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Mind and Soul. Better together.
Grades 5-8

5-8 Math

 
The Hillel Day School math program develops, creative, life-long, confident and independent learners whose critical thinking foundation and communication skills prepare them to analyze and solve problems in real-world experiences. The HDS staff will work collaboratively with parents and students to differentiate instruction while providing a challenging, integrated curriculum that supports Hillel’s core Jewish values and maintains high standards so each student reaches his/her full potential.


 

 
 

List of 4 items.

  • Fifth Grade

    In fifth grade, the primary focus of the curriculum is:
    • Understand the relationship between place values (place value to the left is 10 times as large as the place value to the right), and be able to compare and order numbers to the thousandths. Read and write decimal numbers to the thousandths in standard form, word form and expanded form. Understand place value to round numbers to any place.
    • Add, subtract, multiply and divide multi-digit problems fluently. Students can work with decimals to the hundredths place.
    • Add and subtract fractions with unlike denominators, multiply simple fractions and divide fractions by whole numbers or divide whole numbers by simple fractions.
    • Understand that volume represents the three-dimensional space. Calculate volume for a right rectangular prism, including composed figures and select the appropriate units.
  • Sixth Grade

    There are four core goals for sixth grade:
    • Connect ratio and rate to whole number multiplication and division and use concepts of ratio and rate to solve problems
    • Divide fractions and extend understanding of numbers to rational numbers, including negative numbers
    • Write, interpret and use expressions and equations
    • Develop understanding of statistical thinking
     
  • Seventh Grade

    In seventh grade, the primary focuses of the curriculum are:
    • Manipulate and solve one-variable equations, including equations that apply the distributive property and that have variables on both sides of the equation
    • Add, subtract, multiply and divide rational numbers (integers, fractions, and decimals)
    • Understand and recognize linear relationships. Students must be able to write a linear model for a word problem and graph linear equations and inequalities on the coordinate plane using a table of values, slope and intercept or intercepts alone. Students must also understand the relationship between linear growth, slope and direct variation.
    • Understand proportional relationships and apply the properties of proportions to application problems, including percent problems
    • Know and apply the formulas for area, perimeter and volume of circles, trapezoids, parallelograms and triangles
     
  • Eighth Grade

    Hillel's math program is designed to address the wide range of student needs in our school community. In Eighth grade, students are placed in a math course to enhance skills at an appropriate challenge level. Course offerings include Eighth Grade Math, Algebra 1, and Geometry.

    In Grade 8, instructional time focuses on three critical areas: (1) formulating and reasoning about expressions and equations, including analyzing data that represent direct variation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.

    Algebra 1 consists of three critical units:
    Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and use them to solve problems. Students also apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations. Students also use regression techniques to describe the approximate linear relationship between quantities.
     
    Students learn function notation and develop the concepts of domain and range. They explore many examples of functions, including sequences; they interpret functions given graphically, numerically, symbolically, and verbally, and translate between representations. Students study exponential functions and compare and contrast linear and exponential functions, distinguishing between additive and multiplicative change. Students investigate systems of equations and inequalities.
     
    Students analyze the structure in and learn to create quadratic and exponential expressions. They create and solve equations, inequalities, and systems of equations involving quadratic expressions. Additionally, students compare the key characteristics of quadratic functions to those of linear and exponential functions.
     
    Geometry consists of five areas of study:
     
    Students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They use triangle congruence as a familiar foundation for the development of formal proof. Students prove theorems—using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They apply reasoning to complete geometric constructions and explain why they work.
     
    Students identify criteria for similarity of triangles, use similarity to solve problems, and apply similarity in right triangles to understand right triangle trigonometry, with particular attention to special right triangles and the Pythagorean Theorem. Students develop the Laws of Sine and Cosine in order to find missing measures of general (not necessarily right) triangles, building on students’ work with quadratic equations done in the first course. They are able to distinguish whether three given measures (angles or sides) define 0, 1, 2, or infinitely many triangles.
     
    Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line.
     
    Students use a rectangular coordinate system to verify geometric relationships, including properties of special triangles and quadrilaterals and slopes of parallel and perpendicular lines, which relates back to work done in the first course.
     
    Students prove basic theorems about circles and study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students use the distance formula to write the equation of a circle when given the radius and the coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane, and apply techniques for solving quadratic equations.
Hillel's math program is designed to address the wide range of student needs in our school community. Students who are identified as having exceptional math aptitude have the opportunity to participate in the Math Trailblazers program. With an average class size of five students, the program is designed to meet the needs of the highly capable learner by not only providing instruction at an appropriate pace but also enriching and deepening understanding beyond the age/grade level expectations. Graduates of the Math Trailblazers program complete their high school geometry course before leaving Hillel at the end of eighth grade. Students also have the benefit of a support staff that works with parents and teachers to develop personal goals to allow all students to grow and succeed in a rigorous and challenging curriculum.
Critical Thinking חשיבה ביקורתית
Creativity יצירתיות
COLLABORATION שיתוף פעולה
COMMUNICATION תיקשורת
CHARACTER אישיות
COMMUNITY קהילה
CORE JEWISH VALUES ערכים יהודיים עיקריים
Welcome to Hillel Day School of Metropolitan Detroit, a vibrant community Jewish day school filled with joy, rooted in core Jewish values, committed to halakhah, and devoted to academic excellence. Our families are diverse in their beliefs, affiliations and observances; we work together to create a welcoming community based upon mutual respect and shared values.
Early Childhood Center, Ages 2-5 | Day School, Grades K-8 | 248-851-3220 | 32200 Middlebelt Rd. | Farmington Hills, MI 48334