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Practice standards.

Click on the number to find illustrations for each of the eight Standards for Mathematical Practice.

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council's report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one's own efficacy).

Check out our elaborations of the practice standards: Grades K-5, Grades 6-8

Common Core State Standards Initiative

• Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up : adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

Standards in this domain:

Ccss.math.practice.mp1 make sense of problems and persevere in solving them..

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize —to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize , to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

CCSS.Math.Practice.MP4 Model with mathematics.

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

CCSS.Math.Practice.MP5 Use appropriate tools strategically.

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

CCSS.Math.Practice.MP6 Attend to precision.

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

CCSS.Math.Practice.MP7 Look for and make use of structure.

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x 2 + 9 x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3( x - y ) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y .

CCSS.Math.Practice.MP8 Look for and express regularity in repeated reasoning.

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation ( y - 2)/( x - 1) = 3. Noticing the regularity in the way terms cancel when expanding ( x - 1)( x + 1), ( x - 1)( x 2 + x + 1), and ( x - 1)( x 3 + x 2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Connecting the Standards for Mathematical Practice to the Standards for Mathematical Content

The Standards for Mathematical Practice describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years. Designers of curricula, assessments, and professional development should all attend to the need to connect the mathematical practices to mathematical content in mathematics instruction.

The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word "understand" are often especially good opportunities to connect the practices to the content. Students who lack understanding of a topic may rely on procedures too heavily. Without a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently, justify conclusions, apply the mathematics to practical situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an overview, or deviate from a known procedure to find a shortcut. In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices.

In this respect, those content standards which set an expectation of understanding are potential "points of intersection" between the Standards for Mathematical Content and the Standards for Mathematical Practice. These points of intersection are intended to be weighted toward central and generative concepts in the school mathematics curriculum that most merit the time, resources, innovative energies, and focus necessary to qualitatively improve the curriculum, instruction, assessment, professional development, and student achievement in mathematics.

• How to read the grade level standards
• Introduction
• Counting & Cardinality
• Operations & Algebraic Thinking
• Number & Operations in Base Ten
• Measurement & Data
• Number & Operations—Fractions¹
• Number & Operations in Base Ten¹
• Number & Operations—Fractions
• Ratios & Proportional Relationships
• The Number System
• Expressions & Equations
• Statistics & Probability
• The Real Number System
• Quantities*
• The Complex Number System
• Vector & Matrix Quantities
• Seeing Structure in Expressions
• Arithmetic with Polynomials & Rational Expressions
• Creating Equations*
• Reasoning with Equations & Inequalities
• Interpreting Functions
• Building Functions
• Linear, Quadratic, & Exponential Models*
• Trigonometric Functions
• High School: Modeling
• Similarity, Right Triangles, & Trigonometry
• Expressing Geometric Properties with Equations
• Geometric Measurement & Dimension
• Modeling with Geometry
• Interpreting Categorical & Quantitative Data
• Making Inferences & Justifying Conclusions
• Conditional Probability & the Rules of Probability
• Using Probability to Make Decisions
• Courses & Transitions
• Mathematics Glossary
• Mathematics Appendix A

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NCTM Process Standards and Exemplars

Special thanks to Deb Armitage, Exemplars consultant and task contributor/editor, for her contribution.

Title I teachers are often challenged with assessing students' mathematical understanding. Traditional worksheets, chapter/unit tests, and norm-referenced tests typically do not provide enough support in discovering what a student truly understands about mathematical concepts. Teachers have found much needed support from the research of the National Council of Teachers of Mathematics (NCTM) and Exemplars.

Like the NCTM standards, Exemplars material places a greater emphasis on the "process standards." By focusing on mathematical problem solving and communication, Title I teachers are able to look more closely at what students' work shows about their mathematical understanding. A stronger emphasis on process encourages teachers to demonstrate and support students in learning a variety of strategies for solving a problem. Exemplars encourages students to show different methods for solving problems. A variety of approaches allows teachers and students to discuss the merits of each strategy. The individual student can then embrace an approach that s/he is comfortable using to determine a correct outcome. By encouraging communication in mathematics, Title I teachers are better able to pinpoint where problems in students' thinking arise and can provide more meaningful feedback as a result. This feedback then encourages students to focus on areas that need improvement.

