# Elementary School Grades 3, 4 & 5 Maths - Number Patterns and Sequences - Ages 8-11 eBook

This value was then divided by the EM for numerosity 5 for each child to yield a measure of the decrease in efficiency from small to large numerosities while accounting for individual differences in efficiency. The formula expresses that the greater the increase in the value of the CE index, the larger the size of this effect. Notice that the expected linear increases in EM for numerosities 5 to 8 are related to values of CE close to 1. So, individuals with larger CE are less efficient in counting. The CE values were distributed normally with a skew value of 2. The total score correct responses was calculated for Raven CPM.

Also, EMs of word and pseudoword reading were obtained using the median of RT divided by the proportion of hits in each case. A sheet with basic exercises of addition, subtraction and multiplication, including numbers from 1 to 9, were presented to the children in a combined form. Calculations requiring the use of the rules of 0 e.

The children were asked to make as many calculations as they could in 3 minutes following the numerical order of the columns on the sheet. Internal consistency reliability was. Two tests based on mathematics curriculum were designed for 4 th and 5 th grades, respectively. Each test consisted of four sets of exercises with time constriction by set: Set I. Numeration: Six problems dealing with writing numerals and numbers, rounding and determining successor and predecessor. Set II. Measurement: Six problems for converting magnitudes e.

Set III. Arithmetic: Twelve computational problems e. Word Problems that include four exercises e. How many kilometers will it cover in one hour? Both tests were constructed by selecting problem types representing a proportional sampling of the mathematics skills within the national curriculum. Coefficient alpha was. Children were presented with short passages formed by rows of contextually related words, ordered by reading difficulty; all words were printed in uppercase without any spaces or punctuation between the words e. Children were asked to draw a line between the boundaries of as many recognizable words as possible within 3 minutes e.

The passages became gradually more complex in content, vocabulary, and grammar embedded phrases, sequenced adjectives, affixes, etc. This is a test included in the SAL battery [ 31 ] was used to measure reading achievement. The children were asked to read a grade adjusted text. The text was presented in white, Arial size 12 letter, centered on a black background on the computer screen. After reading, the children were asked to respond true or false to ten propositions referring to the text by pressing the arrow keys left for True and right for False.

The children could not refer to the text for the entire duration of the comprehension task. The questions assessed both literal e. A score was given for each correct answer. The overall reading time and total comprehension scores were calculated. A measure was obtained from the Reading Comprehension test dividing the average reading time per decoded word by the comprehension score.

Tests corresponding to T 1 were administered in April to the children enrolled in 3rd and 4th grades. The assessment was conducted in a quiet and illuminated room within the school. Each child was evaluated individually in a single session that lasted from 20 to 30 min. When evaluating BNC, the child sat next to the experimenter in front of a computer. A Toshiba Satellite laptop P4 - M 1. Tests corresponding to T 2 were administered one year later, between April and May, while the children were in 4 th and 5 th grades.

The Reading Comprehension test was individually administered. All tests were administered individually to children who had moved to other schools. The means and standard deviations of all measures are shown in Table 1. Standard deviations are in parentheses. The expectation that children would subitize quantities up to 3, and count for 4 to 8 was supported by EM data. Because the assumption of sphericity was violated, the within-participants effect and interactions are reported using the Greenhouse—Geisser adjustment.

Means and standard errors of the EMs by numerosity and by grade can be found in Table 2. We found that the main effect of grade was nonsignificant but the main effect of numerosity was highly significant F 3. In addition, we did not find a significant Numerosity x Grade interaction. Differences were, however, significant for numerosities of four to eight. In previous studies the subitizing range had been variably defined, sometimes ranging to three [ 8 , 26 , 33 , 35 , 36 ] and sometimes to four [ 14 , 37 ]. As the current study involved children who might have a comparably restricted subitizing range, we define the subitizing range as the numerosities one to three.

### Dr John Kelliher (E-kitapları)

Numerosity four could not be clearly ascribed to either the subitizing or the counting range and was thus excluded from the statistical analysis. Furthermore, as previous studies e. Based on these results, the size of subitizing and counting effects were calculated to quantify individual differences as was described previously in the Method section. Next, an ANOVA was conducted using EM for each numerical distance three levels: distances 1—3 as the within-participants variable, and grade two levels: 3 rd - 4 th as the between-participants variable.

In this case, the sphericity assumption was confirmed. Mean and standard error of the EM for each numerical distance by grade are shown in Table 2. Finally, we did not find a significant interaction between Grade and Distance. Based on these results, the size of NDE was calculated to quantify individual differences in symbolic comparisons as was described in the Method section.

Although we are testing directional hypotheses, significance values of all correlational analyses come from a two-tailed distribution. As shown in Table 3 , a significant association occurred between all outcome measures R:. Intellectual ability was significantly correlated with the outcome measures, indicating that children who were in general better in nonverbal reasoning also showed better performance in reading and mathematics R:.

However, the numerical effect indexes were not significantly correlated among themselves or with intellectual ability. Figure 1 shows this significant association. Note that the children who exhibited a larger subitizing effect SE values close to zero showed, one year later, higher scores in mathematics fluency. Hierarchical regression analyses were conducted to investigate up to what extent the mechanisms involved in subitizing, counting and comparing numerical magnitudes explain unique variance in mathematics and reading achievement.

