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On this page, you’ll find how this specific lesson plan, Making a Farm, is aligned to the Common Core Mathematics Standards organized by grade level, domain, and standard ID with in-depth explanations and examples.
|Operations & Algebraic Thinking||3.OA.A.3
|Numbers & Operations – Fractions||3.NF.A.1
|Measurement & Data||3.MD.B.3
Represent and solve problems involving multiplication and division.
- CCSS.MATH.CONTENT.3.OA.A.3: Students are using the formulas for perimeter and area to build their farm, which as addendum to their house.
- CCSS.MATH.CONTENT.3.OA.A.4: Students use the formulas for area and perimeter when the length and width have been determined.
Understand properties of multiplication and the relationship between multiplication and division.
- CCSS.MATH.CONTENT.3.OA.B.5: In the Basic House, Farm, and Parthenon lesson plans, students learn are given opportunities to learn about the commutative, associative, and distributive properties of multiplication through the equations for perimeter and area.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
- CCSS.MATH.CONTENT.3.OA.D.8: In the Algebra Architecture lesson plans, students are constantly using the four main operations with letters standing for unknown quantities. Students are using formulas to help them solve other formulas.
Develop understanding of fractions as numbers.
- CCSS.MATH.CONTENT.3.NF.A.1: This farm (below) has dimensions of 10 by 11 with a total area of 110 blocks. 38/110 are the stone blocks that make up the perimeter, 64/110 are dirt blocks, and 8/110 are water blocks. 38/110+64/110+8/110=110/110=1
- CCSS.MATH.CONTENT.3.NF.A.3.D: In the lesson about making a farm, students are dealing with fractions that have the same denominator. In this example below, the Perimeter = 38 and Area = 110. Perimeter/Area = 38/110, Dirt/Area = 64/110, and Water/Area =8/110. When the fractions are added together, it equals 110/110, which equals one farm.
Represent and interpret data.
- CCSS.MATH.CONTENT.3.MD.B.3: Before students make their farms in Minecraft, they will be using graph paper to sketch out what it will look like to ensure that their design will meet the design requirements. The blocks in Minecraft scale perfectly to the individual squares of the graph paper.
Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
- CCSS.MATH.CONTENT.3.MD.C.5.A: In the Algebra Architecture lesson plans which include building a house, farm, road, and Parthenon, students are measuring side lengths by blocks, which are essentially unit squares.
- CCSS.MATH.CONTENT.3.MD.C.5.B: In the Algebra Architecture lesson plans, students are measuring length and width to calculate the area of their structure, which can be measured in units squared.
- CCSS.MATH.CONTENT.3.MD.C.6: Students are using improvised units (e.g. blocks) to measure the area in the Algebra Architecture lesson plans. After calculating their area, they can check their work by counting the number of blocks.
- CCSS.MATH.CONTENT.3.MD.C.7.A: After measuring the length and width of their structure, students calculate the area by multiplying the dimensions. A = LxW
- CCSS.MATH.CONTENT.3.MD.C.7.B: Students are using whole-number side lengths to find the areas of rectangular structures that can easily be translated to real-life contexts (e.g. architecture).
- CCSS.MATH.CONTENT.3.MD.C.7.D: Since structures in Minecraft are already decomposed into clearly visible units of measurement (blocks), it makes it very apparent that area is additive.
Geometric measurement: recognize perimeter.
- CCSS.MATH.CONTENT.3.MD.D.8: In three of the five lessons of Algebra Architecture — Building a House, Farm, and Parthenon — students are solving for perimeter given the measurements of the dimensions of their structures. When given the opportunity to build multiple structures, students can see that different dimensions may have the same area but different perimeters (e.g. 8×5 and 10×4) and vice versa.
Reason with shapes and their attributes.
