6.NS.A.1 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?.
6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2)..
Topic A: Dividing Fractions by Fractions (6.NS.A.1)
Lesson 1: Interpreting Division of a Fraction by a Whole Number PRACTICE PROBLEMS
Lesson 2: Interpreting Division of a Whole Number by a Fraction
Lesson 3: Interpreting and Computing Division of a Fraction by a Fraction PRACTICE PROBLEMS
Lesson 4: Interpreting and Computing Division of a Fraction by a Fraction—More Models
Lesson 5: Creating Division Stories
Lesson 6: More Division Stories PRACTICE PROBLEMS
Lesson 7: The Relationship Between Visual Fraction Models and Equations
Lesson 8: Dividing Fractions and Mixed Numbers
Triangular Region (A triangular region is the union of the triangle and its interior.)
Altitude and Base of a Triangle (An altitude of a triangle is a perpendicular segment from a vertex of a triangle to the line containing the opposite side. The opposite side is called the base. For every triangle, there are three choices for the altitude, and hence there are three base-altitude pairs. The height of a triangle is the length of the altitude. The length of the base is either called the base length or, more commonly, the base. Usually, context makes it clear whether the base refers to a number or a segment. These terms can mislead students: base suggests the bottom, while height usually refers to vertical distances. Do not reinforce these impressions by consistently displaying all triangles with horizontal bases.)
Pentagon (Given different points , , , , in the plane, a -sided polygon, or pentagon, is the union of five segments , , , , such that (1) the segments intersect only at their endpoints, and (2) no two adjacent segments are collinear.)
Hexagon (Given different points , , , , , in the plane, a-sided polygon, or hexagon, is the union of six segments , , , , , such that (1) the segments intersect only at their endpoints, and (2) no two adjacent segments are collinear. For both pentagons and hexagons, the segments are called the sides, and their endpoints are called the vertices. Like quadrilaterals, pentagons and hexagons can be denoted by the order of vertices defining the segments. For example, the pentagon has vertices , , , , that define the five segments in the definition above. Similar to quadrilaterals, pentagons and hexagons also have interiors, which can be described using pictures in elementary school.)
Line Perpendicular to a Plane (A line intersecting a plane at a point is said to be perpendicular to the plane if is perpendicular to every line that (1) lies in and (2) passes through the point . A segment is said to be perpendicular to a plane if the line that contains the segment is perpendicular to the plane. In Grade 6, a line perpendicular to a plane can be described using a picture.)
Parallel Planes (Two planes are parallel if they do not intersect. In Euclidean geometry, a useful test for checking whether two planes are parallel is if the planes are different and if there is a line that is perpendicular to both planes.)
Right Rectangular Prism (Let and be two parallel planes. Let be a rectangular region[1] in the plane . At each point of , consider the segment perpendicular to , joining to a point of the plane . The union of all these segments is called a right rectangular prism. It can be shown that the region in corresponding to the region is also a rectangular region whose sides are equal in length to the corresponding sides of . The regions and are called the base faces (or just bases) of the prism. It can also be shown that the planar region between two corresponding sides of the bases is also a rectangular region called the lateral face of the prism. In all, the boundary of a right rectangular prism has faces: the base faces and lateral faces. All adjacent faces intersect along segments called edges (base edges and lateral edges).)
Cube (A cube is a right rectangular prism all of whose edges are of equal length.)
Surface of a Prism (The surface of a prism is the union of all of its faces (the base faces and lateral faces).)
Greatest Common Factor (The largest positive integer that divides into two or more integers without a remainder; the GCF of and is because when all of the factors of and are listed, the largest factor they share is .)
Least Common Multiple (The smallest positive integer that is divisible by two or more given integers without a remainder; the LCM of and is because when the multiples of and are listed, the smallest or first multiple they share is .)
Multiplicative Inverses (Two numbers whose product is 1 are multiplicative inverses of one another. For example, and are multiplicative inverses of one another because . Multiplicative inverses do not always have to be the reciprocal. For example and both have a product of , which makes them multiplicative inverses.)