Paste a learning goal. SpartaMath analyzes the instructional target, then creates new aligned student problems plus a matching teacher guide.
The learning-goal sentence is treated as a target specification—not as a math problem.
Adding and subtracting within 20
AZ.MATH.1.OA.1
There are 8 birds on a tree. 5 fly away. How many are left?
Making a ten to add
AZ.MATH.1.OA.1
Use make-a-ten: 8 + 5 = ? (Hint: 8 + 2 = 10, then add 3)
Counting to 120
AZ.MATH.1.NBT.1
What number comes after 99?
Tens and ones (place value)
AZ.MATH.1.NBT.1
How many tens and ones are in 47? (4 tens, ___ ones)
Telling time to the hour and half hour
AZ.MATH.1.MD.3
The clock shows the hour hand on 3 and minute hand on 12. What time is it?
2D and 3D shapes
AZ.MATH.1.G.1
How many sides does a triangle have?
Measuring length
AZ.MATH.1.MD.2
Use cubes to measure: a pencil is 8 cubes long. A pen is 5 cubes. How much longer is the pencil?
Adding and subtracting within 100
AZ.MATH.2.OA.1
A store has 45 apples. They sell 18. How many are left?
Counting within 1000
AZ.MATH.2.NBT.2
Skip count by 5s: 35, 40, 45, ___, ___
Place value to 1000
AZ.MATH.2.NBT.2
What is the value of the 4 in 487?
Estimating lengths
AZ.MATH.2.MD.3
A pencil is about how many inches long: 3, 7, or 20?
2D shapes and their attributes
AZ.MATH.2.G.1
How many sides does a pentagon have?
Reading picture and bar graphs
AZ.MATH.2.MD.10
A bar graph shows: cats=8, dogs=12, birds=5. How many more dogs than cats?
Multiplication facts
AZ-3.OA.C.7
What is 7 × 8?
Division facts
AZ-3.OA.B.6
What is 56 ÷ 7?
Two-step word problems
AZ-3.OA.D.8
Sam has 3 bags with 6 apples each. He eats 4 apples. How many are left?
Area of rectangles
AZ-3.MD.C.7
Find the area of a rectangle with length 4 cm and width 6 cm.
Fractions on a number line
AZ-3.NF.A.2
Place 1/2 on a number line from 0 to 1. Is it closer to 0 or 1?
Perimeter of polygons
AZ-3.MD.C.8
Find the perimeter of a rectangle with length 5 cm and width 3 cm.
Rounding to nearest 10 or 100
AZ-3.NBT.A.1
Round 47 to the nearest 10.
Multiplicative comparison
AZ-4.OA.A.1
There are 4 times as many cats as dogs. If there are 3 dogs, how many cats?
Multi-digit multiplication
AZ-4.NBT.B.5
Calculate: 34 × 6
Fraction equivalence
AZ-4.NF.A.1
Is 2/4 equivalent to 1/2? Show using a model.
Add and subtract fractions (like denominators)
AZ-4.NF.B.3
Evaluate: 3/8 + 2/8
Angles and geometry
AZ-4.MD.C.6
Measure this angle: it looks like a right angle. What is its degree measure?
Factors and multiples
AZ-4.OA.B.4
List all factor pairs for 36.
Compare decimals
AZ-4.NF.C.7
Compare: 0.5 ___ 0.50. Use >, =, or <.
Order of operations
AZ-5.OA.A.1
Evaluate: (3 + 4) × 2
Add fractions with unlike denominators
AZ-5.NF.A.1
Evaluate: 3/4 + 2/5
Multiply mixed numbers
AZ-5.NF.B.6
Evaluate: 2 1/3 × 1 1/2
Divide fractions
AZ-5.NF.B.7
Evaluate: 4 ÷ (1/2)
Volume of rectangular prisms
AZ-5.MD.C.5
Find the volume: l=4, w=3, h=5
Decimal operations
AZ-5.NBT.B.7
Evaluate: 3.45 + 2.7
Coordinate plane
AZ-5.G.A.2
Plot the point (3, 5) in the first quadrant. What quadrant is it in?
Ratios and ratio language
AZ-6.RP.A.1
In a class of 12 boys and 15 girls, what is the ratio of boys to girls?
Unit rate
AZ-6.RP.A.2
A car travels 150 miles in 3 hours. What is the unit rate in miles per hour?
Percent problems
AZ-6.RP.A.3
What is 30% of 90?
Unit rate & proportional reasoning
AZ-6.RP.A.3
If 3 apples cost $1.50, how much do 7 apples cost?
Divide fractions by fractions
AZ-6.NS.A.1
Evaluate: 2/3 ÷ 3/4
Integers and rational numbers
AZ-6.NS.C.5
A temperature drops 8°F from 3°F. What is the new temperature?
Algebraic expressions
AZ-6.EE.A.2
Evaluate 3x + 5 when x = 4.
