Tangram Tactics!
Tangrams not only make interesting pictures, but when described mathematically, they reveal geometric fractions, decimals, and percents!
Standards
Idea Sheets are cross-referenced to subjects listed in the Common Core, Next Generation Science Standards, and California Content Standards.
Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 3||Mathematical Practices|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 4||Mathematical Practices|||4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.||Common Core Mathematics||Grade 4||Geometry||Draw And Identify Lines And Angles, And Classify Shapes By Properties Of Their Lines And Angles|||4.NF.1. 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.||Common Core Mathematics||Grade 4||Number And Operations?Fractions3||Extend Understanding Of Fraction Equivalence And Ordering|||4.NF.2. 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.||Common Core Mathematics||Grade 4||Number And Operations?Fractions3||Extend Understanding Of Fraction Equivalence And Ordering|||4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a.||Common Core Mathematics||Grade 4||Number And Operations?Fractions3||Build Fractions From Unit Fractions By Applying And Extending Previous Understandings Of Operations On Whole Numbers|||4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.||Common Core Mathematics||Grade 4||Number And Operations?Fractions3||Understand Decimal Notation For Fractions, And Compare Decimal Fractions|||4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.||Common Core Mathematics||Grade 4||Number And Operations?Fractions3||Understand Decimal Notation For Fractions, And Compare Decimal Fractions|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 5||Mathematical Practices|||5.G.3. Understand that attributes belonging to a category of two- dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.||Common Core Mathematics||Grade 5||Geometry||Classify Two-Dimensional Figures Into Categories Based On Their Properties|||5.G.4. Classify two-dimensional figures in a hierarchy based on properties.||Common Core Mathematics||Grade 5||Geometry||Classify Two-Dimensional Figures Into Categories Based On Their Properties|||5.NBT.7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.||Common Core Mathematics||Grade 5||Number And Operations In Base Ten||Perform Operations With Multi-Digit Whole Numbers And With Decimals To Hundredths|||5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)||Common Core Mathematics||Grade 5||Number And Operations?Fractions||Use Equivalent Fractions As A Strategy To Add And Subtract Fractions|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 6||Mathematical Practices|||6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.||Common Core Mathematics||Grade 6||Geometry||Solve Real-World And Mathematical Problems Involving Area, Surface Area, And Volume|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 7||Mathematical Practices|||7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.||Common Core Mathematics||Grade 7||Ratios And Proportional Relationships||Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems|||7.RP.2. Recognize and represent proportional relationships between quantities.||Common Core Mathematics||Grade 7||Ratios And Proportional Relationships||Analyze Proportional Relationships And Use Them To Solve Real-World And Mathematical Problems|||Mathematical Practices: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||Common Core Mathematics||Grade 8||Mathematical Practices|||8.G.1. Verify experimentally the properties of rotations, reflections, and translations:||Common Core Mathematics||Grade 8||Geometry||Understand Congruence And Similarity Using Physical Models, Trans- Parencies, Or Geometry Software|||8.G.2. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.||Common Core Mathematics||Grade 8||Geometry||Understand Congruence And Similarity Using Physical Models, Trans- Parencies, Or Geometry Software|||8.G.4. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two- dimensional figures, describe a sequence that exhibits the similarity between them.||Common Core Mathematics||Grade 8||Geometry||Understand Congruence And Similarity Using Physical Models, Trans- Parencies, Or Geometry Software
1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions (see Standard 4.0).||CA Mathematics||Grade 4||01. Number Sense||1.0 Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers.|||1.6 Write tenths and hundredths in decimal and fraction notation and know the fraction and decimal equivalents for halves and fourths (e.g., 1/2 = 0.5 or .50; 7/4 = 1 3/4 = 1.75).||CA Mathematics||Grade 4||01. Number Sense||1.0 Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers.|||1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.||CA Mathematics||Grade 4||01. Number Sense||1.0 Students understand place value of whole numbers and decimals to two decimal places, how these relate to simple fractions, and use concepts of negative numbers.|||3.7 Know the definitions of different triangles (e.g., equilateral, isosceles, scalene) and identify their attributes.||CA Mathematics||Grade 4||03. Measurement and Geometry||3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.|||3.8 Know the definition of different quadrilaterals (e.g., rhombus, square, rectangle, parallelogram, trapezoid).||CA Mathematics||Grade 4||03. Measurement and Geometry||3.0 Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems.|||1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number.||CA Mathematics||Grade 5||01. Number Sense||1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of numbers.|||2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).||CA Mathematics||Grade 6||03. Measurement and Geometry||2.0 Students identify and describe the properties of two-dimensional figures.|||1.3 Convert fractions to decimals and percents and use these representations in estimation, computation, and applications.||CA Mathematics||Grade 7||01. Number Sense||1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of forms.
- Grades 3-5
- Grades 6-8
- Math