You will have to complete the whole number, natural number and integer levels to get to the rational and irrational number levels.
Number system review:
2.2 Determine an approximate value of a given irrational number.
2.3 Approximate the locations of irrational numbers on a number line, using a variety of strategies, and explain the reasoning.
2.4 Order a set of irrational numbers on a number line.
2.5 Express a radical as a mixed radical in simplest form (limited to numerical radicands).
entire radical:
radical sign: √
radicand: x
index: n
mixed radical:
2.6 Express a mixed radical as an entire radical (limited to numerical radicands).
2.7 Explain, using examples, the meaning of the index of a radical.
entire radical:
radical sign: √
radicand: x
index: n
mixed radical:
2.8 Represent, using a graphic organizer, the relationship among the subsets of the real numbers (natural, whole, integer, rational, irrational).
to expressions with rational and variable bases and integral and rational exponents, and explain the reasoning.
3.4 Express powers with rational exponents as radicals and vice versa.
3.5 Solve a problem that involves exponent laws or radicals.
3.6 Identify and correct errors in a simplification of an expression that involves powers.
Demonstrate an understanding of the multiplication of polynomial expressions (limited to monomials, binomials and trinomials), concretely, pictorially and symbolically.
[CN, R, V]
(It is intended that the emphasis of this outcome be on binomial by binomial multiplication, with extension to polynomial by polynomial to establish a general pattern for multiplication.)
4.1 Model the multiplication of two given binomials, concretely or pictorially, and record the process symbolically.
Select:
[ Tiles - Binomials 1 ]
[ Tiles - Binomials 2 ]
4.2 Relate the multiplication of two binomial expressions to an area model.
Select:
[ Tiles - Binomials 1 ]
[ Tiles - Binomials 2 ]
4.3 Explain, using examples, the relationship between the multiplication of binomials and the multiplication of two-digit numbers.
Move the sliders to create the two-digit numbers. Observe the output.
Note error: The red dotted line (visible when at least one factor has two-digits) should be horizontal instead of vertical. The grey number on the left should be above the horizontal red dotted line. The grey number on the rigth should be below the horizontal red dotted line. With these changes the base-ten model on the left shows visually the algorithm provided on the right.
Select:
[ Tiles - Binomiials 1 ]
[ Tiles - Binomiials 2 ]
4.4 Verify a polynomial product by substituting numbers for the variables.
Select:
[ Tiles - Monomial(s) ]
[ Tiles - Binomials 1 ]
[ Tiles - Binomials 2 ]
4.5 Multiply two polynomials symbolically, and combine like terms in the product.
Select:
[ Tiles - Monomial(s) ]
[ Tiles - Binomials 1 ]
[ Tiles - Binomials 2 ]
4.6 Generalize and explain a strategy for multiplication of polynomials.
4.7 Identify and explain errors in a solution for a polynomial multiplication.
Demonstrate an understanding of common factors and trinomial factoring, concretely, pictorially and symbolically.
[C, CN, R, V]
5.1 Determine the common factors in the terms of a polynomial, and express the polynomial in factored form.
5.2 Model the factoring of a trinomial, concretely or pictorially, and record the process symbolically.
, a ≠ 0 [Negative Exponents]
, n > 0
, b ≠ 0 [Power of a Quotient]