Fluency or Mastery of Multiplication Math Facts.
Success with 4th grade math concepts are directly correlated to fluency of math facts.
There are many ways to practice math facts. The secret is to use a variety of ways to practice these facts. Our facts go up to 10's x 12's.
There are some great rules for understanding math facts. These include:
Mastery of math facts is a critical component of other 4th grade concepts including; multi-digit multiplication, division, equivalent fractions, and area and perimeter.
Unit One-Place Value and Multi-digit Addition & Subtraction
Common Core Standards Covered in this section of Unit 1:
VOCABULARY associated with this section of Unit 1:
Unit 7 - Fractions & Decimals
The Main Concepts of Unit 7:
Common Core Standards for Unit 6:
Unit 5-Measurement
Common Core Standards in Unit 5:
Unit 3-Whole Number Division
Common Core Standards in Unit 3:
Success with 4th grade math concepts are directly correlated to fluency of math facts.
There are many ways to practice math facts. The secret is to use a variety of ways to practice these facts. Our facts go up to 10's x 12's.
There are some great rules for understanding math facts. These include:
- Any even number multiplied will result in an even product.
- Two odd numbers multiplied will result in an odd product.
- Easy facts to know are 1's, 2's, 5's, and 10's.
- Use "landmark numbers", such as 5 and 10 to help with other facts. For example, 5x12= 5x10 + 5x2 or 7x5= 5x5 + 5x2
- If a student uses "tricks" or needs to use their fingers to count on to understand a math fact, it shows they are not yet proficient. Math fact fluency is the ability to mentally recall a fact within 6 seconds.
- The following link has some great ideas for practicing math facts and making them fun!
Mastery of math facts is a critical component of other 4th grade concepts including; multi-digit multiplication, division, equivalent fractions, and area and perimeter.
Unit One-Place Value and Multi-digit Addition & Subtraction
Common Core Standards Covered in this section of Unit 1:
- 4.NBT.A.1
- 4.NBT.A.2
- 4.NBT.A.3
- 4.NBT.A.4
- comparing multi-digit (up to millions place) whole numbers using <, >, =
- read and write multi-digit whole numbers (up to millions place) in standard form, word/written form and expanded form.
- how size of place value changes (ex: as you move from left to right in a number, each digit's place increases by x10. So, 1000 is 10 times larger than 100.)
- value of a digit in any whole number place value location -ones to millions (ex. 678,054 - 7 = 70,000)
- round to any whole number place value tens to millions.
- using an efficient method, fluently add and subtract multi-digit whole numbers (up to millions place) including where regrouping is needed ~~~you may know regrouping as "carrying" or "borrowing"
- round to any place value tens to millions.
- estimate sums and differences of multi-digit whole number equations by rounding the numbers being added (addends) or numbers in a subtraction problem (minuend and subtrahend)
- understand and apply that addition and subtraction are inverse operations of each other ( 10 + 5 = 15 15 - 5 = 10)
- able to read a word/story problem and create/find and solve the correct equation for the word problem (+ or -)
VOCABULARY associated with this section of Unit 1:
- place value drawing
- place value
- standard form
- written/word form
- expanded form
- greater than >
- less than <
- addend
- sum
- difference
- minuend
- subtrahend
- inverse operations
- *un-group
- *re-group
- *Un-group/re-group you may have learned as "borrow" and "carry"
- Communitive Property of Addition
Unit 7 - Fractions & Decimals
The Main Concepts of Unit 7:
- Compare Non Unit Fractions and Mixed Numbers with unlike denominators using reasoning, number sense, benchmark numbers, placing them on a number line and/or finding a common denominator. (See Figure 1)
- 45/9 > 41/6 since the both have 4 as a whole but 5/9 is close to 1/2 and 1/6 is close to 0.
- 3/5 < 3/4 since 3/5 = 12/20 and 3/4 = 15/20 and 12/20 < 15/20
- 2/3 < 10/12 since 2/3 = 8/12 and 8/12 < 10/12
- 6/8 > 6/15 since 6 our of 8 is more than 6 out of 15.
- 35/6 > 32/3 since 32/3 = 34/6
- EX: 3/8 < 7/9 since 3/8 is just less than 1/2 and half of ninths would be 4.5/9.
- EX: 4/5 > 1/8 because 4/5 is much closer to the whole 5/5 and 1/8 is closer to 0.
- Understand the size of a fraction depends on the size of the whole.
- 1/2 of a large pizza is more than 1/2 of a small pizza.
- Create equivalent fractions using multiplication and division.
- EX: 3/4 x 6/6 = 18/24
- EX: 20/24 ÷ 4/4 = 5/6
- Recognize and be able to compare equivalent fractions and decimals with tenths, hundredths, halves and fourths - including mixed numbers.
- 1/10 = 0.1 or 0.10
- 2/100 = 0.02
- 1/2 = 0.5 or 0.50
- 1/4 = 0.25
- 2.06 = 26/100
- 0.75 = 75/100
- 655/100 = 65.05
- Make and solve problems related to line plots with fractions. (See Figure 2)
- equivalent fractions
- simplify
- divisor
- multiplier
- common denominator
- tenths
- hundredths
- decimal number
- mixed number
- line plot
Common Core Standards for Unit 6:
- 4.NF.3
- 4.NF.3a
- 4.NF.3b
- 4.NF.3c
- 4.NF.3d
- 4.NF.4
- 4.NF.4a
- 4.NF.4b
- 4.NF.4c
- The role of the numerator and the denominator in fractions
- Same size whole vs not same size whole in fractions (half of a small pizza is not the same amount as half of a large pizza)
- express a fraction as a sum of other fractions - including as a sum of unit fractions and the product of a whole number and a unit fraction.