Combine like terms
AZ-6.EE.A.3
Simplify: 5x + 3x - 2
Solve one-variable equations
AZ-6.EE.B.7
Solve: x + 9 = 16
Area, surface area, and volume
AZ-6.G.A.1
Find the area of a triangle with base 8 cm and height 5 cm.
Volume of rectangular prisms (fractions)
AZ-6.G.A.2
Find the volume of a rectangular prism: l=5, w=3, h=4
Mean, median, and data distributions
AZ-6.SP.B.5
Find the mean of: 4, 7, 9, 6, 4
Add and subtract rational numbers
AZ-7.NS.A.1
Evaluate: -5 + (-3)
Multiply and divide rational numbers
AZ-7.NS.A.2
Evaluate: (-4) × 7
Four operations with rational numbers
AZ-7.NS.A.3
Evaluate: (3/4) ÷ (-1/2)
Equivalent expressions
AZ-7.EE.A.1
Simplify: 3x + 5x - 2
Rewrite expressions
AZ-7.EE.A.2
Rewrite: a + 0.10a as a single expression.
Multi-step equations and inequalities
AZ-7.EE.B.4
Solve: 2x + 5 = 17
Scale drawings
AZ-7.G.A.1
A map scale is 1 inch = 50 miles. Two cities are 3.5 inches apart. What is the real distance?
Circumference and area of circles
AZ-7.G.B.4
A circle has radius 7 cm. Find the circumference. (Use π ≈ 3.14)
Supplementary, complementary & vertical angles
AZ-7.G.B.5
Two supplementary angles are in ratio 1:2. Find both angles.
Area and volume of 3D figures
AZ-7.G.B.6
Find the surface area of a rectangular prism: l=5, w=3, h=4
Probability models
AZ-7.SP.C.7
A bag has 4 red, 3 blue, 2 green marbles. What is P(red)?
Solve proportions
AZ-7.RP.A.2
Solve the proportion: 4/6 = x/9
Rational vs irrational numbers
AZ-8.NS.A.1
Is √5 rational or irrational? Explain why.
Approximate irrational numbers
AZ-8.NS.A.2
Approximate √10 to the nearest tenth. Between which two integers does it fall?
Integer exponents
AZ-8.EE.A.1
Simplify: 3² × 3⁴
Square roots and cube roots
AZ-8.EE.A.2
Solve: x² = 144
Scientific notation
AZ-8.EE.A.3
Write 0.000045 in scientific notation.
Operations with scientific notation
AZ-8.EE.A.4
Multiply: (3 × 10⁴) × (2 × 10³)
Graph proportional relationships & slope
AZ-8.EE.B.5
A car travels 120 miles in 2 hours. Write and graph the equation. What is the slope?
Derive y = mx and y = mx + b
AZ-8.EE.B.6
Write the equation of a line through the origin with slope 4.
Solve linear equations & inequalities
AZ-8.EE.C.7
Solve: 3(x + 4) = 2x + 20
Systems of linear equations
AZ-8.EE.C.8
Solve the system: y = 2x + 1 and y = -x + 7
Identify functions
AZ-8.F.A.1
Is this a function? {(1,2), (3,4), (1,5)}
Compare properties of functions
AZ-8.F.A.2
Function A: y = 3x + 1. Function B: (0,2),(1,5),(2,8). Which has the greater rate of change?
Linear vs nonlinear functions
AZ-8.F.A.3
Is y = 3x + 2 linear or nonlinear? Explain.
Model linear relationships
AZ-8.F.B.4
A phone plan charges $10/month plus $0.05/minute. Write a function. What is the rate of change?
Analyze graphs of functions
AZ-8.F.B.5
Describe a graph that is increasing, then decreasing, then constant.
Transformations: rotations, reflections, translations
AZ-8.G.A.1
Translate point (3, -2) right 4 and up 3. What are the new coordinates?
Congruent figures
AZ-8.G.A.2
Triangle A has vertices (0,0),(3,0),(0,4). After reflecting across y-axis, what are the new vertices?
Dilations and similarity
AZ-8.G.A.3
Dilate point (4, 6) by a scale factor of 1/2 about the origin.
Similar figures
AZ-8.G.A.4
Are two figures similar if one is a dilation of the other? Explain.
Pythagorean Theorem
AZ-8.G.B.7
Find the hypotenuse of a right triangle with legs 6 and 8.
Distance between two points
AZ-8.G.B.8
Find the distance between (0, 0) and (3, 4).
Volume of cones, cylinders, and spheres
AZ-8.G.C.9
Find the volume of a cylinder with radius 3 cm and height 10 cm. (Use π ≈ 3.14)
Scatter plots and association
AZ-8.SP.A.1
A scatter plot shows hours studied vs test scores increasing together. What type of association is this?
Linear models for scatter plots
AZ-8.SP.A.3
A linear model is y = 2x + 5. Predict y when x = 8.
Compound probability
AZ-8.SP.B.5
A coin is flipped and a die is rolled. How many outcomes are in the sample space?
Write linear equations
AZ-8.EE.B.6
Write the equation of a line with slope 3 and y-intercept -2.