SPARHAWK MATH
Young children measure their world. Using standard and non-standard tools, they measure all sorts of attributes such as length, perimeter, height, area, volume, and weight.
Evaluating and Teaching Each Individual Child
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Young children naturally vary more at this age than at any other in terms of attention- span, focus, and developmental readiness for certain understandings. For these reasons, we ask that parents read the detailed information for their child’s age-group as well as that for the age-groups above and below theirs. It is perfectly natural for children to move fluidly between age-group expectations with achievements noted in younger and older expectations. We respect this naturally wide variability in developmental pace.
blossoming to come, and what may not reveal itself as a strength early-on may be chief among them later.
Children also vary in terms of innate ability in subject-areas, however, this cannot be reliably assessed at such an early stage of development. Our young children have years and years of
At Sparhawk, we choose to use Saxon’s Math textbooks, as they are distinctive for many reasons. These textbooks are particularly readable for young children and are carefully designed to teach
Math textbooks are ordered after an assessment of each student’s skills. While most students place at grade-level, some accelerate and are placed at the level that best suits their needs. Although math placement is individualized, students are expected to participate at least at grade-level. (Students unable to maintain grade-level performance are referred for tutoring.)
productive thought patterns. In addition, there is an incremental development of concepts leading to the gradual explanation of major topics over time. Each conceptual component is introduced and practiced at one level for a period of time, and then another lesson on the concept is presented at a higher cognitive level. As the problems become familiar, students can look at a problem, recognize it by type, and apply relevant strategies. When concept recognition and skill application become automated, the student is freed from the lower-level mechanics of the problem, and the student can consider the problem at a higher cognitive level.
Children formulate questions and express answers in spoken and written words and using standard math notation.
Elementary Foundational Skills PreK- 2nd • • • • • • • • • • • • •
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Young children measure their world. Using standard and non-standard tools, they measure all sorts of attributes such as length, perimeter, height, area, volume, and weight. Vocabulary is continuously introduced and practiced, and they love "big" words like circumference and hypothesis. They group things and count them and add and subtract from their groups. They formulate questions and express answers in spoken and written words and using standard math notation. Balance-scales create tangible equations that illustrate the concept of equivalency. They experience proportion and analyze relationships through countless activities, interactions, and observations. They engage in reflective discourse and make inferences and evaluate their predictions using data they collect. They represent their learning using manipulatives and pictures, and as readiness allows, abstract explanations are encouraged. They learn about two-dimensional shapes and three-dimensional objects and all the relationships between and among them. They create, duplicate, and extend sequences and other patterns. They learn to recognize and write numbers and demonstrate one-to-one correspondence as they count ever-higher. They play games with math materials that give meaning to the concept of place value. Our base-ten, place-value system is so important that it is introduced often and reviewed often and understanding grows over time. Number sense develops with experience and instruction.
Sparhawk Curriculum Overview by Grade Pre-K Math The Foundational Skills - PreK-2 are the curriculum goals for preschoolers. Students work toward these goals and typically achieve them across the early grades. Mastery requires practice. If an individual student shows readiness for more, they are given more. Because children in preschool through second grade are largely concrete thinkers, our experiential and developmental approach enables them to begin building an understanding of mathematics and the kinds of problems it used to solve. Ultimately, it is a symbolic language of pure abstraction with amazing practical applications. But for now, hands-on is how this age group learns math meaningfully.
quarters; tells time to the hour; tells time to the half hour; understands use of calendar; knows days of the week; knows months of the year, measures using non-standard units; measures using metric and customary units; knows how to use a balance scale; can read a thermometer; identifies and extends patterns; sorts and classifies; uses tallies; uses lists and graphs.
First-Grade Math
The Foundational Skills - PreK-2 described continue to be important in first grade while knowledge and skills grow. The following identifies goals for this specific grade level. If an individual student shows readiness for more, they are given more. Children will skip-count forward and backwards by 1s, 2s, 5s, and 10s; compare and order numbers; identify Kindergarten Math and extend patterns; solve routine and non-routing The Foundational Skills - Prek-2 continue to be problems; work toward mastery of basic addition facts important in kindergarten while knowledge and skills and most of the basic subtraction facts; add two-digit grow. The following identifies goals for this specific grade numbers with and without regrouping; begin learning level. If an individual student shows readiness for more, multiplication through sets; taking apart numbers into 10s they are given more. and 1s and 100s; word-problem division; picture and Counts forward 1-100; recognizes numerals 1-100; name fractions; fractional equivalencies (1/2 = 2/4); writes numerals 1-100; skip counts by 10s; adds sums to simple algebra with addition and subtraction of one and 10; adds sums beyond 10; adds two-digit numbers without two digit numbers; measure using inches, feet, and regrouping; solves word problems; identifies even and odd centimeters; compare volume, mass, and areas; tell time numbers; identifies greater than and less than; estimates; to the half-hour; count pennies, nickels, dimes, and uses and identifies ordinal number; counts with materials quarters; identify and draw polygons; identify perimeter, by ones; counts with materials by tens; recognizes coins; circumference identify geometric solids; tally; create, read, names value of coins; adds dimes and pennies mixed; and write observations from real graphs, pictographs, and addition of money, divides shapes into halves and bar graphs.