The process of problem solving and communication helps students gain confidence in their ability to solve problems. Shifting the major emphasis from finding the correct answer (only) and placing it instead on the process and communication of "thinking" improves the mathematical disposition of many students. Increasingly, Title I students become more comfortable with mathematical problems when they have a "tool kit" of possible strategies to consider, an understanding of mathematical language, and a belief that their way of solving a problem is just as valid as a neighbor's strategy.

Mathematics for Teaching

This site is NOT about making mathematics easy because it isn't. It is about making it make sense because it does.

NCTM Process Standards vs CCSS Mathematical Practices

The  NCTM  process standards, Adding it Up  mathematical proficiency strands, and Common Core State Standards  for mathematical practices are all saying the same thing but why do I get the feeling that the Mathematical Practices Standards is out to get the math teachers.

The NCTM’s process standards of problem solving, reasoning and proof, communication, representation, and connections describe for me the nature of mathematics . They are not easy to understand especially when you think that school mathematics is about stuffing students with knowledge of content of mathematics. But, over time you find yourselves slowly shifting towards structuring your teaching in a way that students will understand and appreciate the nature of mathematics.

The five strands of proficiency were also a great help to me as a teacher/ teacher-trainer because it gave me the vocabulary to describe what is important to focus on in teaching mathematics.

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4 thoughts on “ NCTM Process Standards vs CCSS Mathematical Practices ”

Does your “exposure” mean you personally watched Japanese classrooms or were you told/did you read how classes are taught?

Yes, including development of materials with Japanese math educators. We had a project with them. AlSo, the APEC (Asia Pacific…) project about Lesson Study for math which concluded last year devoted each year of the project for each of the process standards. I think the last one was about representation and communication. If you are familiar with Teaching Gap, the TIMSS video study by Stigler an Hiebert, you’ll get a picture of the Japanese math class. Of course, it doesn’t mean it’s happening they all teach that way.

We teachers are under tremendous pressure to be accountable for what students attain, which means insuring students do well on tests. It’s all about ‘data’ and Grade Level Content Expectations now. I fear both teachers and students will blow a fuse.

Really a nice addition in Mathematics Education

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Encouraging Students to LOVE MATH with One-Straight-Cut Letters

Yi-yin (winnie) ko, connor a. goodwin, lauren ream, and grace rebber.

One-straight-cut activities engage middle-school students in learning about symmetry and geometric transformations.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 116 (2023): Issue 12 (Dec 2023)

Gps: composing and decomposing shapes across the grades, kyle carpenter and sarah roller dyess.

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners' growth as problem solvers across their years of school mathematics.

GPS: Growing Constantly: Building to Systems of Linear Equations

Michelle t. chamberlin and robert a. powers.

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 116 (2023): Issue 7 (Jul 2023)

Problems to ponder, chris harrow, justin johns, and hassan lakiss.

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to [email protected]. If published, the authors of problems will be acknowledged.

The Search for Perfect Donuts

Wayne nirode and norm krumpe.

We define and investigate the concept of perfect donuts—rectangular donuts with a uniform width that is a natural number. Our investigation leads us to an interesting connection between the area of perfect donuts and the area of Pythagorean-triple triangles. We also provide ideas for further investigation.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 116 (2023): Issue 6 (Jun 2023)

Simple mathematical model for designing a corbeled arch, matthew s. neel.

This mathematical method can be used to find the size and shape of the bricks necessary to create a corbeled arch of nearly any shape. This method focuses on finding the minimum lengths of the bricks necessary to create a mathematically stable arch subject to certain constraints.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 116 (2023): Issue 4 (Apr 2023)

Point-line ellipses and hyperbolas, wayne nirode.

