# Math Curriculum

We rely on materials from *Investigations* to deliver our math program in kindergarten through Grade 4 and use materials from *Connected Math 3* (CMP3) to teach the content in Grades 5 through 8. Additional information about each program can be found at the links below.

##### Math Vision Statement

The mathematics program in Grades K–8 at Milton Academy is guided by the following goals and principles.

**Goals:**

- Help students develop the knowledge, skills, and confidence to use mathematics as a tool for solving problems that occur within the confines of math class and beyond.
- Prepare students for success in each successive stage of their educations, including secondary mathematics.

**Principles:**

- Mathematical understanding is ongoing and develops when a learner reflects on prior knowledge, forges new connections between ideas, and communicates his or her thinking.
- Students are curious and natural problem solvers; they actively participate in their own learning and recognize that mistakes are part of the learning process.
- Mathematics curricula should feature challenging problems that promote reflection and communication. Tasks should be meaningful and relevant to the students and motivate them to link mathematical skills to their underlying concepts, formulate strategies, and justify their solutions. Individual lessons within curriculum units should be connected in ways that help students consider ideas from multiple perspectives and make sense of important mathematical relationships.
- Teachers develop students’ mathematical understanding by facilitating whole-class discussions, providing relevant information, sharing mathematical conventions, and suggesting alternate methods.
- Discussions are a critical and core element of math class as they provide students with valuable opportunities to explain particular methods, analyze errors, and compare and contrast different approaches to the same problem. All students have the right to have their ideas heard and considered and are expected to actively respond to the reasoning of others.

##### Our Math Teachers

##### Our Math Program

### Focal Points by Grade Level

##### Kindergarten

- Develop strategies for counting a set of objects.
^{1} - Decompose small numbers into parts.
^{2} - Model and develop strategies for solving addition and subtraction problems with small numbers.
^{3,4} - Compare the lengths of two objects.
^{2}

^{1}See the following link for a progression of ideas related to counting:

https://investigations.terc.edu/library/curric-math/counting_2ed.pdf

^{2}See the following link for more information:

https://investigations.terc.edu/library/curric-gl/math_content_gk_2ed.pdf

^{3}See the following link for a classification scheme of addition and subtraction situations:

http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/

^{4}See the following link for a progression of ideas related to addition and subtraction:

https://investigations.terc.edu/library/curric-math/addsub_2ed.pdf

##### Grade 1

- Model and solve addition and subtraction problems with one- and two-digit numbers.
^{3,4} - Develop fluency with 2-addend combinations of ten.
^{5} - Count and keep track of two-digit amounts by counting by 1s and by groups (e.g., groups of 2s, 5s, and 10s).
^{6} - Use standard units to measure and describe lengths.
- Tell time to the nearest hour.
- Identify coins and their values.
- Find at least one equivalent relationship between coins (e.g., two nickels have the same value as one dime).
- Use mathematics vocabulary to name and describe 2D and 3D shapes.

^{3}See the following link for a classification scheme of addition and subtraction situations:

http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/

^{4}See the following link for a progression of ideas related to addition and subtraction:

https://investigations.terc.edu/library/curric-math/addsub_2ed.pdf

^{5}See the following link for more information on combinations of ten:

https://investigations.terc.edu/library/curric-gl/math_content_g1_2ed.pdf

^{6}See the following link for more information on counting by groups:

https://investigations.terc.edu/library/curric-math/placevalue_2ed.pdf

##### Grade 2

- Demonstrate fluency with addition combinations.
- Solve addition and subtraction story problems with unknowns in all three positions.
^{3,4} - Analyze the structure of 100 and how it is composed of equal groups.
^{6} - Make and test conjectures about adding even and odd numbers.
- Develop efficient methods for adding and subtracting numbers with totals to 100.
^{4} - Understand fractions as equal parts of a whole and as equal parts of a group.
^{7} - Tell time to the half hour and quarter hour.
- Find combinations of coins that equal $1.00.

^{3}See the following link for a classification scheme of addition and subtraction situations:

http://www.corestandards.org/Math/Content/mathematics-glossary/Table-1/

^{4}See the following link for a progression of ideas related to addition and subtraction:

https://investigations.terc.edu/library/curric-math/addsub_2ed.pdf

^{6}See the following link for more information on counting by groups:

https://investigations.terc.edu/library/curric-math/placevalue_2ed.pdf

^{7}See the following link for a progression of ideas related to fractions and rational numbers:

https://investigations.terc.edu/library/curric-math/rationalnumbers_2ed.pdf

##### Grade 3

- Compute and estimate the answers to addition and subtraction problems with three-digit numbers.
- Understand multiplication as combining equal groups.
^{8,9} - Use the inverse relationship between multiplication and division to solve problems.
^{8,9} - Use arrays to find factors of two-digit numbers.
^{8,9} - Use knowledge of the factors of 100 to find factors of multiples of 100.
^{8,9} - Use representations to combine fractions (halves, fourths, eighths, thirds and sixths).
^{7} - Tell time to the nearest minute.