Young children measure their world. Using standard and non-standard tools, they measure all sorts of attributes such as length, perimeter, height, area, volume, and weight.
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Second-Grade Math
Children experience proportion and analyze relationships through countless activities, interactions, and observations.
Children will skip-count by 1s, 2s, 3s, 4s, 5s, 10s, 25s, and 100s; compare and order numbers; identity ordinal position to tenth; identify sorting and patterning rules; solve routine and nonrouting problems; work toward mastery of basic addition and subtraction facts; master multiplication facts to 5; add and subtract two digit numbers; picture and name fractions; measure to nearest halfinch, centimeter, and foot; compare volume; compare and measure mass; measure perimeter quarters; identify geometric solids; identify lines or symmetry; identify angles; tally; create, read, and write observations from real graphs, pictographs, bar graphs, Venn diagrams, and line graphs.
Third-Grade Math Children will skip-count by whole numbers; compare and order numbers; identify and complete patterns; solve routine and non-routine problems; know basic addition, subtraction, multiplication, and division facts; add and subtract multi-digit numbers; multiply a multi-digit number by a singledigit number; divide by single-digit divisors, add positive and negative numbers; picture, name, and order fractions; add and subtract fractions with common denominators; measure to the nearest quarter inch, millimeter, foot, and yard; identify the volume of standard containers; compare and measure mass, measure perimeter and area; tell time to the minute; determine elapsed time; count money; make change for a dollar; identify angles; identify lines of symmetry; identify function rules; graph ordered pairs on a coordinate graph; tally; create, read, and write observations from real graphs, pictographs, bar graphs, Venn diagrams, and line graphs. Children will use mathematics in real-life situations. They will use simulations and games to learn and practice new concepts, and social studies and science curriculum connections will be stressed.
Fourth-Grade Math Sparhawk's fourth grade math contains a thorough review of concepts and procedures related to whole number operations, including single-digit multiplication and division. Word
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problems are incrementally developed and practiced throughout the year. Students receive a balanced, integrated mathematics program that includes continual development of whole number concepts, whole number computation, mental math, problem-solving, patterns and functions, measurement, geometry, fractions, decimals, statistics, and probability. Geometric concepts are reinforced throughout: classifying triangles, quadrilaterals, and other polygons, computing the area and perimeter of planar geometric figures, and the volume and surface areas of geometric solids.
concepts are reinforced throughout: classifying triangles, quadrilaterals, and other polygons, computing the area and perimeter of planar geometric figures, and the volume and surface area of geometric solids.
Real Life Applications
Students at Sparhawk have the opportunity to apply their math skills to real life situations. The fourth-and fifthgrade students run their own pizza business. Each Friday they transform the Lower School lobby into a pizza parlor as they set up shop in preparation for serving pizza and drinks to the entire lower school for lunch. The students are Fifth-Grade Math Sparhawk's fifth grade math reviews in charge of all aspects of the business and expands all of the mathematical from pricing, ordering, serving, and content introduced in earlier grades. The cleaning up to depositing their profits in emphasis on problem solving continues the bank. as students are called upon to apply In addition to the pizza business, mathematical tools and techniques to real every February, the 3rd and 4th-graders mathematical situations through word ready themselves to take over the problems. Fifth grade level math includes Sparhawk Post Office by taking part in a whole number concepts and unit on money. Topics of study include: computation, mental computation, counting, grouping, recognizing values patterns and function, measurement, and and making change for a dollar bill. As statistics and probability. Work with Valentines Day approaches students have fractions, mixed numbers, decimals, and the opportunity to apply what they have geometry is significantly expanded. learned to the daily operation of the Students are introduced to percentages Sparhawk Post Office, which serves all and negative numbers. Geometric the students in the Lower School.