- Ex: 4/5 as a sum of unit fractions: 4/5 = 1/5 + 1/5 + 1/5+ 1/5
- Ex: 4/5 as a product of a whole number and a unit fraction: 4/5 = 4 x 1/5
- Add and subtract fractions with common/like denominators - including when there is a missing component in the equation.
- Ex: 6/9 + 1/9 = 7/9
- Ex: a + 3/5 = 5/5 = 1
- a= 2/5
- Ex: 7/8 - 3/8 = 4/8 = 1/2
- Ex: 5/6 - n = 2/6
- n = 3/6 or 1/2
- Add and subtract mixed numbers with common/like denominators - including regrouping where needed.
- EX: 5 1/3 + 2 2/3 = 8
- Ex: 6 1/9 + 1 3/9 = 7 4/9
- Ex: 9 1/4 - 6 3/4 = 2 2/4 = 2 1/2 (borrow 4/4 {=1} from 9 and regroup it/carry it to 1/4 for a total of 8 5/4 - 6 3/4 )
- Ex: 3 1/6 - 2 2/6 = 5/6 (borrow 6/6 {=1} from 3 and carry it/regroup it to 1/6 for a total of 2 7/6 - 2 2/6 = 5/6)
- Convert between improper fractions and mixed numbers and mixed numbers and improper fractions
- 4 1/3 - 13/3 because 4 wholes is like 4 x 3/3 = 12/3. Then add 1/3 more for 13/3
- 18/5 = 3 3/5 because 18/5 = 18 divided by 3 which is 15. There are still 3 leftover out of the 5 so we write that as 3/5.
- Multiply non-unit fractions by whole numbers
- Ex: 3/8 x 3 = 9/8 = 1 1/8
- Solve real world problems involving line plots and fractions
- Ex: Instead of the x-axis having whole numbers along it, it has fractions and student needs to play fractions. See Lesson 6 - workbook page 214 for an example.
- Ex: A recipe calls for 3/4 cup of whole wheat flour, 1 2/4 cups of white flour and 1/4 cup of rice flour. How much flour is needed in all?
- fraction
- unit fraction
- proper fraction
- improper fraction
- mixed number
- line plot
- convert
- numerator
- denominator
- common/like denominator
Unit 5-Measurement
Common Core Standards in Unit 5:
- 4.MD.1
- 4.MD.2
- 4.MD.3
- 4.MD.5
- 4.MD.5b
- 4.MD.6
- 4.MD.7
- 4.G.1
- 4.G.2
- 4.G.3
- convert within Metric units of measure convert within customary/standard units of measure
- 4th grade is responsible for conversion within the following Metric sizes/prefixes: kilo, hecto, deca, deci, centi, and milli and for the units meter, liter and gram
- tons, pounds, ounces
- gallons, quarts, pints, cups, fluid ounces
- miles, yards, feet, inches, and up to an eighth of an inch
- Convert units of time
- century, decade, year, leap year, month, week, day, hour, minute, second
- Understand and solve problems with elapsed time
- Solve perimeter problems *(l = length and w = width in the below situations)
- Perimeter is totaling up the measures of all sides. If the shape is a rectangle (and all squares are rectangles), you can use the formula
- P = l + w + l + w which can further simplify to
- P = 2(l +w) or 2l + 2w
- P = l + w + l + w which can further simplify to
- Perimeter is totaling up the measures of all sides. If the shape is a rectangle (and all squares are rectangles), you can use the formula
- Solve area problems
- A = l x w for all rectangles
- prefix
- Metric System
- Customary/Standard System
- conversion
- convert
- formula
- units
- square units
- perimeter
- area
- length or distance
- width
- line plot
- mass
- weight
- liquid vloume or liquid capacity
- kilogram, hectogram, dekagram, gram, decigram, centigram, milligram (kg, hg, dag, g, cg, dg, mg)
- kilometer, hectometer, dekameter, meter, decimeter, centimeter, millimeter (km, hm, dam, m, dm, cm, mm)
- kiloliter, hectoliter, dekaliter, liter, deciliter, centiliter, milliliter (kL, hL, daL, L, dL, cL, mL)
- elapsed time
- leap year, year, month, week, day, hour, minute, second
- tons, pounds, ounces
- gallons, quarts, pints, cups, fluid ounces
Unit 3-Whole Number Division
Common Core Standards in Unit 3:
- 4.NBT.6
- 4.OA.2
- 4.OA.3
- Efficiently divide multi-digit whole number dividends by a single-digit divisor. Quotients may or may not have a remainder.
- Ex: 5643 ÷ 6 = 940 R 3
- Ex: 4605 ÷ 5 = 921
- Understand why the value of your remainder must be smaller than the value of your divisor.
- Solve real world problems using division.
- EX: Suzy has 133 stickers she wants to share equally with herself and 5 of her friends. How may stickers does each person get? ANSWER: 133 ÷ 6 (Suzy and 5 friends) = 22 stickers. Suzy donated the leftover 1 sticker to her teacher.
- Make sense of remainders.
- EX: There are 185 students going to a museum. Each van can hold 9 students. How many vans will we need so that all of the students can go? ANSWER: We will need 21 vans since the quotient is 20 R 5 so we need a 21st van for those 5 remaining students.
- Estimate quotients.
- EX: 655 ÷ 8 I know that 640 ÷ 8 = 80 and 720 ÷ 8 = 90 so I know my quotient will be bigger than 80 but less than 90.
- EX: 1286 ÷ 4 I know that 1200÷ 4 = 300 and 1600 ÷ 4 = 400 so I know my quotient will be bigger than 300 but less than 400.
- VOCABULARY associated with Unit 3:
- quotient
- dividend
- divisor
- remainder
- estimate