- developing novel solutions
- asking questions
- problem solving
Key Standards Supported
Expressing Geometric Properties With Equations
|HSG.GPE: Use Coordinates To Prove Simple Geometric Theorems Algebraically|
|HSG.GPE.4||Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).|
Expressions And Equations
|6.EE: Reason About And Solve One-Variable Equations And Inequalities.|
|6.EE.6||Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.|
|6.EE.7||Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.|
|7.EE: Solve Real-Life And Mathematical Problems Using Numerical And Algebraic Expressions And Equations.|
|7.EE.3||Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.|
|7.EE.4||Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.|
|8.EE: Analyze And Solve Linear Equations And Pairs Of Simultaneous Linear Equations.|
|8.EE.8.c||Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.|
|8.G: Solve Real-World And Mathematical Problems Involving Volume Of Cylinders, Cones, And Spheres.|
|8.G.9||Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.|
|Understand And Apply The Pythagorean Theorem.|
|8.G.8||Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.|
Measurement And Data
|2.MD: Represent And Interpret Data.|
|2.MD.10||Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put- together, take-apart, and compare problems4 using information presented in a bar graph.|
|3.MD: Geometric Measurement: Recognize Perimeter As An Attribute Of Plane Figures And Distinguish Between Linear And Area Measures.|
|3.MD.8||Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.|
Modeling With Geometry
|HSG.MG: Apply Geometric Concepts In Modeling Situations|
|HSG.MG.3||Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).★|
Operations And Algebraic Thinking
|2.OA: Represent And Solve Problems Involving Addition And Subtraction.|
|2.OA.1||Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1|
|3.OA: Represent And Solve Problems Involving Multiplication And Division.|
|3.OA.3||Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1|
|Solve Problems Involving The Four Operations, And Identify And Explain Patterns In Arithmetic.|
|3.OA.8||Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3|
|4.OA: Use The Four Operations With Whole Numbers To Solve Problems.|
|4.OA.2||Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1|
|4.OA.3||Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.|
|5.OA: Analyze Patterns And Relationships.|
|5.OA.3||Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.|
Ratios And Proportional Relationships
|6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems.|
|6.RP.3.a||Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.|
|7.RP: Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems.|
|7.RP.3||Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.|
The Number System
|6.NS: Apply And Extend Previous Understandings Of Numbers To The System Of Rational Numbers.|
|6.NS.8||Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.|
|7.NS: Apply And Extend Previous Understandings Of Operations With Fractions To Add, Subtract, Multiply, And Divide Rational Numbers.|
|7.NS.3||Solve real-world and mathematical problems involving the four operations with rational numbers.|
|HSF.TF: Model Periodic Phenomena With Trigonometric Functions|
|HSF.TF.7||(+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.★|
Using Probability To Make Decisions
|HSS.MD: Use Probability To Evaluate Outcomes Of Decisions|
|HSS.MD.7||(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).|
For each problem, teachers are supported with suggestions for possible approaches, questions to ask, possible extensions, and support ideas. Solutions are available for every problem; however, kids can see them, too. A Professional Development section contains articles for teachers on mathematical pedagogy, classroom ideas, and research.
ProsThe site's approach to problem-solving challenges kids to think mathematically, giving them the tools to do so.
ConsVisual presentation needs to better adapt to its audience, with less text and easier "click" targets for younger kids in particular.
Bottom LineIt's an excellent classroom companion that can be implemented quickly with little adjustment and a high probability of success.
Graphite Expert Review
Common Sense Graphite Reviewer
As they generate solutions to problems with real-world relevance, kids should engage with these sharp student pages. Site navigation is a bit tricky, so kids may need adult guidance to find relevant activities.
Kids are encouraged to "explore, question, notice, and discuss," and submit solutions -- as a group or solo. Every problem has links to help kids get started, and a fully explained solution adds depth.
Online interactives and single-player and multiplayer offline games reinforce skills. In a community section, kids can discuss math with other kids or get homework help; experts give support but not answers. Spanish translation is available.
NRICH is a website featuring activities to challenge and engage kids with math problems, games, and projects set in relevant contexts. The site is divided into four student homepages representing the "5 Key Stages," or grade bands within the British education system, and corresponding U.S. K-12 grade level info is available. Problems for younger kids involve numbers and operations, shape, position, data and measurement with algebra, geometry, trigonometry, and statistics (added as they get older). Problems are presented with text and some video, so there’s quite a bit of reading. They’re printable and can always be read aloud.
To access age-appropriate problems by topic, use the Other Resources link in the Collections box on any student or teacher homepage. Click Topics at the top of the page to access all of NRICH’s problems.
Other extras NRICH offers include:
• Online interactives that work on a whiteboard
• Offline games
• Projects that promote STEM education
• Articles about math for all grades
• Tips for preparing for college math
• Professional development for teachersRead More Read Less
The "explore, question, notice, and discuss" approach is evident in the Getting Started suggestions link or in the problems themselves. The several solutions offered per problem highlight the relationship between creativity and math; it’s not just about the answer. Thorough corresponding teacher pages for each problem share possible approaches, questions to ask, and possible extensions to other support ideas. NRICH makes math a social activity, which is rare and fantastic. Kids will need to work away from the computer with pencil, paper, and other materials to sketch and model problems, but they don’t have to work alone. Have kids work in groups to submit a solution; NRICH always names the solver(s) of the solutions they accept. If small groups are not possible, kids can work alone or use the online community to find a partner.Read More Read Less
From their own student homepage, kids can choose to solve problems, check out trending math topics, or search for problems by collection or keyword, or from a list. Problems use text, video, and graphics, but kids will most often work offline with pencil and paper (problems can be printed). There are offline games for young kids to play, often with a partner. Kids at all grade levels can explore concepts via interactive online activities such as a peg board, Cuisenaire rods, modeling activities, or games.
Teacher homepages are also grouped by grade bands; you can visit them directly or through the Teacher Resources link that accompanies every problem.Read More Read Less
What's Inside NRICH
NRICH: Upper Secondary – Developing as MathematiciansChallenging activities prepare kids for more advanced workGraphite Rating 4Teacher Rating Not Yet RatedMathGrade 11-12
NRICH: Lower Secondary - Thinking MathematicallyFocus on mathematical practice features brainteaser activitiesGraphite Rating 4Teacher Rating Not Yet RatedMathGrade 5-12
NRICH: Lower Primary - Be a MathematicianNovel activities encourage problem solving and critical thinkingGraphite Rating 4Teacher Rating Not Yet RatedMathGrade 1-3
NRICH: Lower Primary - School Maths TopicsThrough creative exploration, kids practice important math skillsGraphite Rating 4Teacher Rating Not Yet RatedMathGrade 1-3
NRICH: Upper Primary – Be A MathematicianChallenging puzzles get kids to focus on mathematical processesGraphite Rating 4Teacher Rating Not Yet RatedMathGrade 2-5
NRICH: Upper Primary - School Maths TopicsProblems and games challenge kids to think outside the boxGraphite Rating 4Teacher Rating Not Yet RatedMathGrade 2-5
See How Teachers Are Using NRICH
Field Notes Field Notes are reviews by teachers for teachers. In Field Notes, teachers rate products as well as share their hands-on experience with using the products in the classroom.
- Great product to use for whole group or small group or individual engagementKirsten T.
Fox Ridge Middle School
Aurora, CO5May 13, 2014
- NRICH can be used as part of a website list for Algebra homework help.Lisa K.
Wellesley, MA2August 18, 2013
- Nrich is a brainy website for promoting math problem solving skills.Jason S.
Odyssey Charter Elementary School
Denver, CO3June 17, 2013