Section 4.1
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Students learned how to calculate decimal numbers and whole numbers by multiplying. They learned the commutative and associative properties of multiplication. The document provided examples of multiplying decimal numbers, estimating products, and identifying the commutative and associative properties of multiplication.
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x -2 -1 0 1 2 3
y = x3 – 2x2 -8 -1 0 1 4 9
2) Sketch the graphs in the coordinate planes:
3) Describe the movements of each graph:
- The graph of y = x3 – 2x2 rises from left to right as x increases. It is always increasing.
- The graph of y = x4 rises from left to right as x increases. It is always increasing. The rate of increase gets larger as x increases.
4) Identify any noticeable points on the graphs:
- The graph of y
Simultaneous Equations Practical Construction
The document discusses solving simultaneous equations using algebraic methods and graphing. It provides examples of setting up and solving systems of two equations with two unknowns to find the values of the unknowns. Various word problems are presented and worked through step-by-step to show how to set up the appropriate equations to find the unknown values being asked about, such as costs, numbers of items, etc. Strategies for setting up simultaneous equations from word problems are emphasized.
Decimal Numbers Part 3
1. The document discusses multiplying decimal numbers, including multiplying decimals by whole numbers, decimals by decimals, and decimals by 10, 100, and 1,000.
2. Key rules covered are counting decimal places to determine the product's decimal placement and moving the decimal over when multiplying by powers of 10.
3. Examples provide step-by-step workings of multiplying decimals using partial products and placing the decimal point correctly in the final product.
Ch. 4, Sec 2: Exponents
This document provides an overview of exponents and exponential notation:
- Exponents show repeated multiplication, with the base being the factor and the exponent showing how many times the base is multiplied by itself.
- Exponential notation compactly writes repeated multiplication, such as 2^6 representing 2 x 2 x 2 x 2 x 2 x 2.
- Negative integers raised to an even power are positive, while raised to an odd power are negative.
- A word problem example calculates 10^3 = 10 x 10 x 10 = 1,000.
- Order of operations must be followed when evaluating expressions with exponents.
3 math lm q2
The document is a table of contents for a mathematics textbook for third grade students in the Philippines. It lists 46 lessons on topics like multiplication, division, properties of operations, and solving word problems involving these operations. The document also provides information about copyright and permissions for using materials in the book. It was developed by the Department of Education of the Republic of the Philippines.
Properties of Operations in Integers Education
This document discusses properties of operations with integers, including the commutative and associative properties. It provides examples of how these properties can be applied to addition and multiplication but not subtraction or division. Readers will learn to differentiate between the commutative and associative properties and apply them in integer operations. Examples are provided to illustrate the commutative property of addition and multiplication and the associative property of addition and multiplication.
3 math lm q2
This document is an instructional material for mathematics grade 3 published by the Department of Education of the Republic of the Philippines. It was collaboratively developed by educators and contains lessons on multiplication and division of whole numbers up to 3 digits long, including properties of multiplication and division. The material is freely available for public use but prior approval is needed for commercial exploitation.
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Section 4.1
- 1. Learning Target:Students will learn how to calculate decimal numbers and whole numbers by multiplying. Students will learn the communicative and associative properties of multiplication.
- 2. Rule:Multiply like normal. Then count the number of place values behind (to the right) the decimal point in the problem.Start at the right of the product and move the decimal the number of placed to the left that you counted from in the step above.
- 3. Find the product. Then write the product in words.2.36 64 0.024
- 4. Answers:2.36 6 =14.16Fourteen and sixteen hundredths4 0.024 =0.096Ninety-six thousandths
- 5. Find the product. Use estimation to check.12.706 31.505 8
- 6. Answers: 12.706 338.118est. 13 3 = 391.505 8 12.04est. 2 8 = 16; 1 8 = 8
- 7. Properties of Multiplication:Commutative Property – You can multiply numbers in any order2 6.5 = 6.5 2a b = b aAssociative Property – Changing the grouping of factors will not change the product.(2 6.5) 4 = 2 (6.5 4)(a b) c = a (b c)
- 8. Tell which property of multiplication is shown. Explain your choice. (3.25 5) 2 = 3.25 (5 2)0.4 32 5 = 32 0.4 5
- 9. (3.25 5) 2 = 3.25 (5 2)Associative property of multiplication(changing the grouping) 0.4 32 5 = 32 0.4 5Commutative property of multiplication(changing the order)
- 10. You complete the first leg of a bike race in about 12 hours over two days. Your cyclometer shows that your average speed for this leg was 15.95 miles per hour. About how long was this leg of the race?
- 11. Answer:15.95 12 = 191.4about 192 miles
- 12. Can you calculate decimal numbers and whole numbers by multiplying?