^{7}See the following link for a progression of ideas related to fractions and rational numbers:

https://investigations.terc.edu/library/curric-math/rationalnumbers_2ed.pdf

^{8}See the following link for a progression of ideas related to multiplication and division:

https://investigations.terc.edu/library/curric-math/multdiv_2ed.pdf

^{9}See the following link for a classification scheme of multiplication and division situations:

http://www.corestandards.org/Math/Content/mathematics-glossary/Table-2/

##### Grade 4

- Understand multiplication and division in terms of arrays and comparison.
^{8,9} - Demonstrate fluency with multiplication facts through 10 x 10.
^{10} - Compute and estimate the answers to multiplication and division problems with two- and three-digit numbers.
^{8,9} - Order and compare fractions, decimals, and percents.
^{7} - Add and subtract fractions and decimals.
^{7} - Solve problems about the surface area and volume of 3D shapes.

^{7}See the following link for a progression of ideas related to fractions and rational numbers:

https://investigations.terc.edu/library/curric-math/rationalnumbers_2ed.pdf

^{8}See the following link for a progression of ideas related to multiplication and division:

https://investigations.terc.edu/library/curric-math/multdiv_2ed.pdf

^{9}See the following link for a classification scheme of multiplication and division situations:

http://www.corestandards.org/Math/Content/mathematics-glossary/Table-2/

^{10}See the following link for a helpful article on multiplication fact fluency:

https://www.youcubed.org/fluency-without-fear/

##### Grade 5

- Understand the relationships between the prime factorization and factors and multiples of that number.
^{11} - Multiply and divide fractions and decimals.
^{12} - Compute and estimate the results of arithmetic operations involving fractions and decimals.
^{12} - Understand ratios as comparisons of two numbers.
^{13} - Locate fractions and decimals on a number line.
^{13} - Build and use rate tables to solve problems about ratios.
^{13} - Solve problems about percents including problems about tax, tips, discounts, and percent change.
^{13} - Solve problems about measures of circles and cylinders.

^{11}For more information, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-6/

and scroll down to the unit, “Prime Time.”

^{12}For more information, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-6/

and scroll down to the unit, “Let’s Be Rational.”

^{13}For more information on fraction operations, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-6/

and scroll down to the unit, “Comparing Bits and Pieces.”

##### Grade 6

- Explore problem situations involving variables and relationships.
^{15} - Represent situations that change over time with tables, graphs, and equations.
^{15} - Develop strategies for using similar figures to solve problems.
^{16} - Add, subtract, multiply, and divide positive and negative rational numbers.
^{17} - Develop and use strategies for solving problems that require proportional reasoning.
^{18} - Set up and solve proportions that arise from real-world applications.
^{18} - Understand and apply the Pythagorean Theorem.
^{19}

^{15}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-6/

and scroll down to the unit, “Variables and Patterns.”

^{16}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-7/

and scroll down to the unit, “Stretching and Shrinking.”

^{17}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-7/

and scroll down to the unit, “Accentuate the Negative.”

^{18}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-7/

and scroll down to “Comparing and Scaling.”

^{19}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Looking for Pythagorus.”

##### Grade 7

- Explore and develop probability models by identifying possible outcomes and analyzing probabilities.
^{20} - Determine the expected value of a probability situation.
^{20} - Represent linear relationships with tables, graphs, and equations.
^{21} - Connect the slope of a line to the rate of change between two variables that have a linear relationship.
^{21} - Solve linear equations using symbolic methods, tables, and graphs.
^{21} - Compare inverse variation relationships with linear relationships.
^{22} - Represent an exponential function with a table, graph, or equation.
^{23} - Solve problems about exponential growth and exponential decay from a variety of real-life contexts including science and business.
^{23} - Identify the pattern of change between two variable that represent a quadratic function in a situation, table, graph, or equation.
^{24} - Predict the x- and y-intercepts and line of symmetry of a parabola from an equation, graph, or table of the related quadratic function.
^{24} - Write and interpret a quadratic equation.
^{24}

^{20}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-7/

and scroll down to “What Do You Expect?”

^{21}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-7/

and scroll down to “Moving Straight Ahead.”

^{22}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Thinking with Mathematical Models.”

^{23}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Growing, Growing, Growing.”

^{24}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Frogs, Fleas, and Painted Cubes.”

##### Grade 8

- Use algebra to solve problems about irrational numbers and repeating decimals.
^{25} - Describe the special properties of a 30-60-90 triangle.
^{25} - Represent and solve problems about linear relationships in standard (Ax + By = C) form.
^{26} - Solve a system of two linear equations using symbolic methods.
^{26} - Generalize about the characteristics of systems that have zero, one, or no solutions.
^{26} - Solve linear inequalities and systems of inequalities.
^{26} - Use function notations to describe and operate with functions.
^{27} - Identify, analyze, and solve problems related to arithmetic and geometric sequences.
^{27} - Sketch the graphs of quadratic functions written in vertex form.
^{27} - Solve quadratic equations by factoring, “complete the square,” and the Quadratic Formula.
^{27} - Use the form of a quadratic equation to predict whether it has 0, 1, or 2 unique, real solutions.
^{27} - Display numerical data in dot plots, histograms, and box plots.
^{28} - Use scatter plots and correlation coefficients to describe patterns of association in pairs of variables.
^{28} - Distinguish and identify measures of center (e.g., mean and median.)
^{28} - Distinguish and identify measures of spread (e.g., range, interquartile range, standard deviation.)
^{28} - Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more data sets.
^{28}

^{25}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Looking for Pythagorus.”

^{26}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “It’s in the System.”

^{27}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Function Junction.”

^{28}For more information on this topic, visit

https://connectedmath.msu.edu/families/helping-with-math/cmp3-grade-8/

and scroll down to “Thinking with Mathematical Models” and “Samples and Populations.”