Predictor variables were entered in a fixed order to provide the most stringent test for the roles of variables predicting reading and mathematics skills after controlling for the effect of prior general cognitive skills. The constant order of entry was based on the outlined predictions and predictive correlations. In a complementary set of analyses, steps 6, 7 and 8 were switched to determine the specific contribution of NDE and CE in explaining variance over and above general predictors and the other numerical predictors.

The values of standardized beta coefficients, incremental R 2 and F obtained for all variables included in the models are shown in Table 4. Note that the total amount of the variance explained by general, reading and numerical factors in predicting Mathematics Fluency and Mathematic CBM were The hierarchical regression analyses showed that the size of SE was a domain-specific predictor of both mathematics outcomes assessed one year later.

In fact, after controlling for other variables, the size of SE significantly predicted 7. The size of CE explained a marginally significant amount of unique variance in fluency 5. Furthermore, the reading predictors did not explain additional variance of later mathematics skills after controlling for the effects of general cognitive skills. Complementary analyses were run to test the domain specificity of the numerical predictor variables. In this case, hierarchical regressions were run following the same procedure described above. Here, Reading Fluency and Reading Comprehension were defined as outcomes in separate prediction models statistical power.

As shown in Table 5 , the general cognitive, numerical and reading predictors explained Note that the numerical predictors did not significantly contribute to explaining individual variability in reading skills. However, the efficiency in lexical decoding explained a significant amount of unique variance found for Reading Fluency and Reading Comprehension 8.

Interestingly, the efficiency in phonological processing did not significantly contribute to explaining individual variability in later reading achievement. We first examined the associations of the numerical effects with contemporaneous cognitive and linguistic variables, as well as with mathematics and reading skills, and then we tested, with hierarchical regression analyzes, whether numerical effects predict academic skills such as mathematics and reading one year later, after controlling for the effects of other predictor variables.

The results showed that the size of SE in intermediate grades was a significant domain-specific predictor of mathematics fluency and also curricular mathematics achievement, but not reading skills, assessed at the end of elementary school. Furthermore, the size of CE also predicted fluency in calculation, although this association only approached significance.

This finding makes sense given that mathematics fluency and subitizing require quick recognition and combination of small magnitudes [ 19 ]. One possibility is that children having a strong foundation for subitizing and mapping the corresponding quantities are at an advantage in learning number facts.

This explanation is in agreement with the point of view of Gallistel and Gelman [ 38 ] who consider that subitizing involves the use of a fast preverbal estimation of numerosities and the mapping from the resulting magnitudes to number words in order to rapidly generate the number words for small numerosities. On the other hand, the retrieval of the number facts is mediated via the inverse mappings from verbal and written numbers to preverbal magnitudes and the use of these magnitudes to find the appropriate cells in the tabular arrangements of the answers.

This may explain the smaller subitizing range of children with mathematics disability found by Koontz and Berch [ 39 ]; it may also explain the common finding that children with mathematics disability have difficulties learning number facts [ 40 ]. It is noteworthy that the domain-specific relationship found for subitizing and fluency is generalized to other mathematical domains in which small numerosities are embedded.

In line with this result, Fuchs and colleagues [ 19 ] found that precise representations of small quantities was uniquely predictive of mathematics fluency and word-problem tasks that change, combine, compare and equalize numerical relationships. As highlighted in the Method section, one such common process used in both the enumeration task and the mathematics tasks, is the speed of processing.

Thus, it could be argued that the predictive value of the SE in later mathematics skills is simply due to both kinds of tasks being speeded. Moreover, our regression analysis demonstrated that the SE explained a significant amount of variance in mathematics outcomes after controlling individual differences in general processing speed. Previous longitudinal studies have found that processing small numerosities is closely related to early mathematics learning [ 8 , 41 , 42 ], confirming that subitizing and counting constitute domain-specific foundational skills on which the formally acquired mathematics knowledge is built.

This finding therefore encourages more empirical work to clarify the extent to which the Small Number System and mathematics knowledge are related [ 14 , 43 ]. Further research into this relationship that would examine a broader developmental age range in a longitudinal approach could reveal how subitizing modulates numerical symbolic acquisition from early to more advanced stages of mathematics knowledge above and beyond domain-general cognitive and linguistic mechanisms. On the other hand, it is known that the size of the subitizing effect decreases over developmental time [ 15 ].

However, it is unclear if this reduction simply reflects developmental changes in domain-general speed of processing and whether it is specific to numerical compared with nonnumerical stimuli. To examine these open questions, children at different ages and adults could be tested with numerical and nonnumerical subitizing tasks controlling for a measure of processing speed. Contrary to previous reports [ 21 , 44 ], we found that NDE did not account for a significant proportion of the variance for mathematics fluency and achievement in mathematics curriculum.

Since these studies included children younger than those recruited for the present study, a possible explanation to this is that the predictive value of NDE decreases in the course of mathematics acquisition. Several authors [ 45 , 46 ] reported that the NDE decreases from kindergarten to fourth grade, with minor changes occurring thereafter. In fact, Holloway and Ansari [ 21 ] found a significant correlation between NDE and mathematical competence in 6 year-old children but this association was not significant in 8 year-olds.

