Lessons begin with an opener that can be projected on a screen for the whole class to view. Teachers can move through the prompts using an interactive Whiteboard or wireless mouse. Prompts encourage kids to think, share with a partner, and discuss ideas with the whole class. Following the openers, kids individually move through the lessons at their own pace on computers. Following an 8- to 15-minute guided lesson, students get a skills check that provides immediate feedback, and teachers can circulate to help students interpret their results.
An important note for implementation: It's best for students to wear headphones during digital lessons to reduce distractions, as multiple devices will be running videos at the same time.Continue reading Show less
Conceptua Math is a math curriculum program focused on visual learning and data-driven instruction. Content in the program is clustered into units called "big ideas" and based on the Common Core Math Standards. The program is meant to work with the careful guidance of a classroom teacher, not as a stand-alone instructional tool. Available units include third through fifth grade, Fractions (which covers some sixth-grade standards), and more.
Conceptua Math encourages teacher and student participation, and the program is not entirely Web-based. For example, in a think-pair-share opener, students think about models on the board and then share their ideas with a partner. Students might then move into a digital lesson where they would, say, move digital tiles to simulate the distributive property. As a closing activity, the class would reconvene to decide if they agree with a fictitious student’s solution to a problem.Continue reading Show less
One of Conceptua Math's biggest strengths is that it provides differentiation for individual students while also allowing whole classes to learn about math concepts together. While digital lessons are individualized, classes will have the same opener and closer together, offering teachers the opportunity to add to, or augment, the program's instruction.
Unfortunately, the Web-based tool alone isn't as adaptive as it could be. Students get the same number of problems to complete, regardless of how many earlier problems they get right. This might get boring for kids who “already get it”; more opportunities for differentiation would make the program even more impactful. Nevertheless, the online simulations allow students to manipulate concepts and see the results. This is very similar to using actual math manipulatives in the classroom, but the online technology has the benefit of individualized, immediate feedback.Continue reading Show less
Key Standards Supported
Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.
Number And Operations—Fractions
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Interpret multiplication as scaling (resizing), by:
Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a.
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
Operations And Algebraic Thinking
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.
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.
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
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 = ?.
Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.
The Number System
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?