The author alters the definitions of ellipses and hyperbolas by using a line and a point not on the line as the foci, instead of two points. He develops the resulting prototypical diagrams from both synthetic and analytic perspectives, as well as making use of technology.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 116 (2023): Issue 3 (Mar 2023)

Chris harrow, justin gregory johns, ryne cooper, and vivekanand mandel, “fostering mathematical thinking and problem solving: the teacher’s role”, nicole r. rigelman and introduction by: sam rhodes.

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 116 (2023): Issue 1 (Jan 2023)

Delving deeper: what else comes after 1 + 2 = 3, charles f. marion.

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.

In  Mathematics Teacher: Learning and Teaching PK-12 Volume 115 (2022): Issue 12 (Dec 2022)

© 2024 National Council of Teachers of Mathematics (NCTM)

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There’s A Genuinely Good Chance That You Haven’t Seen These 37 Problem-Solving Kitchen Products

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Promising review: "This clip is amazing. No more towels falling on the floor. It was becoming a routine thing since my cat thinks it's fun to pull the kitchen towels off the oven. Not now, bad kitty! Great product...wish I had bought one sooner!" — Joanna

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Promising review: "I never know how much of a bottle I want; the nice part about this wine storage is that it’s easy, it’s beautiful, it’s clear, so you know how much is left, and it’s super easy to clean . As a busy mom, sometimes I want 1 glass, sometimes I want 1.5, LOL. This makes it both fun and easy to keep the wine fresh! " — Evan

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10. A cast-iron scrubber  that'll lift leftover food grit — not the pan's seasoning. This'll save you a heck of a lot of time now that you're not trying to scrub away stubborn stains with a fragile sponge.

Because this scrubber is metal, you should avoid using it on nonstick pans as it can scratch and damage the surface.

Promising review: "I love the product. I wish I had known about it when I first got my cast-iron skillet over a year ago. It is really easy to use and did a great job getting the crud off of the skillet without stripping the seasoning away and it was fast. I find myself using my cast-iron more frequently since purchasing this product because I no longer dread the cleanup process. If you have cast-iron cookware then you need one of these babies. I will definitely recommend it to others." — KeCaRi

Get it from Amazon for $17.99 . This customer review is long but it's full of great tips if you end up purchasing this scrubber.

11. A set of refrigerator drip catchers  so there isn't always  a puddle in the water tray...and the floor in front of your fridge. They sit securely in the tray thanks to their magnetic design.

Promising review: "This pad fits perfectly in our Samsung four-door in-door ice/water dispenser. Catches the occasional drips and matches the color of the dispenser perfectly. The four-pack lets you wash one and place another one into service immediately." — Amazon Customer

Get a two-pack for $12.93+ (available in three colors and packs of four).

12. A 2-in-1 kitchen scale and measuring cup  to reduce the number of dirty dishes you create and ensure your measurements are accurate.

Promising review: "This scale with a built-in cup is the best thing for my baking tools. No more whipping out 1,000,000 cups. Also, [rather than] always trying to figure out grams or cups, now I just press a button, and it tells me I love this." — Corin lonigro

Get it from Amazon for $20.29+ (available in three colors).

13. A  Souper Cube  if weeknight dinners take you no less than an hour and a half to make (and that's not counting cleanup time!). This silicone freezing tray stores perfectly portioned soups, stews, sauces, and more so you can meal prep in bulk over the weekend and then freeze it in these trays. It's so easy to quickly grab them as needed and defrost them for an easy meal.

Each tray has four fill lines — 1/2 cup, 1 cup, 125 mL, and 250 mL — which is ideal for people who like to portion their food.

You may remember Souper Cube from Shark Tank  (Lori invested in the company!). This small business was started by four friends who loved soup but hated food waste.

Promising review: "So happy that I found these. I’m the only one in my household who enjoys soup year-round. Have you ever tried to make homemade soup for one? I say it’s impossible! But no longer. I can brew up the stock pot with bone broth or my favorite home soup. Fill up my Souper Cubes, freeze, pop out, store my goodies in a freezer bag, and I’m ready for the next batch!" — Debbie R. Texas

Get it from Amazon for $19.95  (available in three colors and in a two-pack).