Additionally, in our study word and pseudoword decoding tests also failed to explain additional variance of mathematics fluency and other mathematics skills above and beyond general cognitive and numerical mechanisms. However, there is much support for the relationship between phonological awareness and mathematics achievement see [ 47 ]. The triple-code hypothesis [ 48 ] states that language itself is needed to construct concepts of exact numbers greater than four, and several authors [ 40 , 49 , 50 ] argue that phonological awareness reflects the ability to differentiate between meaningful segments of language and to manipulate them, and this should consequently facilitate the differentiation and manipulation of single words in the number word sequence.

However, some previous reports are in line with our finding; for instance, Durand and colleagues [ 51 ] found that phoneme deletion was a unique predictor of individual differences in reading but did not predict subsequent arithmetic skills. Moreover, Jordan and colleagues [ 12 ] reported that although basic reading proficiency was a strong predictor of mathematics achievement, it did not predict mathematics achievement above and beyond BNC.

In another study, Fuchs and colleagues [ 17 ] reported that phonological processing measured by rapid digit naming, first sound matching, and last sound matching was a unique determinant of fact fluency, but did not predict other aspects of mathematics performance e. In a subsequent study [ 52 ], the authors reported similar results when phonological processing was measured by phonological decoding of pseudowords.

These findings lend support to the notion that fluency in calculation and curricular achievement may represent distinct domains of mathematical cognition. In line with this assumption, Fuchs and colleagues [ 53 ] found that children situated at the lower-end of the performance range for calculation tasks exhibited distinctive cognitive profiles compared with children at the lower-end of the performance range for verbal problem-solving; whereas Hart and colleagues [ 54 ] demonstrated that mathematics problem solving has different genetic and environmental influences compared with fluency in calculation.

In summary, in the present research, we find substantial evidence supporting that the domain-specific capacities, specifically subitizing and to a lower extent counting, are significantly related to more sophisticated mathematics skills acquired at the end of elementary school above and beyond domain-general abilities. This finding contrasts with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. As practical implication, the present research supports the importance of training low-level numerical processing for enhancing mathematical competence in typically developed children even in later grades of elementary school.

Finally, certain considerations should be taken into account for interpreting the findings of the present study. Firstly, our sample size was modest. A small sample size makes it difficult to detect differences when following up significant multivariate interactions. However, power analyses were referred systematically in the Results Section to assist readers in evaluating whether power is a concern. This is particularly important as the conclusions are based partially on nonsignificant findings in certain relationships.

Secondly, our measures of mathematics outcomes came from self-constructed tests without standardization. Although, this could be a partial limitation considering that the analysis was based on individual differences rather than on classifying children according to performance. National Center for Biotechnology Information , U.

PLoS One. Published online Nov 8. Philip Allen, Editor. Author information Article notes Copyright and License information Disclaimer. Received Jun 26; Accepted Oct 4. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

This article has been cited by other articles in PMC. Abstract The first aim of the present study was to investigate whether numerical effects Numerical Distance Effect, Counting Effect and Subitizing Effect are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. Introduction The Number System [ 1 , 2 ] is thought to be responsible for the basic processing that engages mental representations of numerical quantities.

Tests of the first point of the study T 1 Ravens CPM test [ 29 ] This test was administered as a measure of nonverbal reasoning ability. Basic numerical battery BNB [ 23 ] This battery comprises item-timed computerized tests, with a structure similar to that of the Dyscalculia Screener [ 30 ]. Simple reaction time. Dot enumeration.

### What Is Dysgraphia?

Symbolic comparison. Word and pseudoword reading This is a test included in the SAL battery [ 31 ]. Variables calculated for tests of T 1 Numerical effect variables These variables were calculated to quantify individual differences in the size of typical effects elicited when some kind of numerical information is processed.

Tests used in the second point of the study T 2 Mathematics fluency A sheet with basic exercises of addition, subtraction and multiplication, including numbers from 1 to 9, were presented to the children in a combined form. Mathematics curriculum-based measures CBM Two tests based on mathematics curriculum were designed for 4 th and 5 th grades, respectively. Reading comprehension This is a test included in the SAL battery [ 31 ] was used to measure reading achievement. Procedure Tests corresponding to T 1 were administered in April to the children enrolled in 3rd and 4th grades.

Results The means and standard deviations of all measures are shown in Table 1. Table 1 Means and standard deviations for all measures. T 1 T 2 3rd grade 4th grade 4th grade 5th grade General Predictors Age 9. Open in a separate window. Table 2 Means and standard errors of efficiency measures for each level of numerosity and distance. Standard errors are in parentheses. Variables 1 2 3 4 5 6 7 8 9 10 11 Outcomes 1 Mathematics Fluency -. Figure 1.

Scatterplot showing significant correlation between mathematics fluency and the size of the subitizing effect. The solid line represents the linear regression for this relationship. Table 4 Hierarchical Regression Models predicting mathematics fluency and curriculum competence from numerical effect indexes. Table 5 Hierarchical Regression Models predicting reading achievement from numerical effect indexes. Funding Statement The authors have no support or funding to report. References 1. Dev Sci 10 : PubMed: Trends Cogn Sci 8 : Learn Individ Differ 20 : Karmiloff-Smith A Development itself is the key to understanding developmental disorders.

