Grades 6–8 Math Standards Alignment for Tile Farm Academy
Tile Farm Academy is a supplemental daily math routine designed to strengthen number sense, fluency, reasoning, visual modeling, mathematical communication, algebra readiness, and creative problem-solving alongside the curriculum schools already use.
The alignment below shows how Tile Farm supports key Grades 6–8 mathematical domains connected to the Common Core State Standards. Tile Farm is not intended to replace a full core curriculum. Instead, it gives students repeated, joyful opportunities to strengthen the foundational ideas, flexible strategies, and habits of mind that make middle school mathematics more meaningful, accessible, and lasting.
By middle school, many students have already developed a complicated relationship with math. Some students see mathematics as stressful, abstract, or disconnected from how they think. Tile Farm helps students rebuild confidence while strengthening the number sense, fluency, reasoning, and algebraic thinking they need for grade-level mathematics, high school math, and more advanced learning.
Ratios and Proportional Relationships
Tile Farm Academy supports proportional reasoning by helping students connect multiplication, division, fractions, decimals, percentages, rates, scaling, and equivalent relationships. Through Daily Digits, Tile Talk, and Number Portraits, students encounter ratios and proportional situations as meaningful relationships that can be represented visually, numerically, verbally, and symbolically. Tile Farm helps students develop the flexible number sense needed to reason about proportional relationships with confidence.
Grade 6 Ratios and Proportional Relationships Standards Supported by Tile Farm Academy:
6.RP.A.1
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.A.2
Understand the concept of a unit rate associated with a ratio.
6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems.
6.RP.A.3.a
Make tables of equivalent ratios, find missing values, and plot pairs of values.
6.RP.A.3.b
Solve unit rate problems.
6.RP.A.3.c
Find a percent of a quantity as a rate per 100 and solve problems involving parts, wholes, and percents.
6.RP.A.3.d
Use ratio reasoning to convert measurement units.
Grade 7 Ratios and Proportional Relationships Standards Supported by Tile Farm Academy:
7.RP.A.1
Compute unit rates associated with ratios of fractions.
7.RP.A.2
Recognize and represent proportional relationships between quantities.
7.RP.A.2.a
Decide whether two quantities are in a proportional relationship.
7.RP.A.2.b
Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions.
7.RP.A.2.c
Represent proportional relationships by equations.
7.RP.A.2.d
Explain what a point on the graph of a proportional relationship means in terms of the situation.
7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems.
The Number System
Tile Farm supports number system understanding by helping students reason flexibly with whole numbers, fractions, decimals, percentages, positive and negative numbers, and rational numbers. Daily Digits helps students maintain fluency with core number concepts while extending their understanding to increasingly abstract middle school topics. Tile Talk and Number Portraits give students opportunities to represent, explain, compare, and justify numerical relationships in multiple ways.
Grade 6 The Number System Standards Supported by Tile Farm Academy:
6.NS.A.1
Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions.
6.NS.B.2
Fluently divide multi-digit numbers.
6.NS.B.3
Fluently add, subtract, multiply, and divide multi-digit decimals.
6.NS.B.4
Find greatest common factors and least common multiples, and use the distributive property to express sums.
6.NS.C.5
Understand positive and negative numbers as describing quantities in opposite directions or values.
6.NS.C.6
Understand a rational number as a point on the number line.
6.NS.C.6.a
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line.
6.NS.C.6.b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane.
6.NS.C.6.c
Find and position integers and other rational numbers on horizontal and vertical number line diagrams and coordinate planes.
6.NS.C.7
Understand ordering and absolute value of rational numbers.
6.NS.C.7.a
Interpret statements of inequality as statements about relative position on a number line.
6.NS.C.7.b
Write, interpret, and explain statements of order for rational numbers.
6.NS.C.7.c
Understand the absolute value of a rational number as its distance from 0.
6.NS.C.7.d
Distinguish comparisons of absolute value from statements about order.
6.NS.C.8
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
Grade 7 The Number System Standards Supported by Tile Farm Academy:
7.NS.A.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers.
7.NS.A.1.a
Describe situations in which opposite quantities combine to make 0.
7.NS.A.1.b
Understand addition of rational numbers on a number line.
7.NS.A.1.c
Understand subtraction of rational numbers as adding the additive inverse.
7.NS.A.1.d
Apply properties of operations as strategies to add and subtract rational numbers.
7.NS.A.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.NS.A.2.a
Understand rules for multiplying signed numbers.
7.NS.A.2.b
Understand division of integers and rational numbers.
7.NS.A.2.c
Apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.A.2.d
Convert rational numbers to decimals using long division.
7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.
Grade 8 The Number System Standards Supported by Tile Farm Academy:
8.NS.A.1
Know that numbers that are not rational are called irrational and understand decimal expansions of rational numbers.
