MATH



MATH

Grade 4 Overview

Operations and Algebraic Thinking

o Use the four operations with whole numbers to solve problems.

o Gain familiarity with factors and multiples.

o Generate and analyze patterns.

Number and Operations in Base Ten

o Generalize place value understanding for multi-digit whole numbers.

o Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number and Operations—Fractions

o Extend understanding of fraction equivalence and ordering.

o Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

o Understand decimal notation for fractions, and compare decimal fractions.

Measurement and Data

o Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

o Represent and interpret data.

o Geometric measurement: understand concepts of angle and measure angles.

Geometry

o Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Mathematical Practices

1. 1. Make sense of problems and persevere in solving them.

2. 2. Reason abstractly and quantitatively.

3. 3. Construct viable arguments and critique the reasoning of others.

4. 4. Model with mathematics.

5. 5. Use appropriate tools strategically.

6. 6. Attend to precision.

7. 7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Operations and Algebraic Thinking - Use the four operations with whole numbers to solve problems.

□ I can understand what a multiplication problem means (ex: 35 = 7 x 5 means that 35 is 5 times as many as 7 and 7 times as many as 5).

□ I can multiply to solve word problems by using drawings or an equation with a symbol to represent the missing number.

□ I can divide to solve word problems by using drawings or an equation with a symbol to represent the missing number.

□ I can solve word problems with whole numbers that require more than one step by using addition, subtraction, multiplication or division.

□ I can solve word problems where remainders are involved, and I can say what those remainders mean.

□ I can use mental math and estimation to say whether my answer makes sense.

□ I can use rounding to say if my answer makes sense.

Gain familiarity with factors and multiples.

□ I know what a factor is.

□ I can find factor pairs for any whole number between 1-100.

□ I can know what a multiple is.

□ I can say whether a whole number (1-100) is a multiple of another one-digit whole number.

□ I know what a prime number is.

□ I know what a composite number is.

□ I can say whether a number is prime or composite.

Generate and analyze patterns.

□ I can make a number or shape pattern based on a certain rule.

□ I can figure out patterns in number sequences that are not given in a certain rule (ex: The rule is +3; start at 1 and figure out the next three numbers in the pattern and notice that the numbers alternate between even and odd).

Numeration: Base Ten - Generalize place value understanding for multi-digit whole numbers.

□ I can look at a number with more than 2 digits, and know that a digit in one place value is ten times the same number in the place to the right (ex: In 700 ÷ 70 = 10, students can use the above concept to find a missing number in that equation).

□ I can read a multi-digit number using number names.

□ I can read a multi-digit number using expanded form (2,567 = 2,000+500+60+7).

□ I can compare two multi-digit numbers based on which digits are in which place values, and use < or > or = to explain my comparison.

□ I can use what I know about place value to round multi-digit whole numbers to any place value.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

□ I can add multi-digit whole numbers using paper and pencil (without drawing).

□ I can subtract multi-digit numbers using paper and pencil (without drawing).

□ I can multiply a whole number that is up to four digits with another whole number by a one-digit number.

□ I can multiply two 2-digit numbers together using different strategies.

□ I can explain how I multiplied two 2-digit numbers by showing my work, illustrations or lattice multiplication.

□ I can find quotients (division answers) and remainders when I divide a 4-digit number by a one-digit number.

□ I can use different strategies to do long division, such as using place value knowledge, properties of operations, and/or the relationship between multiplication and division.

□ I can draw/write and explain how to do long division by using equations, models, or rectangular arrays.

Numeration: Fractions - Extend understanding of fraction equivalence and ordering.

□ I can explain why a fraction (a/b) is equal to another fraction (n x a)/(n x b) by using a visual fraction model. (Ex: 2/3 = 2x2/2x3)

□ I can explain how, even if a fraction is equal to another fraction, how the number and size of the parts are different between the different fractions.

□ I can find equivalent fractions.

□ I know what a numerator is.

□ I know what a denominator is.

□ I can compare two fractions with different numerators and different denominators.

□ I can compare two fractions with different numerators and different denominators by making common numerators or common denominators or by comparing the fractions to common fractions (such as ½).

□ I know that I can only compare fractions when the whole is the same thing (can’t compare apples to oranges ( ).

□ I can compare two fractions using or = and explain my answer.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

□ I can understand that adding fractions is the same as joining parts that refer to the same whole.

□ I understand that subtracting fractions is the same as separating parts of the same whole.

□ I can break a fraction down into the sum of two fractions with the same denominator in more than one way, and I can write those equations. (Ex: 5/8 = 3/8 + 2/8, or 5/8 = 1/8 + 1/8 + 3/8)

□ I know what a mixed number is.

□ I can add mixed numbers with the same denominators by creating equivalent fractions.