Trends Cogn Sci 2 : Jordan NC, Levine SC Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Math 1. Math 2. Mikhail Chernobilsky. Math 3. Math 3 New 4. Math 4a. Mary Marvin. Math 5. However, the focus is on problem solving with topics studied throughout the school year, all done at a deep level.

Many multi-step problems will be done in class and assigned for homework. Included are long multiplication and division with 2 and 3-digit numbers, continuation of fractions, with addition and subtraction with different denominators, and many word problems, introduction to decimals and how they relate to fractions, and further development of geometry, area and perimeter, volume. Along with the rigorous arithmetic program, challenging and exciting Olympiad and contest type problems will be included each week as part of the lesson.

Math 5ab. This is a class for students who have deep understanding of foundations of number system, and can work comfortably with whole numbers, including addition, subtraction as well as multiplication by two-digit number, division by a one-digit number, have good understanding of fractions and decimals, including addition and subtraction of fractions with different denominators. We will continue with multiplication and division of whole numbers, order of operations, with multiplication of mixed numbers, multiplication and division of decimals, percentage and the connection of percent-fraction-decimals, harder word problems involving especially fractions as a part of a whole.

Geometry moves to the different parts of geometric objects such as angles, focusing especially on properties of a triangle, perpendicular and parallel lines and solid figures. Math 5b. This is a class for students who have thoroughly mastered the basics of fractions and decimals, including addition and subtraction of fractions with different denominators and beginning multiplication and division of decimals. We will continue with multiplication of mixed numbers, multiplication and division of decimals, order of operations, percentage and the connection of percent-fraction-decimals, harder word problems involving especially fractions and percents, triangle and quadrilateral geometry.

Language of algebra and algebraic expressions will be introduced. Math 6. Students will deepen their understanding of fractions and decimals, and do many hard numerical and word problems with them. We will move into percentages, ratios and some introductory pre-algebra. Geometry will continue, with harder area and perimeter problems, and now area of a triangle and composite figures. Along with the rigorous arithmetic program, there will be a heavy component of challenging and exciting Olympiad and contest type problems on topics like probability, sets, counting principles and combinatorics.

Math 6B. Math 7 VC. Students will move into topics of Pre-Algebra, including negative numbers, and the concept of a variable and simple equations and how they are useful. The topics of arithmetic — fractions, decimals, rate, ratio, percentages, will now be deepened with hard word problems on each. Geometry will continue, with more complex area, perimeter and volume problems, and now quadrilaterals and angles in polygons.

Math 7B new Math 8ab. Math 8b The class will continue the study of Algebra I. Students should already have knowledge of basic algebra techniques, equation of a line, solving 1st degree equations and inequalities, forming and solving simple algebraic word problems. We will move further into working with integer exponents, radicals, and quadratic equations, including factoring methods, solving quadratic equations, the quadratic formula, and accompanying word problems. Different kinds of equations, such as fractional, radical will be studied.

Math A1, Geom. Math Alg 2 VC. Students will continue learning how to deal with fractions, including finding common denominators for more than two fractions, multiplication of mixed numbers and more difficult fraction word problems. Decimals, to the ten-thousandths place and their equivalent fractions will be covered. Other topics will include finding the average of a group of numbers, ratio, percent, graphs and geometry such as area of a triangle and other geometric shapes besides squares and rectangles. Logic problems and puzzles will be part of each lesson, as well as practice for the Common Core tests next spring so kids will be thoroughly prepared and ready.

Math Algebra2VC. Math Calc VC. Math Calculus. An intensive and demanding mathematics class for students with a strong background in all prerequisite subject matter up to and including Precalculus. A pllacement test is required for entrance into this class. Math CalculVC. Math Early K. Math K. Math Kangaroo 1. Math M 6. Math M2b. Math M3b. Math M9c. Math Math 4a. Math mmmm. Math na. Math na 0. Math na 2. Math nan. Math New 5B 4B.

Math 4A and 4B These classes are identical, that is they will follow the exact same program with the same homework each week. Students will move further into the topic of fractions, including adding and subtracting of mixed numbers, and with different denominators. Fraction multiplication will be introduced. There will be many word problems requiring understanding of these fraction concepts. Long division and multiplication will now include 3 and 4 digit numbers. Second semester will see the introduction of decimals and how they relate to fractions.

And geometry will be developed further, with more complex problems on area and perimeter, and now volume of cubes and cuboids. Topics like set theory, probability, logic, and combinatorics will be taught — yes, young kids can do these things, if taught at an age-appropriate level. Students should have a strong mastery of arithmetic through 3rd grade to succeed in this class. Math notavailab.

Math Precalcul. Math SAT. Math Saturday P. Math x. Math xx. This class will study second year Algebra. A strong command of Algebra I is necessary. We will study quadratic equations and their graphs more deeply, two-variable equations and inequalities, setting up and solving harder algebra word problems, more complex radicals and fractional exponents, and the notion of a function and how to work with a function.

