Advanced Math 4

Singapore Dimensions Math 4A / 4B

Exam: NC Grade 4 EOG. 17 units.

Units

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   Numbers to 1,000,000

   place-value-million

   Place value is the grammar of every later number system: each place is ten of the place to its right. Students read, write (standard and expanded form), compare, order, and round numbers through one million. Decimals, scientific notation, and polynomials all reuse this idea with a different unit.

   Watch for

   4,050,000 read as “four million fifty”; rounding 45,000 to the nearest ten thousand as 40,000.

   Qty 3Practice 3 items →
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   Addition and subtraction

   multi-digit-add-sub

   The algorithm is regrouping; the thinking is compensation and bar models for comparison. Students add and subtract multi-digit numbers with several regroupings (including across zeros), estimate to check, and solve two-step comparison problems from a bar model.

   Watch for

   subtracting across zeros (5003 − 278); treating “difference” as the leftover bar rather than the comparison.

   Qty 3Practice 3 items →
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   Multiples and factors

   factors-multiples-intro

   The first real number theory. A prime has exactly two distinct factors; the sieve is a process, not a poster. Students list factor pairs, find common factors and multiples, classify primes and composites to 100, and apply the divisibility tests for 2, 3, 4, 5, 6, 9, and 10. Everything about fractions later is GCF and LCM in disguise.

   Watch for

   1 classified as prime; 15 called prime because it is odd; divisibility by 3 tested on the last digit.

   Qty 3Practice 3 items →
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   Multiplication

   multi-digit-multiplication

   Area model first, standard algorithm second; the area model is the same picture used for (x+2)(x+3) in Math 1. Students multiply by 10, 100, 1,000, by 1-digit and 2-digit numbers, estimate with compatible numbers, and solve multi-step product stories.

   Watch for

   $24 \times 10 = 24+0$; partial products added in the wrong place.

   Qty 3Practice 3 items →
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   Division

   long-division-remainders

   Remainders are the whole point: a remainder is a number, a fraction, or a reason to round up, depending on the story. Students divide up to 4-digit by 1-digit with and without remainders, interpret the remainder, and draw part–whole and grouping bar models.

   Watch for

   “7 buses for 36 children, 5 per bus” answered 7 R 1 instead of 8 buses.

   Qty 3Practice 3 items →
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   Fractions

   fraction-fundamentals

   A fraction is a number on the line, not a pizza slice that has to be less than one. Students place fractions on a number line, generate equivalents, simplify, convert improper and mixed forms, and compare using common denominators or the benchmarks one half and one.

   Watch for

   $\frac35 > \frac34$ because 5 > 4; mixed numbers compared by whole part only.

   Qty 3Practice 3 items →
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   Adding and subtracting fractions

   fraction-add-sub

   Common denominators are LCM; renaming mixed numbers is regrouping. Students add and subtract like and unlike fractions and mixed numbers with renaming, and solve multi-step fraction stories with a bar model.

   Watch for

   adding denominators ($\frac12+\frac13=\frac25$); $3\frac15 - 1\frac25$ stalled because the fraction part of the first is smaller.

   Qty 3Practice 3 items →
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   Multiplying a fraction and a whole number

   fraction-times-whole

   Two readings of the same symbols: n times a/b as repeated addition, and a/b of N as a part of a set. Students compute both and use a bar model for fraction-of-a-quantity stories, including two-stage ones.

   Watch for

   $\frac23$ of 12 drawn as two of three items instead of two of three equal parts of the bar.

   +−1 formula

   Fraction times whole

   $$n \times \frac{a}{b} = \frac{n\cdot a}{b}$$
   Qty 3Practice 3 items →
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   Line graphs and line plots

   line-plots-graphs

   Data is a number with a unit and a scale. Students build line plots with bins of one half, one quarter, and one eighth, read a single-line graph, and answer questions about trends and totals — multiplying by the bin value rather than counting marks.

   Watch for

   counting Xs instead of multiplying by the bin value when asked for a total length.

   Qty 3Practice 3 items →
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    Measurement

    measurement-conversions

    Conversion is multiplication by one, written as a fraction of units. Students convert within metric and customary length, mass, and capacity, and solve elapsed-time problems including the 24-hour clock.

    Watch for

    2.5 kg = 250 g; elapsed time 9:40 → 11:15 counted as 2 h 15 min.

    Qty 3Practice 3 items →
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    Area and perimeter

    area-perimeter-rectilinear

    Perimeter is a length; area is a count of unit squares; they do not move together. Students use the rectangle and square formulas, find a missing side from a known area or perimeter, and decompose composite rectilinear figures.

    Watch for

    doubling both $A$ and $P$ when both sides double; using the outer path as area.

    +−3 formulas

    Rectangle area

    $$A = \ell w$$

    Rectangle perimeter

    $$P = 2(\ell + w)$$

    Square area

    $$A = s^2$$
    Qty 3Practice 3 items →
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    Decimals

    decimal-place-value

    Tenths are a new place, not a new kind of number. Students use tenths, hundredths, and thousandths, convert between fractions and decimals for those places, and compare, order, and round decimals.

    Watch for

    0.19 > 0.2 because 19 > 2; 0.30 called bigger than 0.3.

    +−1 formula

    Decimal places

    $$\tfrac{1}{10} = 0.1,\quad \tfrac{1}{100} = 0.01,\quad \tfrac{1}{1000} = 0.001$$
    Qty 3Practice 3 items →
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    Addition and subtraction of decimals

    decimal-add-sub

    Align the points, not the last digits. Students add and subtract decimals with regrouping and solve money and measurement stories.

    Watch for

    $3.4 + 0.25$ added with the last digits aligned (as if $34 + 25 = 59$, giving $0.59$ or $5.9$) instead of the points aligned ($3.65$).

    Qty 3Practice 3 items →
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    Multiplication and division of decimals

    decimal-mul-div-intro

    Place value still runs the algorithm: multiply or divide as whole numbers, then place the point. Students multiply and divide a decimal by a 1-digit whole number and round a quotient to a given place.

    Watch for

    $0.4 \times 0.2 = 0.8$ (wrong place count — that is Math 5, but the seed is here if they try it).

    Qty 3Practice 3 items →
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    Angles

    angle-measure-types

    An angle is a turn; degrees are the unit of turn. Students name ray, vertex, and angle, measure and draw with a protractor, classify acute, right, obtuse, straight, and reflex angles, and use angles on a line and at a point.

    Watch for

    reading the wrong protractor scale; calling $90^\circ$ acute; reflex angles ignored.

    +−2 formulas

    Angles on a line

    $$\text{angles on a line} = 180^\circ$$

    Angles at a point

    $$\text{angles at a point} = 360^\circ$$
    Qty 3Practice 3 items →
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    Lines and shapes

    lines-symmetry-quadrilaterals

    Parallel and perpendicular are relationships, not decorations on a square. Students identify and draw parallel and perpendicular lines, list square and rectangle facts, and complete a symmetric figure.

    Watch for

    “a rectangle is not a square” treated as “a square is not a rectangle.”

    Qty 3Practice 3 items →
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    Properties of cuboids

    cuboids-isometric

    3D is 2D plus depth. A cuboid has 6 faces, 12 edges, and 8 vertices — a count you can check. Students identify cubes and cuboids, build from unit cubes, and draw isometric and orthographic views without double-counting hidden cubes.

    Watch for

    hidden cubes in a drawing counted twice or not at all.

    Qty 3Practice 3 items →