Check out my colleague's  Souper Cubes review !

14. A 6-in-1 kitchen tool  for replacing a ton of kitchen utensils, which means fewer things for you to wash! Use it as a whisk, egg separator, slotted spoon, colander, masher, or grinder/grater.

Promising review: "This is quite possibly my favorite new kitchen gadget. It is so sturdy, well-made, and versatile. I will be buying more to add to gifts for friends who are having bridal showers and housewarming parties." — Nancy Holmes

Get it from Amazon for $8.99 .

15. A Spoon Buddy utensil rest and holder  because not only does it help keep your countertops clean when you need to put down a dirty spoon or spatula, but it also functions as a measuring cup and a jar gripper. 

Promising review: "This product makes it easy to keep your spoon close and prevents getting a mess from drips on the stove." — John H. Parton

16. A lasagna trio pan that'll help you prepare meals for everyone, regardless of their dietary restrictions. Mamma mia! *insert chef finger kiss*

Promising review: "In a family of six, there are always SOME who don't like what everyone else is eating. This is a pan where making three different kinds of lasagna doesn't require much if any, more effort than making a single lasagna with the same dimensions.  It takes the same amount of time to layer the noodles and the same amount of time to build the things...but you have three different builds to satisfy those darned picky kids. Or hey, go adult gourmet in a way that Olive Garden cannot. What's fun with this pan is it's not just lasagna. I tried making bread with it to good effect. Yeah, the loaves looked a little weird, but I DON'T CARE. I did it, and that's all. It gives me what I prize most in cooking gear...versatility. Easy to clean, certainly...and nonstick, though that requires a little care (use wood, not metal utensils). With proper care and feeding, these are made to last pretty much forever. I love it." — J. Tant

Get it from Amazon for $22.99 .

17. Some lemon wedge wraps  so you can squeeze your citrus with reckless abandon and never worry that you'll find a seed in your drink or dish.

Promising review: "I love lemonade and lemon juice drizzled over my baked fish, but I hate those slippery little seeds. These lemon covers are perfect. They stop me from calling the seeds dirty names because they are sometimes hard to pick up. I use them all the time." — Wanda C.

Get a 12-pack from Amazon for $6.13 .

18. A salad sling  (from Shark Tank !) to dry greens, lettuce, and herbs without a salad spinner. Yep! Just wrap 'em in this green microfiber cloth and start slinging it around your kitchen — just don't let go or your romaine will go flying.

Promising review: "Don't even ask me what my previous process was for drying my greens because this one takes the cake ! It works effectively at drying your greens in seconds and then you just throw it in the wash once you're done, which frees up space in your dishwasher if you're used to using a salad spinner. Bonus use: When I was done drying the greens, I had other vegetables that I needed to wash, so I placed them on the Salad Sling and dabbed them dry before chopping. Since the waterproof liner traps moisture, it worked much better than an un-environmentally friendly paper towel or annoyingly thin dishtowel. I highly recommend this for people who are sick of salad spinning and using paper towels/thin dishtowels to dry their greens/veggies." — Kristen N.

Get it from Amazon for $23.99 .

19. A set of toss-and-chop salad tongs  if you don't want to waste time pulling out a whole chopping board (that you will have to clean later) to transform your romaine into bite-sized pieces. Scissor supremacy! Use these blades to slice your greens as well as your toppings: eggs, tomatoes, radishes, cucumbers, pieces of chicken, olives, apples, and more.

Promising review : "Love these! I hate big leafy salads, so I bought these, and they're perfect for chopping greens into bites. I also use them to quickly chop cherry tomatoes, onions, and other veggies. VERY nice quality." — asoon

Get it from Amazon for $18.76 . 

20. An onion holder  for a more secure grip and more evenly sized slices of onions, tomatoes, lemons, eggs, potatoes, and fruits. You can even use it as a meat tenderizer!