- CCSS.MATH.CONTENT.3.G.A.2: When constructing their farms, students can partition the area into equal parts (e.g. plots of dirt separated by water), and they are challenged to convert the area each component of the farm (perimeter, dirt, water) into a fraction, coming to a realization that they are part of a whole.
|Here, the farm has been separated into equal parts that make up a whole.|
Build fractions from unit fractions.
- CCSS.MATH.CONTENT.4.NF.B.3.A: When sketching the designs of their farms, students must break down each of the components (dirt, water, perimeter enclosing) into fractions.
- CCSS.MATH.CONTENT.4.NF.B.3.B: After designing their farms, students are tasked with creating fractions for the perimeter, dirt, and water. In this example below, the Perimeter = 40 and Area = 121. Perimeter/Area = 40/121, Dirt/Area = 64/121, and Water/Area =17/21. When the fractions are added together, it equals 121/121, which equals one farm.
- CCSS.MATH.CONTENT.4.NF.B.3.D: In designing their farm, students are turning parts of the whole into fractions and adding them back together, with like denominators. By building a digital farm, students are using a visual fraction model to learn about the concept.
Solve problems involving measurement and conversion of measurements.
- CCSS.MATH.CONTENT.4.MD.A.3: Students are directly using the formulas for area and perimeter to build digital structures, which can be applied to real-life contexts, such as architecture.
Write and interpret numerical expressions.
- CCSS.MATH.CONTENT.5.OA.A.1: In the house, farm, and Parthenon lesson plans, students use various formulas, including area and perimeter, that contain parentheses; they must be able to evaluate these calculations correctly by applying the order of operations.
- CCSS.MATH.CONTENT.5.OA.A.2: When creating walls or columns, students will understand that finding the number of blocks involves manipulating the perimeter (multiplying and/or dividing the perimeter by a whole-number). By setting up the formula without solving it, students will be able to interpret the numeral expression before solving it.
Solve real-world and mathematical problems involving area, surface area, and volume.
- CCSS.MATH.CONTENT.6.G.A.1: This farm is a polygon that is composed of a decomposition of shapes. For example, this farm (belowt) has an area of 110 total blocks. Of the 110 blocks, 38 are in the perimeter enclosure, there are two 4 x 8 areas of dirt, and 1 x 8 area of water.
Apply and extend previous understandings of arithmetic to algebraic expressions.
- CCSS.MATH.CONTENT.6.EE.A.2.A: In designing their farm, students must solve for the unknown variables of perimeter (P) and area (A).
- CCSS.MATH.CONTENT.6.EE.A.2.B: When solving the equation for perimeter in Minecraft, P = 2(L+W) – 4, students should be able to explain that perimeter is the “product of two times the sum of the length and width, minus four.” They will do this throughout as the lessons challenge students to use language to describe each of the formulas being used.
Reason about and solve one-variable equations and inequalities.
- CCSS.MATH.CONTENT.6.EE.B.6: The equations for the basic house, road, farm, and Parthenon lesson plans are comprised of perimeter, area, height, length, width – all mathematical terms that are used in real-life. Furthermore, students begin to build an understanding of how to read algebra as a language where variables stand for unknown numbers.
- CCSS.MATH.CONTENT.6.EE.B.7: In the house, farm, road, and Parthenon lesson plans, students must evaluate expressions in which letters stand for numbers on both sides of the equation (e.g., A = LxW), and build an understanding of the relationship between variables in a given expression.
Represent and analyze quantitative relationships between dependent and independent variables.
- CCSS.MATH.CONTENT.6.EE.C.9: Since many formulas used in the house, road, farm, and Parthenon lesson plans involve variables on both sides of the expression (A = LxW, P = 2(L+W) – 4, S = 3L/2), students will see that changing one variable will result in the change of the other variable.
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- CCSS.MATH.CONTENT.7.EE.B.4.A: In using the formulas for perimeter and area in the house, farm, and Parthenon lesson plans, students are manipulating the variables to determine their given values. For example, if a student wants to make their Area = 35 and are given width = 5, they must set up the equation to determine what the length would be.