8.NS.A.2
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them on a number line, and estimate their values.
Expressions and Equations
Tile Farm Academy supports expressions and equations by helping students understand symbols as meaningful representations of numerical relationships. Students practice evaluating expressions, reasoning about equivalence, using properties of operations, solving problems with unknown values, and making connections between arithmetic and algebra. Tile Farm helps students see algebra not as a separate subject, but as a natural extension of the structure and relationships they have been building through number sense and visual reasoning.
Grade 6 Expressions and Equations Standards Supported by Tile Farm Academy:
6.EE.A.1
Write and evaluate numerical expressions involving whole-number exponents.
6.EE.A.2
Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.A.2.a
Write expressions that record operations with numbers and letters.
6.EE.A.2.b
Identify parts of an expression using mathematical terms.
6.EE.A.2.c
Evaluate expressions at specific values of their variables.
6.EE.A.3
Apply properties of operations to generate equivalent expressions.
6.EE.A.4
Identify when two expressions are equivalent.
6.EE.B.5
Understand solving an equation or inequality as answering which values make it true.
6.EE.B.6
Use variables to represent numbers and write expressions when solving problems.
6.EE.B.7
Solve real-world and mathematical problems by writing and solving equations.
6.EE.B.8
Write an inequality to represent a constraint or condition and recognize that inequalities have infinitely many solutions.
6.EE.C.9
Use variables to represent two quantities that change in relationship to one another.
Grade 7 Expressions and Equations Standards Supported by Tile Farm Academy:
7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions.
7.EE.A.2
Understand that rewriting an expression in different forms can reveal different information about a problem.
7.EE.B.3
Solve multi-step real-world and mathematical problems using positive and negative rational numbers.
7.EE.B.4
Use variables to represent quantities in real-world or mathematical problems and construct equations and inequalities to solve problems.
7.EE.B.4.a
Solve word problems leading to equations of the form px + q = r and p(x + q) = r.
7.EE.B.4.b
Solve word problems leading to inequalities and graph the solution set.
Grade 8 Expressions and Equations Standards Supported by Tile Farm Academy:
8.EE.A.1
Know and apply the properties of integer exponents.
8.EE.A.2
Use square root and cube root symbols to represent solutions to equations.
8.EE.A.3
Use numbers expressed in scientific notation to estimate very large or very small quantities.
8.EE.A.4
Perform operations with numbers expressed in scientific notation.
8.EE.B.5
Graph proportional relationships and interpret the unit rate as the slope of the graph.
8.EE.B.6
Use similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line.
8.EE.C.7
Solve linear equations in one variable.
8.EE.C.7.a
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
8.EE.C.7.b
Solve linear equations with rational number coefficients.
8.EE.C.8
Analyze and solve pairs of simultaneous linear equations.
Functions
Tile Farm supports early function thinking by helping students recognize patterns, relationships, inputs and outputs, and rules that connect quantities. While Tile Farm’s strongest middle school focus is number sense and algebra readiness, many activities support the habits of mind students need to understand functions: noticing regularity, identifying structure, representing relationships, and explaining how one quantity changes in relation to another.
Grade 8 Functions Standards Supported by Tile Farm Academy:
8.F.A.1
Understand that a function is a rule that assigns to each input exactly one output.
8.F.A.2
Compare properties of two functions represented in different ways.
8.F.A.3
Interpret the equation y = mx + b as defining a linear function.
8.F.B.4
Construct a function to model a linear relationship between two quantities.
8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph.
Geometry
Tile Farm is inherently geometrical and supports geometry through visual composition and decomposition, spatial reasoning, symmetry, patterning, transformation, measurement, coordinate reasoning, and development of geometric vocabulary. In Number Portraits especially, students use shapes and digital manipulatives to build, arrange, transform, and describe mathematical ideas. Students learn that shapes can be combined, broken apart, compared, rotated, reflected, repeated, scaled, classified, and used as tools for representing number relationships.
Grade 6 Geometry Standards Supported by Tile Farm Academy:
6.G.A.1
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing and decomposing shapes.
6.G.A.2
Find the volume of a right rectangular prism with fractional edge lengths.
6.G.A.3
Draw polygons in the coordinate plane given coordinates for the vertices.
6.G.A.4
Represent three-dimensional figures using nets and use nets to find surface area.
Grade 7 Geometry Standards Supported by Tile Farm Academy:
7.G.A.1
Solve problems involving scale drawings of geometric figures.
7.G.A.2
Draw geometric shapes with given conditions.
7.G.A.3
Describe two-dimensional figures that result from slicing three-dimensional figures.
7.G.B.4
Know formulas for the area and circumference of a circle and use them to solve problems.
7.G.B.5
Use facts about supplementary, complementary, vertical, and adjacent angles to solve problems.