Promising review: "I’ve used this on different fruits and veggies and love it! I have a mandolin slicer and a food processor that slices, but it is easier just to use this tool . Nice and even slices of tomatoes and onions every time !" — Bekkster

Get it from Amazon for $9.98 .

21. A set of modular sheet pan dividers  because no, you don't need to suffer through veggies that are burned to a crisp because you had to leave the pan in the oven to make sure the salmon was fully cooked. With this handy system, you can just remove individual trays when the ingredients are fully cooked.

Promising review: "Brilliant. 100,000% Recommend them! It lets me separate veggies by how long they take to cook so they are all ready at the same time and nothing is over/undercooked. I love these cheat sheets. They are a great tool for my kitchen. " — yule

Get a set of four from Amazon for $29.99  (lids available for purchase separately). 

22. A set of  oven liners  that'll catch crumbs  before  they can permanently attach themselves to your oven and create a big freaking mess you'll spend hours cleaning. Raise your hand if you hate cleaning your oven. Great. Now take that same hand and click the "add to cart" button.

Promising review: "I got tired of cleaning the bottom of my oven out after every drip and spill or running the 'oven clean' option, which uses up so much energy and makes my house HOT during the process. I used to have foil on the bottom of the oven to help with spills, and that improved things greatly — but then you have to replace the foil after a while. I had to cut them to size, which was easy to do with a simple pair of household scissors. Then I placed them in the oven ( they look nice! ), and I waited for them to get messy. I cooked something super messy and finally needed to clean the liner. It was SO easy ; I put it in the sink and used my sink sprayer, and everything immediately slid right off the liner. No problem! I have a double oven, so I was glad this pack came with more than one. I have one in each oven and one on standby in case I need it. I know that having a dirty oven isn't the worst thing in the world, but if it matters to you, try these! " — Hpg

Get a set of three from Amazon for $13.99 .

23. A super-convenient tofu press so you can squeeze out as much water as possible from your tofu (preventing it from getting soggy and also helping it better absorb yummy marinades and spices) without needing to come back every 30 minutes to place a heavier book on top of your paper towel–wrapped tofu block.

Plus, all the water collects at the bottom, so there's no mess and no need for paper towels.

Promising review: "I've been eating tofu quite often. What I needed was a way to improve the texture. Even the 'extra firm' was too mushy. I searched through the many types of tofu presses and found this one. I like that there are only three parts, and everything is easy to clean. The tofu comes out perfect every time and doesn't take long at all. By the next day, it's ready to use. Even a few hours will do the trick!" — Margaret B.

Get it from Amazon for $21.99 .

24. A pouring chute  to save you a lot of frustration when you're baking. Both wet and dry ingredients slide down seamlessly and into the mixing bowl instead of ending up on the counter...which you will now have to clean. 

Promising review: "I have struggled with the pouring shields that came with my KitchenAid and Cuisinart stand mixers. They were messy and hard to use. I purchased this and forgot I had it! LOL. This weekend, I have been making tons of cookies and tried the New Metro chute out, and OMG! It works great. No mess. The flour or liquids go into the bowl and nowhere else. It's sturdy and super easy to use and clean. I highly recommend it. It's a quality product." — Retep

Get it from Amazon for $22.31 (also available in a two-pack).

25. A pair of silicone stands  if you don't wash your emotional support water bottle as much as you should because it's annoying how long it takes for it to dry. These provide a sturdy base so your bottles don't tip over while also allowing air to flow to ensure your bottles fully dry.

These are designed to work with a variety of brands including Stanley, Hydro Flask, Owala, Yeti, and more.

Promising review: "I wash my thermal cups by hand and found these individual drying racks to be helpful for getting my cups dry quickly and without taking up space in my drying rack . They fit a wide variety of thermal cup sizes. [They are made of] pliable rubber and don't allow the cups to tip over while drying. They vent air well and allow for excess water to sluice off the inside of the cup and drain." — Sonya Groves

Get a two-pack from Amazon for $8.88 (also available in four- and six-packs).