Fall Math 8c This is a class for students who have command of elementary algebra. We will continue with different kinds of equations, e. Linear inequalities, as well as inequalities in two variables will be studied. Relation of quadratic equation to the graph of a parabola will be studied. A small amount of geometry will be included, but this is NOT a geometry course. Photography Parents. Victor Kligler. In this class we use real-world activities and interactive design to help the students develop computational thinking and creativity. We do this using the Scratch programming environment, adding some robotics and math problem modeling.

We start with storytelling and animations, and move on to computer games programming. Students plan and design interactive multimedia projects, in line with their own ideas and interests. Our students learn and actively use mathematics, including areas and concepts that are not usually covered in elementary school: geometry, logic, coordinates, negative numbers, decimals, random numbers and variables. Children bring their laptops to class. Their parents are encouraged to help them with set up, and are welcome to stay in class — to observe and help.

It is easy to use and learn, but it allows design very complex projects. Sergey Torubarov. We concentrate more on applications of programming e. Our students learn to put together multi-part projects, cooperate with each other and share their work. The emphasis is more on planning of the projects and on user-computer interaction than on coding. We continue to use microcomputers and robotics kits. We touch upon the topics of electric circuits, circuit logic, and artificial intelligence; and tie them with mathematics.

It is easy to use and learn, but it allows design very complicated projects. Marina Malysheva. Russian Russian 2 new 3. Russian 3a. Russian 3B. Russian 4. Julia Gordeeva. Russian 6b. Russian 6n. Russian A. Liliya Brammer. Russian AP. Russian B. Russian Benimovich. Russian Biling2. Russian Bilingual-. Russian BL4. Russian Book Club. Russian C. Russian I. Russian K0 new Russian kk. Russian na. Russian nnn. Russian Reading. Russian Russian 1. Russian X. Speech Speech A. Art 2hours.

## Dr John Kelliher (E-kitapları)

Art A. Art ac. Art B. Art C. Art D. Art Dr-Part. Art E. Art extra. Art GA. Art Jacob. Art Simon Cast. Art Sophie. Art x1. Chess 1a. Chess Begin. Slava Koza. For young children yo. All classes are in Russian. English 1. English 1A. English 2. English 4. English 5. Novels will be utilized as well as short stories to encourage each student to read. Since reading is an essential tool in improving writing skills, all students will be expected to complete the reading assignments in preparation for each lesson.

Students will learn all parts of a basic sentence and progress through grammar and writing lessons designed to prepare each student for middle school language arts courses. Students will also receive instruction designed to increase PARC and other standardized test scores. Weekly assignments will be posted on the School Plus website.

English 7. Robert Capriles. English 8.

## HMI - Mathematics 5 to 11 ()

Course: English 8 Objective: To prepare each student for honors and advanced placement level English courses. Since these skills are required for individuals to excel in any career, instruction is differentiated to ensure each student is challenged and students will gain important insight into the need to utilize these skills beyond high school, the SAT, and their college experience. Levitt and Stephen J. English cancelled. English CD. Students who have previously participated in School Plus English classes will review material, but will quickly build upon what each has mastered.

New students will be fine, for Mr. Lancaster will ensure each student understands the material. Novels will be utilized to encourage each student to read. Students will begin with a review of a basic sentence and progress through grammar and writing lessons designed to prepare each student for middle school language arts courses. Students will also receive instruction designed to increase NJASK and other standardized test scores. English kB. English ll. English n. English na. English VC Grade 2 This is a class for students who have thoroughly mastered addition and subtraction of numbers to 10 using number bond and number line strategies; We will continue on with addition, subtraction, multiplication and division, paying special attention to mental calculation as well as using place value concept for numbers up to The teacher of this class is also going to teach some mental math strategies and engage students in visible thinking.

The main idea is to help students develop deep feeling and understanding of numbers. Math Math 1B. Grade 1 Primary math 1A textbook and workbook Process skills level 1 The students are expected to have the following skills upon enrollment: Add and subtract fluently within 10 and add and subtract numbers under 40 mentally through the use of number lines.

Students should also be able to count up to a forward and backward beginning with any number and a given sequence. In addition, students should be able to compose and decompose given numbers from 11 to 19 into ten ones and other ones. Math 2A. Math 2B. In addition, students should be able to Compose and decompose numbers from 11 to 39 into ten ones and other ones. Fall Fall Grade 5 This is a class for students who have thoroughly mastered addition and subtraction of numbers to using vertical algorithm as well as using mental calculation strategies; have deep knowledge of place value; know multiplication table up to 12 and related division facts, can solve multi-step word problems and have developed clear understanding of equivalent fractions.

We will continue with addition, subtraction and multiplication of fractions and decimals. Geometry moves from finding perimeters and areas of rectangles and squares to finding perimeters and areas of composite shapes, defining - points, rays, lines and line segments including parallel and perpendicular lines and types of angles and types triangles based on their angles and lengths of their sides.

Math 6A. Participants should have deep understanding of the very foundations of our number system, thoroughly mastered fractions and decimals, percentage and the connection of percent-fraction-decimals, compare and contrast new knowledge with prior knowledge and come to deeper conclusions. We will start with the four operations on integers, fractions and mixed numbers and continue with introduction to algebra, which includes writing and simplifying algebraic expression, solving equations and formulating an algebraic equation to represent problem situations.