7.G.B.6
Solve real-world and mathematical problems involving area, volume, and surface area.
Grade 8 Geometry Standards Supported by Tile Farm Academy:
8.G.A.1
Verify experimentally the properties of rotations, reflections, and translations.
8.G.A.2
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by rotations, reflections, and translations.
8.G.A.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.A.4
Understand that a two-dimensional figure is similar to another if the second can be obtained by rotations, reflections, translations, and dilations.
8.G.A.5
Use informal arguments to establish facts about angles.
8.G.B.6
Explain a proof of the Pythagorean Theorem and its converse.
8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles.
8.G.B.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
8.G.C.9
Know and apply formulas for the volumes of cones, cylinders, and spheres.
Statistics and Probability
Tile Farm supports statistics and probability through mathematical discussion, data interpretation, visual representation, comparison, pattern recognition, and reasoning about quantities in context. While Tile Farm’s deepest emphasis is number sense, fluency, and algebra readiness, many activities invite students to interpret visual information, organize mathematical observations, notice relationships, and explain patterns in data-like situations.
Grade 6 Statistics and Probability Standards Supported by Tile Farm Academy:
6.SP.A.1
Recognize a statistical question as one that anticipates variability in data.
6.SP.A.2
Understand that a set of data has a distribution that can be described by its center, spread, and overall shape.
6.SP.A.3
Recognize that a measure of center summarizes all values with a single number, while a measure of variation describes how values vary.
6.SP.B.4
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5
Summarize numerical data sets in relation to their context.
Grade 7 Statistics and Probability Standards Supported by Tile Farm Academy:
7.SP.A.1
Understand that statistics can be used to gain information about a population by examining a sample.
7.SP.A.2
Use data from a random sample to draw inferences about a population.
7.SP.B.3
Compare two data distributions using measures of center and variability.
7.SP.B.4
Use measures of center and variability to draw comparative inferences.
7.SP.C.5
Understand that probability is a number between 0 and 1 that expresses the likelihood of an event.
7.SP.C.6
Approximate probability by collecting data and observing long-run relative frequency.
7.SP.C.7
Develop a probability model and use it to find probabilities of events.
7.SP.C.8
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Grade 8 Statistics and Probability Standards Supported by Tile Farm Academy:
8.SP.A.1
Construct and interpret scatter plots for bivariate measurement data.
8.SP.A.2
Know that straight lines are widely used to model relationships between two quantitative variables.
8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data.
8.SP.A.4
Understand that patterns of association can also be seen in bivariate categorical data.
Standards for Mathematical Practice in Grades 6–8
Tile Farm also supports the Standards for Mathematical Practice in Grades 6–8 by giving students frequent opportunities to reason, model, explain, create, revise, and look for structure in mathematical situations.
MP1. Make sense of problems and persevere in solving them
Students work through visual and numerical challenges that encourage persistence, strategy testing, revision, and problem-solving stamina, especially as mathematics becomes more abstract.
MP2. Reason abstractly and quantitatively
Students connect quantities, symbols, diagrams, visual models, expressions, equations, and explanations as they move between concrete, visual, numerical, and abstract representations.
MP3. Construct viable arguments and critique the reasoning of others
Tile Talk and classroom discussion invite students to explain strategies, compare approaches, analyze mistakes, justify conclusions, and respond to the reasoning of classmates.
MP4. Model with mathematics
Number Portraits and visual routines help students represent mathematical relationships using quantities, shapes, patterns, diagrams, expressions, equations, and digital manipulatives.
MP5. Use appropriate tools strategically
Students choose from different visual tools and representations, learning that different tools can reveal different mathematical relationships and support different kinds of reasoning.
MP6. Attend to precision
Students calculate carefully, use mathematical vocabulary, label representations, and communicate strategies, relationships, expressions, and visual designs with increasing clarity and accuracy.
MP7. Look for and make use of structure
Tile Farm’s visual environments help students notice structure in number systems, factors, multiples, proportional relationships, expressions, equations, functions, geometry, symmetry, transformations, and patterns.
MP8. Look for and express regularity in repeated reasoning
Students reuse familiar structures and strategies across activities, helping them move from solving individual problems toward recognizing broader mathematical patterns, generalizations, and algebraic relationships.
Summary
Across Grades 6–8, Tile Farm Academy supports the development of strong middle school mathematical foundations: number sense, rational number reasoning, proportional relationships, expressions, equations, functions, geometry, statistics, mathematical modeling, explanation, and algebra readiness.
Most importantly, Tile Farm helps students experience mathematics as something joyful, creative, and deeply understandable—something they can see, build, discuss, and explore. Through playful daily routines, visual problem-solving, math talk, and creative work like Number Portraits, students develop not only standards-based skills, but also the confidence, curiosity, perseverance, and flexible thinking they need for success in middle school, high school, and beyond.