26. An air fryer basket  you can use in the oven for whipping up crispy, crunchy foods that *taste* like they came straight from the air fryer...no air fryer needed! It's great for people who 1) don't want to shell out for an air fryer (esp. one that's bulky/an appliance you're not sure you'll use), or 2) want to cook larger quantities of food than their air fryer can currently hold. 

Promising review: "I wanted to simulate air-frying in a countertop or conventional oven. This product does the trick, more so in my conventional oven; it has a 'speed-bake' feature that simulates a confection oven. It’s small enough to fit in my countertop oven. Love that the tray catches drips, and it doubles up nicely as a cookie sheet for small batches of chocolate chips! Cleanup is a dream. I cook-spray it prior to use, then treat it as cast iron while cleaning it (i.e., very hot water and a scrubby sponge — no soap on the baking surface). I use a little soapy water on the rim and 'feet,' so there is no oily buildup there. (I also foil or parchment paper line the drip sheet to make cleanup that much easier, but that’s just me. I’m pretty sure it’s not necessary as the non-stick finish seems pretty danged good so far.)" — Joanna Aislinn

Get it from Amazon for $19.89+  (available in three sizes).

27. A pair of  meat shredder claws  because pulling apart pounds of pork with two measly forks is not efficient or fun. 

Promising review: "I just made 26 pounds of pork butt for a large family gathering. Several months ago, I did the same thing, and my husband and I shredded it together with four forks. We scorched our hands repeatedly, and it took over 70 minutes. I looked at several shredding forks and settled in on these and I sure am glad I did! They are solid, light, and sharp. They are not hollow on the back side, so meat doesn't get stuck in them. It didn't take long to get the hang of them. They double as handles to pick the large 8.5 pounds of butts, which was very nice. They really do become extensions of your hands! I had read reviews that said that these don't let you get meat shredded finely, but that was certainly not my experience. Although I haven't used them on other sorts of meat yet, this pork was fall-off-the-bone tender, and it shredded very finely for me. And it did it so fast! I shredded all 26 pounds by myself in less than 30 minutes and didn't burn my hands once.  I wish I hadn't waited so long to get these...It really does beat the two-fork system!" — L. Smith

Get it from Amazon for $14.99  (available in four colors).

28. A bagel knife  that'll ensure a quick and even slice. Raise your hand if every time you cut a bagel, you have one side that's 1-inch thick while the other side is barely 1/2-inch thick. Great! Now take that hand and add this to your cart.

Promising review: "I bought this for my husband, who is the "official" bagel cutter in the house. He doesn't like bagel guillotines and our knives are too sharp and present an issue with accidental finger cuts. So far this has worked on varied girth bagels with ease. This is a great item!" — JW

Get it from Amazon for $17.99 .

29. A pizza storage container  so you don't lose the *entire* second shelf in your fridge to a pizza box. This expandable container grows to hold up to *5* slices of 'za, and creates an airtight lid that keeps your cheesy, pepperoni-y from getting stale or soggy. AND! The dividers prevent your pieces from sticking together while also serving as plates when you want to microwave your pizza.

Promising review: "I love this! I used the pizza pack to store four slices. They fit great and they were full-size slices. I also used the pizza trays included to warm up the pizza in the microwave. It did a pretty good job of getting the slices hot. I love the collapsible aspect. Great for easy storage. Great product, really good price, and made in the USA!!" — Tom Angiolillo

Get it from Amazon for $24.99  (available in eight colors).

30. A portable range hood  with five activated charcoal filters designed to suck up the odors, oils, and smoke that stink up your kitchen after cooking bacon, fish, and other delicious-yet-fragrant foods. It's also a great option for apartment dwellers or folks without a range hood.

Promising review: "This works exactly as stated and well. We just moved into a new place with no vent hood, so when we cook things like bacon on the stovetop we were worried about all the smoke and smell. This thing sucks it right away and works exactly as intended! " — Jennifer Billie

Get it from Amazon for $199.99 (available in four colors).

