Use of the Drum Loop by math teachers could support the following requirements from the New York State Learning Standards and Core Curriculum for Mathematics.
- CCSS.Math.Content.3.NF.A.1 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.
- CCSS.Math.Content.3.NF.A.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
- CCSS.Math.Content.3.NF.A.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
- CCSS.Math.Content.4.NF.B.3a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
- CCSS.Math.Content.4.NF.B.3b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
- CCSS.Math.Content.4.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
- CCSS.Math.Content.4.NF.B.4a Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
- CCSS.Math.Content.4.NF.B.4b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
Ratios & Proportional Relationships—Grade 6
- CCSS.Math.Content.6.RP.A.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.”
- CCSS.Math.Content.6.RP.A.3b Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 34 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Ratios & Proportional Relationships—Grade 7
- CCSS.Math.Content.7.RP.A.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
- CCSS.Math.Content.7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Representation Strand—Grade Eight
- 8.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
- 8.R.2 Explain, describe, and defend mathematical ideas using representations
- 8.R.3 Recognize, compare, and use an array of representational forms
- 8.R.4 Explain how different representations express the same relationship
- 8.R.5 Use standard and non-standard representations with accuracy and detail
- 8.R.6 Use representations to explore problem situations
- 8.R.9 Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects)
- G.PS.3 Use multiple representations to represent and explain problem situations (e.g., spatial, geometric, verbal, numeric, algebraic, and graphical representations)
- G.CM.2 Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams
- G.CN.1 Understand and make connections among multiple representations of the same mathematical idea
- G.CN.3 Model situations mathematically, using representations to draw conclusions and formulate new situations
- G.CN.6 Recognize and apply mathematics to situations in the outside world
- G.R.1 Use physical objects, diagrams, charts, tables, graphs, symbols, equations, or objects created using technology as representations of mathematical concepts
- G.R.2 Recognize, compare, and use an array of representational forms
- G.R.3 Use representation as a tool for exploring and understanding mathematical ideas
- G.R.5 Investigate relationships between different representations and their impact on a given problem
- G.G.21 Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles
- G.G.54 Define, investigate, justify, and apply isometries in the plane (rotations, reflections, translations, glide reflections)
- G.G.55 Investigate, justify, and apply the properties that remain invariant under translations, rotations, reflections, and glide reflections
- G.G.56 Identify specific isometries by observing orientation, numbers of invariant points, and/or parallelism
- G.G.57 Justify geometric relationships (perpendicularity, parallelism, congruence) using transformational techniques (translations, rotations, reflections)
- G.G.60 Identify specific similarities by observing orientation, numbers of invariant points, and/or parallelism
- G.G.61 Investigate, justify, and apply the analytical representations for translations, rotations about the origin of 90o and 180o, reflections over the lines, and dilations centered at the origin
Algebra 2 and Trigonometry
- A2.R.6 Use mathematics to show and understand physical phenomena (e.g., investigate sound waves using the sine and cosine functions)
- A2.A.56 Know the exact and approximate values of the sine, cosine, and tangent of 0o, 30o, 45o, 60o, 90o, 180o, and 270o angles
- A2.A.60 Sketch the unit circle and represent angles in standard position
- A2.A.61 Determine the length of an arc of a circle, given its radius and the measure of its central angle
- A2.A.69 Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function
- A2.M.1 Define radian measure
- A2.M.2 Convert between radian and degree measures