Place Value
Place Value Link
Common Core Link
Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: place value, greater than, less than, equal to, ‹, ›, =,comparisons/compare, round
4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Addition and Subtraction with and without Regrouping (using place value)
Khan Academy Regrouping
Place Value, Greater Than, Less Than, Ordering from Least to Greatest
Greater Than, Less Than
Greater Than, Less Than 2
Ordering Large Numbers
Ordering Game!
4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.
Example:
Round 368 to the nearest hundred. This will either be 300 or 400, since those are the two hundreds before and after 368. Draw a number line, subdivide it as much as necessary, and determine whether 368 is closer to 300 or 400. Since 368 is closer to 400, this number should be rounded to 400.
What is "Rounding" ?Rounding means reducing the digits in a number while trying to keep its value similar.
The result is less accurate, but easier to use.
Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.
Common MethodThere are several different methods for rounding, but here we will only look at the common method, the one used by most people ...
How to Round Numbers
- Decide which is the last digit to keep
- Leave it the same if the next digit is less than 5 (this is called rounding down)
- But increase it by 1 if the next digit is 5 or more (this is called rounding up)
- We want to keep the "7" as it is in the 10s position
- The next digit is "4" which is less than 5, so no change is needed to "7"
(74 gets "rounded down")
Example: Round 86 to the nearest 10
- We want to keep the "8"
- The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9"
(86 gets "rounded up")
So: when the first digit removed is 5 or more, increase the last digit remaining by 1.
What Are You Rounding to?When rounding a number, you first need to ask: what are you rounding it to? Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, and so on.
Consider the number 4,827.
- 4,827 rounded to the nearest ten is 4,830
- 4,827 rounded to the nearest hundred is 4,800
- 4,827 rounded to the nearest thousand is 5,000
- 34 rounded to the nearest ten is 30
- 6,809 rounded to the nearest hundred is 6,800
- 1,951 rounded to the nearest thousand is 2,000
Webmath
4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
A multiplicative comparison is a situation in which one quantity is multiplied by a specified number to get another quantity (e.g., “a is n times as much as b”). Students should be able to identify and verbalize which quantity is being multiplied and which number tells how many times.
4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.
Examples:
Unknown Product: A blue scarf costs $3. A red scarf costs 6 times as much. How much does the red scarf cost?
(3 x 6 = p).
Group Size Unknown: A book costs $18. That is 3 times more than a DVD. How much does a DVD cost?
(18 ÷ p = 3 or 3 x p = 18).
Number of Groups Unknown: A red scarf costs $18. A blue scarf costs $6. How many times as much does the red
scarf cost compared to the blue scarf? (18 ÷ 6 = p or 6 x p = 18).
4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
A common misconception is that the number 1 is prime, when in fact; it is neither prime nor composite. Another common misconception is that all prime numbers are odd numbers. This is not true, since the number 2 has only 2 factors, 1 and 2, and is also an even number.
Prime vs. Composite:
A prime number is a number greater than 1 that has only 2 factors, 1 and itself. Composite numbers have more than 2 factors.
Students should understand the process of finding factor pairs so they can do this for any number 1 -100,
Example: Factor pairs for 96: 1 and 96, 2 and 48, 3 and 32, 4 and 24, 6 and 16, 8 and 12.
Multiples can be thought of as the result of skip counting by each of the factors. When skip counting, students should be able to identify the number of factors counted e.g., 5, 10, 15, 20 (there are 4 fives in 20).
Factor Pairs of number from 1 - 100, using arrays.
Prime and Composite Numbers...see above.
Refresher on place value...
7 hundreds, 18 tens, 13 ones = 700 + 180 + 13 = 893 or/ regroup 1 ten from the ones to the tens = 3 ones 19 tens then regroup 10 tens or 1 hundred to the hundreds place = 9 tens and 8 hundreds your new number is 893.
Students need to know how to regroup or use expanded form to find the new number. Remember that the highest digit in any place is a "9". Anything higher must be regrouped to the next place value.
We will be working on this throughout the year.
4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Distributive Property of Multiplication
4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Partial Quotients Videso
Array Method of Division
Properties for Multiplication
Associative Property of Multiplication
When three or more numbers are multiplied, the product is the same regardless of the order of the multiplicands. For example (a x b) x c = a x (b x c)
Commutative Property of Multiplication
When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example a x b = b x a
Distributive Property
The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example a x (b + c) = a x b + a x c
Identity Property of Multiplication
The product of any number and one is that number. For example a x 1 = a.
Multiplication Property of Zero
Multiplying any number by 0 yields 0. For example a x 0 = 0.
Area and Perimeter
I AM PA...
Area - Multiply
Perimeter - Add
Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing, and analyzing two-dimensional shapes, students deepen their understanding of properties of two-dimensional objects and the use of them to solve problems involving symmetry.
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: classify shapes/figures, (properties)-rules about how numbers work, point, line, line segment, ray, angle, vertex/vertices, right angle, acute, obtuse, perpendicular, parallel, right triangle, isosceles triangle, equilateral triangle, scalene triangle, line of symmetry, symmetric figures, two dimensional. From previous grades: polygon, rhombus/rhombi, rectangle, square, triangle, quadrilateral, pentagon, hexagon, cube, trapezoid, half/quarter circle, circle, cone, cylinder, sphere, kite.
The term “property” in these standards is reserved for those attributes that indicate a relationship between components of shapes. Thus, “having parallel sides” or “having all sides of equal lengths” are properties. “Attributes” and “features” are used interchangeably to indicate any characteristic of a shape, including properties, and other defining characteristics (e.g., straight sides) and nondefining characteristics (e.g., “right-side up”).
4.G.1 Draw points, lines, line segments rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.
4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
A polygon is a plane (2D) shape with straight sides.
Triangle
Square
Rectangle
Rhombus
Trapezoid
Parallelogram
Quadrilaterals
Pentagon
Hexagon
Octagon
A circle can not be a polygon because it does not have straight sides!!
points
lines
line segments
rays
perpendicular lines
parallel lines
angles - acute, obtuse, right
triangles - equilateral, isosceles (I see two), scalene (scary scalene)
Find shapes, lines, geometry help!
Video Link
Geometry Link
Extend understanding of fraction equivalence and ordering.
Students develop understanding of fraction equivalence and operations with fractions. They recognize that two different fractions can be equal (e.g., 15/9 = 5/3), and they develop methods for generating and recognizing equivalent fractions.
Mathematically proficient students communicate precisely by engaging in discussion about their reasoning using appropriate mathematical language. The terms students should learn to use with increasing precision with this cluster are: partition(ed), fraction, unit fraction, equivalent, multiple, reason, denominator, numerator, comparison/compare, ‹, ›, =, benchmark fraction
4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
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.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, 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?
4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.2 For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 2 Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters;
locate 0.62 on a number line diagram.
4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
The following are subtraction with regrouping across zeros, division (Big 7) and Box method for multiplication. These are areas that your child may need help in...
https://www.youtube.com/watch?v=LeHQn_5GtF0
https://www.youtube.com/watch?v=PdB7kO2lcK0
https://www.youtube.com/watch?v=d0-a4GLXT-Y