31. A 2-in-1 garlic press  if you're the type of person who's going to add three cloves (minimum!) when the recipe calls for two. This press slices *and* minces, so you don't need two separate gadgets.

Promising review: "I have carpal tunnel, so I like to minimize straining my muscles. I also have pretty small hands. This garlic press is really comfortable to use, albeit a little bit annoying to clean. I recently tried using a friend's garlic press, and the amount of force I needed to use really hurt my hands and wrists. If you've been avoiding getting a garlic press because you fear you lack wrist strength, this is the product for you. I'm never mincing or slicing garlic again. " — Jamie Sarmiento

Get it from Amazon for   $14.99 .

32. A pack of sink sound dampeners  for absorbing noise so the sound of running water or simply setting a pot in the sink to be cleaned doesn't make you cringe.

Promising review: "This product took the annoying ring out of my stainless sink and changed it to a dull thud. Just what I expected. Pads were easy to install and haven't had any adhesion issues in the month of heavy use with very hot water." — G. Fischer

Get nine pads from Amazon for $23.93 .

33. A time-saving  Thaw Belt  because you didn't remember to move your chicken from the freezer to the fridge, and now you're home from work, starving, exhausted, and seriously considering ordering takeout. This silicone strap keeps your meat submerged so it defrosts in minutes instead of hours.

Promising review: "I have never defrosted food so easily. Food that would've taken about 20 minutes normally (due to floating or having other items holding stuff down changing water temp) now only took a few minutes! " — Carissa Flowers

Get it from Amazon for $9.90 .

34. An ice cube tray  that'll make hollow cylindrical ice cubes — aka the perfect shape for your giant Stanleys and Hydro Flasks.

This tray is designed to make cubes that will fit in 30-oz. and 40-oz. tumblers.

Promising review: "I use these in my brumate and meoky cups, and they fit perfectly. I always struggle with getting my straw through the ice and in the middle so the lid will close. These ice cubes stay on the edge of the cup and allow plenty of room for the straw." — sarah schultz

Get it from Amazon for $16.99 (available in four colors).

35. An investment-worthy  MicrowavaBowl  so you don't have to constantly pause the microwave to mix your bowl to prevent cold spots. Yep, this dishwasher-safe bowl is designed to evenly distribute heat so your meal is perfectly warmed throughout.

Promising review: "These bowls are high quality and very convenient. They heat up food very quickly and evenly, therefore saving you valuable time and energy. Its ability to heat the food and not the bowl itself is very valuable to me. Prior to this purchase, I would have to use a hot bowl holder to avoid burning my fingers. The size of the bowls is perfect for the dishwasher, making them easy to clean and use. These bowls are sold at a reasonable price for what they have to offer. I would highly recommend them to friends and family!" — Alana

Get two from Amazon for $34.99 . 

36. A countertop composter  to turn your food scraps into natural fertilizer in less than 24 hours. Its compact size makes it a great option for people who don't have room for a backyard compost bin. And if you've tried composting already but were turned off by the smell and the pests it attracted, don't fret! This model is designed to be odor-free.

You'll get the composter, one filter, and two compost accelerator pods.

Promising review: "I held off on buying this because it seemed expensive, but I finally broke down and got the Lomi and am so glad I did! It makes compost efficient, and there's no smell at all. I've thrown kitchen scraps like fruit skins, lettuce scraps, egg shells, and some expired (and buggy) pasta, and it reduced it all down to lovely compost in a surprisingly short time. It does have a sound, but it's not obnoxious or loud. Being able to get these scraps broken down quickly helps keep the kitchen smelling clean, and I'm able to use the compost in my garden immediately. So great!" — Amazon Customer

Get it from Amazon for $449 .

37. A  cutting board with a built-in colander  if you're all about efficiency in the kitchen. Now you don't have to waste paper towels drying off your produce or sprint from the sink to the counter trying to prevent your freshly washed potatoes from dripping all over your floor.

