Research-based curriculum and alignment to Common Core
Sokikom's research-based curriculum offers students an effective learning environment using social learning and adaptive instruction to develop a strong mathematical foundation. Our curriculum aligns with these Common Core standards.
First Grade Content:
| Operations and Algebraic Thinking |
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| Understand subtraction as an unknown-addend problem. |
| Relate counting to addition. |
| Add and subtract within 20. |
| Demonstrating fluency for addition and subtraction within 10. |
| Use strategies such as counting on and using the relationship between addition and subtraction in order to complete simple computation. |
| Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. |
| Number and Operations in Base Ten |
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| Understand that the two digits of a two-digit number represent amounts of tens and ones. |
| Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10. |
| Measurement and Data |
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| Tell and write time in hours and half-hours using analog and digital clocks. |
| Express the length of an object as a whole number of length units. |
| Order three objects by length. |
| Understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. |
| Geometry |
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| Distinguish between defining attributes, such as triangles are closed and three-sided, versus non-defining attributes, including color, orientation, overall size. |
| Build and draw shapes to possess defining attributes. |
| Compose two-dimensional or three-dimensional shapes to create a composite shape and compose new shapes from the composite shape. |
| Understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. |
Second Grade Content:
| Operations and Algebraic Thinking |
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| Fluently add and subtract within 20 using mental strategies. |
| Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. |
| Number and Operations in Base Ten |
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| Count within 1000; skip-count by 5s, 10s, and 100s. |
| Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones. |
| Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. |
| Add up to four two-digit numbers using strategies based on place value and properties of operations. |
| Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. |
| Measurement and Data |
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| Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. |
| Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. |
| Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. |
| Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. |
| Geometry |
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| Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. |
| Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. |
Third Grade Content:
| Operations and Algebraic Thinking |
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| Determine the unknown whole number in a multiplication or division equation relating three whole numbers. |
| Apply properties of operations as strategies to multiply and divide. |
| Understand division as an unknown-factor problem. |
| Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division. |
| Identify arithmetic patterns (including patterns in the addition table or multiplication table). |
| Determine the unknown whole number in a multiplication or division equation relating three whole numbers. |
| Number and Operations in Base Ten |
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| Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. |
| Multiply one-digit whole numbers by multiples of 10 in the range 10–90. |
| Measurement and Data |
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| Measure masses of objects using standard units of grams (g) and kilograms (kg). |
| Add, subtract, and multiply to solve one-step word problems involving masses that are given in the same units. |
| Tell and write time to the nearest minute and measure time intervals in minutes. |
| Solve word problems involving addition and subtraction of time intervals in minutes. |
| Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. |
Recognize area as an attribute of plane figures and understand concepts of area measurement:
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| Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units). |
| Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, and finding an unknown side length. |
| Geometry |
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| Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). |
| Numbers & Operations- Fractions |
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| 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. |
Understand a fraction as a number on the number line; represent fractions on a number line diagram:
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Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size:
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Fourth Grade Content:
| Operations and Algebraic Thinking |
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| Generate a number or shape pattern that follows a given rule. |
| Number and Operations in Base Ten |
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| Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. |
| Fluently add and subtract multi-digit whole numbers using the standard algorithm. |
| Multiply a whole number of up to four digits by a one-digit whole number using strategies based on place value and the properties of operations. |
| Multiply two two-digit numbers using strategies based on place value and the properties of operations. |
| Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors. |
| Measurement and Data |
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| Know relative sizes of measurement units within one system of units within a single system of measurement and express measurements in a larger unit in terms of a smaller unit. |
| Use the four operations to solve word problems involving intervals of time, masses of objects, and money, including problems decimals, and problems. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. |
| Apply the area and perimeter formulas for rectangles in real world and mathematical problems. |
Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
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| Measure angles in whole-number degrees using a protractor. |
| Recognize angle measure as additive. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems. |
| Geometry |
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| Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. |
| Classify two-dimensional figures based on the presence or absence of angles of a specified size, parallel lines, or perpendicular lines. Recognize right triangles as a category and identify right triangles. |
| Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. |
| Numbers & Operations- Fractions |
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| Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. |
| Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. |
Understand a fraction a/b with a > 1 as a sum of fractions 1/b:
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| Understand decimal notation for fractions and compare decimal fractions by either using a number line diagram or visual fraction model. |
Fifth Grade Content:
| Operations and Algebraic Thinking |
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| Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. |
| Number and Operations in Base Ten |
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| Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. |
| Fluently multiply multi-digit whole numbers using the standard algorithm. |
| Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors. |
| Measurement and Data |
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| Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems. |
Recognize volume as an attribute of solid figures and understand concepts of volume measurement:
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| Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. |
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume:
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| Geometry |
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| Use a pair of perpendicular number lines, called axes, to define a coordinate system. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis. |
| Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation. |
| Understand that attributes belonging to a category of two dimensional figures also belong to all subcategories of that category. |
| Classify two-dimensional figures in a hierarchy based on properties. |
| Numbers & Operations- Fractions |
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| Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. |
Sixth Grade Content:
| Geometry |
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| Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes. |
| Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. |
| Draw polygons in the coordinate plane given coordinates for the vertices. Apply these techniques in the context of solving real-world and mathematical problems. |
| Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. |
| The Numbers System |
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| Fluently divide multi-digit numbers using the standard algorithm. |
| Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. |
| Interpret and compute quotients of fractions, e.g., by using visual fraction models to represent the problem. |
| Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. |
| Expressions & Equations |
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| Apply the properties of operations to generate equivalent expressions. |
| Evaluate numerical expressions involving whole-number exponents. |
| Identify parts of an expression using mathematical terms. |