Students will be solving more challenging word problems involving fractions and percentage, ratio and rate as well as area and circumference of a circle, triangle and quadrilateral geometry, more complex area, perimeter and volume problems. Furthermore, we will be solving many non-routine word problems and puzzles from different areas of mathematics. Math 7K. Fall Math 6 This is a class for students who have deep understanding of the very foundations of our number system, and can work comfortably with whole numbers, thoroughly mastered the basics of fractions and decimals, percentage and the connection of percent-fraction-decimals.

We will continue with the four operations on integers, fractions and mixed numbers, order of operation, writing and simplifying algebraic expression, solving equations and formulating an algebraic equation to represent problem situations. Students will be solving more challenging word problems involving fractions and percents, ratio and speed, area and circumference of a circle, triangle and quadrilateral geometry, more complex area, perimeter and volume problems.

Finally, we will be solving many non-routine word problems and puzzles from different areas of mathematics. Math 8. Math 8 prep HS. Math 9. Math adanced. Primary math textbook and workbook 1A and 1B Common Core Intensive math practice books 1A and 1B Challenging Word Problems 1 The students are expected to have the following skills upon enrollment: Add and subtract fluently within 10 and add and subtract numbers under 40 mentally through the use of number lines.

Math B. Fall This is a class for students who have mastered addition and subtraction of numbers to using vertical algorithm as well as using mental calculation strategies; know multiplication table up to 5 and related division facts; have basic understanding of fractions; can solve simple word problems including problems which involve multiplication and division. We will continue on with addition, subtraction, multiplication and division, paying special attention to mental calculation as well as developing deep understanding of a place value for 3-digit numbers.

We will also learn how to find a number given a sum and a difference of two numbers, how to make a whole with fractions with like denominators. We will learn how to solve problems with money, time intervals and units of weight and length. Students will learn how to sort out polynomials by their attributes such as length of the side and measure of angles, In addition, they will learn to find perimeters and areas of basic and composite shapes.

Math C. Fall This class is for students who have mastered addition and subtraction with 3-digit numbers, demonstrated fluency in multiplication table and related division facts up to 10 and have basic understanding of fractions; In addition, students must demonstrate the ability to read, interpret and solve word problems involved with all four operations.

We will learn all main concepts from a common core curriculum for 3 grade and some from a 4 grade. In addition, the teacher of this class is going to teach complex strategies for solutions of challenging word problems, for example, supposition and replacement methods. These interventions will include the following concepts and ideas: arithmetic progression, scale problems with symbols as elements of algebra, square and square numbers and will help students develop deep feeling and understanding of numbers.

Math Geometry I. Math Math 0. Math new B gr3. Zoya Koza. Fall This is a class for students who have thoroughly mastered addition and subtraction of numbers to 20 using mental calculation strategies; We will continue on with addition, subtraction, multiplication and division, paying special attention to mental calculation as well as using place value concept vertical algorithm for numbers up to Students will learn how to compare fractions by drawing models and on the number line.

Students will be introduced to several strategies for solving multi-step word problems such as model approach and guess and check. These enrichment lessons will help students develop deep feeling and understanding of numbers. Math new C gr4. In addition, this class is for students who have developed visible thinking skills as well as process skills such as supposition, restate and replace methods and other strategies described in the Process Skills level 3, model and heuristic experimental approach to problem solving.

The goal of this class is: continuous implementation of strategies described above reaching the level 4 of the Singapore math system. Level 4 is compatible only with the grade 5 of common core as well as other higher-level mathematical thinking concepts. Fall math A This is a class for students who have thoroughly mastered addition and subtraction of numbers to 40 using vertical algorithm as well as using mental calculation strategies; know multiplication table up to 5 and related division facts; have basic understanding of fractions; can solve simple word problems including problems which involve multiplication and division.

We will continue on with addition, subtraction, multiplication and division, paying special attention to mental calculation as well as developing deep understanding of a place value. We will learn how to solve problems with money, time and time intervals and other units of time. Math NNN. Math Prep HS Ad. Math sorokina. Math Tests adva. The course covers all the math topics and tricks students will need to know for the test. Emphasis throughout the course is given to solving problems without using a calculator because the use of calculators is not allowed on the Bergen Academies admission test.

The course forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Explanations and discussions focus on both reasoning and execution. Some of the most dreaded categories of problems are thoroughly represented: mixtures, rates, and problems that engage comprehension. Mixture problems are among the problems that are underrepresented in a common school curricular while being some of the more challenging word problems on the admission tests.

As the assessments, students will take the full length BCA math practice tests that are identical in level and format to the actual BCA practice tests. Math v. Fall Math 2 This is a class for students who have thoroughly mastered addition and subtraction of numbers to , especially mentally; have knowledge of place value; understand, recognize and correlate repeating patterns of numbers, letters and objects. We will continue with addition and subtraction of numbers to , paying special attention to mental calculation. Students will learn multiplication table up to 12 and related division facts.

