# Thinking Blocks

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- addition
- division
- fractions
- multiplication
- ratio
- subtraction

- applying information
- defining problems
- part-whole relationships

###### Pros

Clear explanations and guidance demonstrate how the models help students understand underlying math concepts.###### Cons

Few engaging elements mean kids might quickly lose interest.###### Bottom Line

Good instructional tool for trying out a non-traditional way to teach math.There's no area dedicated specifically to teachers. Teachers can use the modeling tool to design their own word problems or read the About page for info on the site and links to Singapore Math-related information and products.

Simple, straightforward setup means info and usage is clear, but there’s not a whole lot to excite kids. Kids who like math will have fun playing with new ways to represent math concepts; kids who don’t might need encouragement.

Kids get good hints when they make mistakes, which guides them in building their math models. However, the purely didactic approach makes it feel like work, and the site is only as successful as the Singapore Math method it represents.

Each activity has an accompanying demo video. A simple tracking tool tracks progress, but only in a single session. The only resources for extending learning are links to other Singapore Math method sites.

Enhance and make the math concepts accessible to kids of all learning styles by using Thinking Blocks as a part of a larger math curriculum. This approach could really help kids who are strong visual learners, though keep in mind that building the models online eliminates the kinesthetic aspect of actually manipulating blocks. You can offer the site to everyone to explore a new way of thinking about math, but knowing your students will help you decide which of them will really benefit from using the site. Teachers can use the modeling tool with an interactive whiteboard for class demonstrations of customized word problems. They can also use Thinking Blocks for drill practice or as an alternative way to look at math concepts in the computer lab or for homework. Have kids print the certificate to show what they've accomplished. The landing page features a convenient Common Core standards-alignment chart.

Read More Read LessThinking Blocks is an online version of the Singapore Math method, which uses blocks to model word problems that require addition, subtraction, multiplication, fractions, or ratios to solve. Pre-loaded word problems and step-by-step block model building are organized by math topic. When it’s time to solve the problem, a helpful calculator tool ensures that kids can focus on the underlying math concept (for example, what does it mean to talk about a 2:3 ratio?) rather than the simple mechanics of mental number calculations.

Students can track their progress in a single session by collecting stars (up to five for each subtopic) and printing a certificate of completion. There's also an open design section where students or teachers can design their own block representation and write their own word problems.

Read More Read LessThinking Blocks uses a simple design and is a nice online tool for the Singapore Math method. For example, Fred has three boxes of books (set out three blocks) with five books in each box (label each block, five books), how many total books does Fred have? The problems and block representations get more complicated as the underlying math concepts get more sophisticated. After building the correct model, kids must construct and solve the equation that will produce the correct answer. Unfortunately, kids get guidance here only when they input an incorrect answer. Also, the only way to customize the difficulty level is to use the modeling tool, which requires consistent hands-on input. However, generally good feedback, clear explanations, and video demonstrations make for a solid learning experience. The main thing missing is fun; using the site might seem like a chore and may not hold kids' interest.

Read More Read Less## Key Standards Supported

4.NF: Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers. | |

4.NF.3.d | Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. |

4.NF.4.c | Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie? |

## Number And Operations—Fractions | |

5.NF: Apply And Extend Previous Understandings Of Multiplication And Division To Multiply And Divide Fractions. | |

5.NF.7.a | Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. |

5.NF.7.b | Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. |

5.NF.7.c | Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins? |

Use Equivalent Fractions As A Strategy To Add And Subtract Fractions. | |

5.NF.2 | Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions |

## Operations And Algebraic Thinking | |

1.OA: Represent And Solve Problems Involving Addition And Subtraction. | |

1.OA.1 | Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 |

1.OA.2 | Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. |

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.1 | Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. |

3.OA.2 | Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. |

3.OA.4 | Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?. |

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.1 | Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. |

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. |

## Ratios And Proportional Relationships | |

6.RP: Understand Ratio Concepts And Use Ratio Reasoning To Solve Problems. | |

6.RP.1 | Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” |

6.RP.2 | Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1 |

6.RP.3.b | Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? |

6.RP.3.c | Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. |

#### See how teachers are using Thinking Blocks

#### Teacher Reviews

- Solving Word Problems with Block Visuals4March 5, 2015
- Required apps for Common core and PARCC4March 27, 2014
- Singapore Math DeMystified!5February 15, 2014