Promising review: "This is an extremely useful cutting board with a collapsible bowl for washing vegetables and/or fruits, draining them, or depositing scraps. It fits nicely over my sink and is easily cleaned and stored. Find myself using it every day!" — Patty Boh

Get it from Amazon for $24.99+ (available in five colors).

The reviews for this post have been edited for length and clarity.  

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Nvidia and Microsoft are solving a big problem with Copilot+

When Microsoft announced Copilot+ PCs a few weeks back, one question reigned supreme : Why can’t I just run these AI applications on my GPU? At Computex 2024 , Nvidia finally provided an answer.

Nvidia and Microsoft are working together on an Application Programming Interface (API) that will allow developers to run their AI-accelerated apps on RTX graphics cards . This includes the various Small Language Models (SLMs) that are part of the Copilot runtime, which are used as the basis for features like Recall and Live Captions.

With the toolkit, developers can allow apps to run locally on your GPU instead of the NPU. This opens up the door to not only more powerful AI applications, as the AI capabilities of GPUs are generally higher than NPUs, but also the ability to run on PCs that don’t currently fall under the Copilot+ umbrella.

It’s a great move. Copilot+ PCs currently require a Neural Processing Unit (NPU) that’s capable of at least 40 Tera Operations Per Second (TOPS). At the moment, only the Snapdragon X Elite satisfies that criteria. Despite that, GPUs have much higher AI processing capabilities, with even low-end models reaching to 100 TOPS, and higher-end options scaling even higher.

In addition to running on the GPU, the new API adds retrieval-augmented generation (RAG) capabilities to the Copilot runtime. RAG gives the AI model access to specific information locally, allowing it to provide more helpful solutions. We saw RAG on full display with Nvidia’s Chat with RTX earlier this year.

Outside of the API, Nvidia announced the RTX AI Toolkit at Computex. This developer suite, arriving in June, combines various tools and SDKs that allow developers to tune AI models for specific applications. Nvidia says that by using the RTX AI Toolkit, developers can make models four times faster and three times smaller compared to using open-source solutions.

We’re seeing a wave of tools that enable developers to build specific AI applications for end users. Some of that is already showing up in Copilot+ PCs, but I suspect we’ll see far more AI applications at this point next year. We have the hardware to run these apps, after all; now we just need the software.

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• Artificial Intelligence

The controversial Recall feature has grabbed all the headlines from Microsoft’s Copilot+ announcements yesterday, but this new AI feature is also making Paint relevant again.

It’s called Cocreator, and it’s a new AI feature that can turn your quick sketch, augmented by text, into a much more realistic and impressive image. The exciting thing is that it does all this in real time. It might not get it right the first time, so you'll need patience, and the more details you give about what you want in the image, the better.

Whether successful or not, Copilot+ PCs are a huge deal. They represent a major shift in the landscape of Windows laptops, integrating support for ARM chips and AI at a systemwide level. There's a lot at play in this new transition -- and lots of room for confusion.

Here's the best answers we have to the most important questions surrounding Copilot+ PCs. What are the hardware requirements? When it comes down to it, devices must hit the following requirements to be considered a Copilot+ PC: 16GB of RAM, 256GB of storage, and a 40 Tera Operations Per Second (TOPS) neural processing unit (NPU). Microsoft hasn't provided specifics around things like CPU performance, battery life, and portability, but there may be standards in these regards too that we don't yet know about. Many of the massive claims in performance and battery life that make these devices true MacBook killers come from the Snapdragon X chips from Qualcomm -- but ARM isn't a requirement.

Microsoft has a lot more than AI riding on Copilot+ PCs. Although AI is the current buzzword of the tech industry, Microsoft's push into a new era of PCs has just as much to do with declining PC sales over the past several years, as well as Microsoft's decade-long drive to get Windows on ARM working.

With so much going on, it's left me wondering what Microsoft's real reason and motivation behind the transition might be. Copilot+ PCs are a new category of device that, yes, come with some AI features, but I'm convinced this transition might have more to do with addressing a stagnant Windows laptop market than simply just AI. A simple question