They will learn about standard units of length, weight and capacity in the metric and customary systems and the relationships among units. We will also cover fractions including equivalent fractions and addition and subtraction of fractions with like denominators, money, time and time intervals, graphs as well as area and perimeter.

Throughout the year we will be solving harder word problems involving multiplication, division and fractions. Last, but not least, we will be solving exciting problems and puzzles from different areas of mathematics. Math XX. MetMuseum III. Antonina Lifshits. Music C. Music nn. Music Performanc. Olga Shyp. By learning singing, dancing and theatrical performance in Russian, students will unveil and enrich their musical talents and the Russian language.

Music preschool. Music x. Photography Visual Per. Russian 0. Russian 2. Russian 2new. Russian 30 min. Russian 31 min. Russian 5. Russian 8. Russian adv 4,5,7. Russian Advanced. Russian Beginner. Russian BL. Russian Chase new. Russian indiv. Russian K. Russian mm. Russian need help. Russian nn. Russian speakers. Theater teatr. Nadya Shavarina. Diana Zeltser. Nina Pascal. Art 4. English advanced A. Timothy Palumbo. English advanced B. Extra Linguistic. Andrey Antonenko. French 0. Elena Tikhonova.

French 1A. Tatiana Tchoubar. French 1B. Italian 1. Marina Villacis. Italian 2. Tatiana Yurchenko. Larisa Yakimenko. Elena Lukina. Dmitry Zaslavsky. Tatyana Portnaia. Math 4 A. Math 4 B. Math y. Math 6 A. Corina Mata. Math 6 B. Alexander Kirillov. Math 7. Igor Zaliznyak. Physics 1. Sergey Suchalkin. Physics 1B. Physics 2. Alexei Tkachenko. Physics 3. Physics 4. Russian 0 A. Tatiana Tcherevik. Russian 0 B. Russian 1 B. Russian 1A. Russian 3 A. Marta Kondratyuk. Russian 3 B. Russian 6. Tatiana Sorochenko. Russian 7. Russian 9. Russian adults beg. Olga Fuchs.

Russian beginners. Russian interm. Science Earth. Spanish 0. Jennifer Zenteno. Spanish 1. Spanish 2, interm. Theater Russian. Art a. Art I. Teacher TBA. Jackson Hueckel. Chess I Chess II Chess III English 0-Kk. Natalie Sabini. Andrew Mark Mayer. KellyAnne Gallo. English English. English II. English III English Test Prep. English V B. English VII English VIn. English X SAT.

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Hilda Portalatin. Math 0-K. Valentina Dyakova. Kasandra Sulton. Paul Doubowsky. Nader Shehata. Irina Goldman. Math Friday. Math grade-K. Math I. Math II Math III B. Math III Math IV BZ. Math IV Irina Shmandina. Math Nick. Danielle Falzone. Math V Math VBA. Math VI BA. Math VI Math VIIPractic. Math X SAT MetMuseum I. MetMuseum II. Nadezhda sher. Russian II. Russian Nick. Irina Tolkacheva. Spanish I. Spanish II. Fall 18 Little singers This group is formed by students from Pre-K to 2nd grade, ages 4 to 7 and intended to choral practice.

Architecture4Kids 1. Greg Gurevich. Fall 19 Besides getting to know significant buildings and architects in the world, as well as styles, we will also do sketching, some photography outdoors, and walking tours to see nearby buildings. Kids will learn how architecture integrates art, math, science, nature and critical thinking. We will do fun projects, like building a miniature tree house, house for bird or pet, or for an imaginary creature of alien. Architecture4Kids 2. Fall 19 The class offers students a chance to get to know some of the significant buildings and architects in the world, become familiar with some architectural styles, understand how architecture incorporates art, math, science, nature and critical thinking, and have a chance to work on their own projects and create their own designs.

We will also look into the subject from age appropriate mathematical point of view: how to calculate some basic structures, area, and volume, how architects calculate how many people are allowed in a building, how stairs are calculated, and how to calculate the life-cycle cost of construction from an energy point o view. Architecture4Kids 3. Fall 19 For years old it is a chance to learn the basics of architecture, how buildings work, how they are built through drawing and calculations.

Students will learn how to assemble their own creations. Materials to be used: lego, wood, paper, cardboard, duct tape, straws, tooth pics, leaves and clay. Architecture4Kids 4. Alina Obeeva. Fall 19 The main premise of this class rests upon the idea that drawing is a technical skill and as such can be acquired and perfected by anyone at any age and regardless of perceived abilities. We will learn how to plan our work, how to concentrate, and how to take our time with our work. We will also talk about perfection and how as far as art is concerned there is no such thing as mistakes.

There are, however, steps that can be taken to alter or add to those parts of our drawings that do not make us happy. This will help us talk about the way our creative process makes us feel and how to get the most out of those feelings. We will draw from graphics and still life. We will use pencils, markers, oil pastels and crayon pastels as mediums to see how each differs from the rest and how certain mediums are more desirable for expressing our creative impulses.

There will be an occasional homework assignment which will be emailed ahead of time. Enjoy the class! Art 1 English. Classes in drawing contribute to the development of excellent motor skills, imagination, perseverance, accuracy, ability to bring work to an end. We will learn: 1. Figure and Painting: pencil, pastel, colored pencils, charcoal, markers, gouache, watercolor composition, color light and shadow, perspective plot works, sketches still life landscapes drawing plants, animals, people 2.

