions. However, the same developer has other apps that address these skills, and students may begin to notice patterns (e.g., 2/4 of a watermelon can look just like a 1/2 watermelon) and start to figure out equivalent fractions on their own.

Is It Good For Learning?

This app is thoughtfully designed to build kids' understanding of fractions and to dispel major misconceptions. Kids tend to view fractions as two disconnected numbers separated by a line; here, instead of seeing the numerator and denominator as unrelated numbers, kids repeatedly drag multiple unit fractions (like 1/4) together to build a concept of what a fraction (like 3/4) actually means. This app's biggest strength is its clear scaffolding: As kids move through the game, new sections become available, keeping kids locked out of the higher levels until they've mastered the lower ones. Kids can go back to these early activities to review in any order once they've demonstrated mastery. There's a built-in timer, too; kids who are acing the early levels can race each other later on to hone their skills and keep up the challenge.

The only odd feature is the silly fruit diving cartoon that appears after every five levels. Its point might be lost on the target age group, and it seems superfluous: This app is fun and rewarding as it is, and there's no need for this momentary distraction.

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How Can Teachers Use It? Fruity Fractions works best if each student has his or her own device. However, there should be frequent opportunities for students to stop and share what they've discovered. In many problems, there's more than one right answer; give kids a chance to pause and organically learn from each other's thinking.