□ I can subtract mixed numbers with the same denominators by creating equivalent fractions.

□ I can solve word problems where I need to add or subtract fractions that have the same whole and the same denominators by using pictures or an equation.

□ I can understand that any fraction (a/b) is a multiple of (1/b). Ex: 5/4 is the product of 5 x (1/4)

□ I can multiply a fraction by a whole number. Ex: For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)

□ I can solve word problems where I have to multiply a fraction by a whole number by using pictures or an equation. Ex: If each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Understand decimal notation for fractions, and compare decimal fractions.

□ I can write a fraction with 10 as the denominator as an equivalent fraction with a denominator of 100.

□ I can use equivalent fractions to add two fractions with denominators of 10 and 100. (Ex: 3/10 + 4/100 = 34/100)

□ I can rewrite fractions with denominators of 10 or 100 as a decimal. (Ex: 3/10 = 0.3, 3/100 = 0.03)

□ I can compare two numbers with decimals up to the hundredths place by talking about their size.

□ I know that I can only compare two numbers with decimals only when the numbers are referring to the same whole.

□ I can compare two numbers with decimals by using these symbols: , = and explain my reasoning with a picture/visual model.

 

Measurement and Data - Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

□ I know what different measurement units within one system of units (ex: km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec).

□ I can say smaller units of measurement in terms of the larger equivalent unit (ex: 1 ft is 12 times as long as 1 in; a 4ft snake is 48 in.).

□ I can solve word problems with distances using addition.

□ I can solve word problems with distance using subtraction.

□ I can solve word problems with distance using division.

□ I can solve word problems with distance using multiplication.

□ I can solve word problems with intervals of time using addition.

□ I can solve word problems with intervals of time using subtraction.

□ I can solve word problems with intervals of time using division.

□ I can solve word problems with intervals of time using multiplication.

□ I can solve word problems with liquid volumes using addition.

□ I can solve word problems with liquid volumes using subtraction.

□ I can solve word problems with liquid volumes using division.

□ I can solve word problems with liquid volumes using multiplication.

□ I can solve word problems with masses of objects using addition.

□ I can solve word problems with masses of objects using subtraction.

□ I can solve word problems with masses of objects using division.

□ I can solve word problems with masses of objects using multiplication.

□ I can solve word problems with money using addition.

□ I can solve word problems with money using subtraction.

□ I can solve word problems with money using division.

□ I can solve word problems with money using multiplication.

□ I can solve word problems that include simple fractions.

□ I can solve word problems that include decimals.

□ I can solve word problems that need measurements given in a larger unit, in terms of a smaller unit.

□ I can show measurement quantities using number lines with a measurement scale.

□ I can use the area formula for rectangles in the real world AND math problems.

□ I can use the perimeter formula for rectangles in the real world AND math problems.

□ I can solve a real world problem about the perimeter of a rectangle with one known side and one unknown side.

□ I can solve a real world problem about the area of a rectangle with one known side and one unknown side.

Represent and interpret data.

□ I know what a line plot is.

□ I can make a line plot to display a set of measurements in fractions of a unit.

□ I can solve problems involving addition of fractions by using information from line plots. (Example: I can tell the difference between the length of two plants by reading a line graph.)

Geometric measurement: understand concepts of angle and measure angles.

□ I can recognize angles as geometric shapes.

□ I know that an angle is formed by two rays and they share a common endpoint.

□ I can understand that an angle is a measurement that compares to a circle.

□ I know that an angle that turns through 1/360 of a circle is called a “one-degree angle” and can be used to measure angles.

□ I know that an angle measurement is the same as saying that an angle turns through a certain number of one-degree angles. (Example: a 57º angle turns 57 one-degree angles)

□ I can use a protractor to measure whole-number degrees.

□ I can draw angles based on a given measurement.

□ I can recognize that I can add different angle measures together to form another angle.

□ I can solve addition and subtraction problems to find unknown angle measurements in real world math problems.

□ I can do this by writing an equation with a symbol for the missing angle measurement.

Geometry - Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

□ I can draw a point.

□ I can draw a line.

□ I can draw a line segment.

□ I can draw a ray.

□ I can draw a right angle.

□ I can draw an acute angle.

□ I can draw an obtuse angle.

□ I can draw parallel lines.

□ I can draw perpendicular lines.

□ I can pick out lines, line segments, rays and angles in 2-D figures.

□ I can group 2-D figures based on whether or not they have parallel or perpendicular lines.

□ I can group 2-D figures based on whether or not they angles of a specific size.

□ I can identify right triangles.

□ I can recognize a line of symmetry for a 2-D figure.

□ I can tell whether a figure has line symmetry.

□ I can draw the lines of symmetry in a figure.

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