Tie from the chenille wire 3. Molding from polymer clay, plasticine, and salted dough 4. Quilling, application, and collage. Art Photo. Greg Khitrov. The goal is to spend approximately 30 min on the hands on portion of the class, for the last in we will come to class to transfer all the images into a computer, and look at few to discuss. Students need to bring any point and shoot camera of their choice. No need to invest in any expensive equipment. By the end of the semester students will be able to create a collage of all their work to show off their artistic views. Lessons plans will be distributed.

Chess A. Scott Chaiet. Fall 19 Chess has been played for thousands of years and is a great way to develop concentration skills. In the beginners class we will study the basics of chess. We will learn the rules. Basic checkmates and tactics will be studied. Opening ideas will be discussed. Lots of practice games will reinforce the principles.

We will learn notation so that the students will be ready to start playing in chess tournaments. Chess B. Fall 19 In the intermediate class we will learn more advanced combinations and strategies. The four basic checkmates will be studied. Opening theory will be discussed with examples from the games of Paul Morphy, Jose Capablanca , Alexander Alekhine and more. Hypermodern chess ideas will be looked at. The interaction of strategy and tactics will be considered as this will take the student to the next level. The student will have to bring in their games, and they will be reviewed.

This area is most important to analyze their own games critically. Chess D. Chess E. Spring We will explore basic challenges and children will be encouraged to build creatively in hands on environment. We will touch upon basic physics and engineering principles such as friction, simple levers, motion, and momentum, and various design principles. In some sessions team building will be encouraged to solve problems like planning a city or building simple items for use around the house, in others individual work will be the focus and in either case, children will be encouraged to gain a different perspective on their environment, use creativity and imagination and have lots of fun.

For Fall this class will be building all around writing skills. We will still have discussions and collaborative story and essay writing. However, we will also put more emphasis on improving vocabulary and grammar. The class is still very much oriented around helping students be comfortable with writing and figuring out how to eloquently express their thoughts through ink. Dance 1. Kierstyn Sharrow. Fall 14 This class will focus on the fundamentals of ballet. The students will begin learning ballet terminology and the technique to execute those steps correctly.

Along with enhancing the students physical awareness, they will learn to coordinate movements with music and learn how to use the music to express their artistry and creativity. Ballet class teaches discipline, the importance of routine, team work, and inspires self-motivation. The culmination of this class will be a dance performance piece showcasing all the students have learned and achieved as, not only individuals, but also as a group.

Each week the children will progress on the knowledge from the prior class and add one new concept. The class will culminate in an expressive and creative dance performance for their parents and their peers. Mila Filatov Antonina Lifshits. Fall 19 Getting into a good school program is one of the major challenges that New York kids and their parents have to face. As unfair and ridiculous this situation may be, letting your children obtain some useful learning skills early, is not a bad idea. This class is designed to develop their logic and reasoning skills, introduce basic mathematical concepts, and help our students be more aware and learn more about the world they live in.

The aim of this class is to develop memory, attention and cognitive skills. Most of the assignments will improve the study skills of children by focusing their attention on rules, examples and following the procedure in solving a problem. I use methods that foster both creativity and self-control, and our homework assignments are tailored to the individual capabilities of each student. Aidan O Connor. The goal is also to ensure students perform to the best of their abilities on the State Exam.

Each student will finish the course with a reliable and well-developed foundation to build off in the ELA subject area. The course will tackle fiction reading, non-fiction reading, figurative language, active reading, a few ELA test-taking strategies, basic grammar, analyzing text and more. The class will also provide test prep for the 4th grade NY State Exams. Scores on these exams can be very important for students looking to gain acceptance to new Middle Schools.

Much of class and homework will involve reading and responding to text age and grade appropriate material. Digesting complex text is an invaluable skill in both high school and college. Building strong focus and mental stamina at this age will benefit your child immensely in the years to come. The course will focus mostly on reading comprehension and writing with a very small amount of grammar.

Students can expect 30 minutes to 1 hour of homework each week. English 6. Fall 19 ELA 6 will be a reading and writing enhancement course based on the sixth-grade level. The class may also be feasible for advanced 5th-grade students. The class will also prepare students for the 6th grade State ELA Exam with test strategies, explanation of the exam, and practice.

The writing aspect of the course will split its focus between persuasive, fact-based writing and creative, personal-based writing. The class will also feature a small amount of grammar. Assignments will include persuasive essays, personal essays, literary-response essays, and poetry. The first half of the course will lean towards persuasive, fact-based writing research papers, persuasive writing , the class will then send some time prepping for the State Exam in April and then will move to more creative processes in the tail end of the course.

Feel free to contact me with any questions about the course. English ps - 1. English TestPrep. Each lesson will consist of a do now exercise, of doing a portion of a sample test question from a Verbal Section, focusing on Comprehension. For the remainder of the class each day we will focus on test taking strategies for the material that we worked on for the lesson, the lessons that the questions bring up in the material.

Ultimately, each child will be prepared for the test taking conditions of the Gifted and Talented program.