Arizona's Mathematical Practices, explained for parents
Alongside the content standards for each grade, Arizona's Mathematics Standards include eight Standards for Mathematical Practice. They describe how students should think and work when they do math: making sense of a problem, sticking with it, explaining their thinking and checking it. They are the same in every grade and grow as children do. Teachers build them into math lessons; they are not graded as a separate subject.
1. Make sense of problems and keep trying
Understanding what a problem asks and sticking with it when it's hard.
- Understand first. Reading the problem, picturing it and asking what it is really asking.
- Plan. Choosing a way to start and changing course if it isn't working.
- Check. Asking whether the answer makes sense.
Ideas for home
- Before solving a word problem, ask your child to tell you what it's about in their own words.
- When your child is stuck, ask “What could you try first?” instead of giving the answer.
- Praise sticking with a hard problem, not just getting it right.
2. Reason with numbers and quantities
Moving between a real situation and the numbers that describe it.
- Numbers mean something. Knowing what each number stands for: dollars, inches, people.
- Back to the story. Checking that an answer fits the real situation.
Ideas for home
- Ask what an answer means: “So 12 what? Twelve cookies or twelve dollars?”
- Estimate before you calculate, then compare.
3. Explain thinking and listen to others
Giving reasons for an answer and making sense of someone else's.
- Explaining. Saying why an answer is right, with words, drawings or examples.
- Critiquing. Listening to another way and finding what works or what's wrong.
Ideas for home
- Ask “How do you know?” often, even when the answer is right.
- Solve a problem two different ways and talk about which you like and why.
4. Use math in everyday life
Using math to describe and solve real problems.
- Real problems. Turning a situation into an equation, a drawing, a table or a graph.
- Good enough. Making sensible assumptions and improving the model if needed.
Ideas for home
- Plan a trip, a recipe or a budget together and let your child do the math.
- Look at a graph in the news or a sports page and talk about what it shows.
5. Choose the right tools
Knowing when a ruler, a drawing, a calculator or mental math is the best choice.
- Tools. Using rulers, number lines, blocks, graph paper or technology.
- Choosing. Picking a tool that fits the job and knowing its limits.
Ideas for home
- Measure things around the house with a ruler or measuring cups.
- Ask whether a calculator is needed or whether mental math is quicker.
6. Be precise
Using clear words, correct units and careful calculations.
- Clear words. Using math words correctly, like equal, factor and perimeter.
- Units and labels. Saying what is being measured, and checking calculations.
Ideas for home
- Ask your child to include the units: 5 feet, 3 hours, $2.50.
- When cooking, measure carefully and talk about what happens if you don't.
7. Look for structure
Noticing how numbers and shapes are built and using that to solve problems.
- Patterns in numbers. Seeing that 8 × 7 is 8 × 5 plus 8 × 2, or that 99 is one less than 100.
- Breaking apart. Splitting shapes and numbers into easier pieces.
Ideas for home
- Ask for shortcuts: “Is there a quicker way to add 98 + 47?”
- Find shapes inside other shapes on signs, tiles and quilts.
8. Spot repeated reasoning
Noticing when a calculation repeats and finding a general rule.
- Repeats. Seeing the same steps come up again and again.
- Rules. Turning a repeated pattern into a shortcut or formula.
Ideas for home
- Count by 5s, 10s or 25s and ask what pattern you notice.
- Build a growing pattern with coins or blocks and ask what the 10th step would be.
Common questions
No, not as a subject of their own. Teachers build them into math lessons, and some report cards comment on problem solving or explaining thinking, but they are not graded separately.
Yes. The same eight practices appear in every grade of Arizona's Mathematics Standards. What changes is the math they are used with, from counting in kindergarten to algebra in high school.
They are part of Arizona's Mathematics Standards, adopted by the Arizona State Board of Education in 2016. Each grade's standards document lists them before the content standards.
No. Gradelings practices the math content standards. Hints, a second try and worked examples help children make sense of problems and keep going, but these habits grow best when you talk about math together.
Ask your child's teacher how the class talks about problem solving, and what kinds of explanations they hope to hear from students.
Next: understand the Arizona report card levels or browse all Arizona parent guides. Gradelings practices subject skills; these habits grow through talking about problems together, not only through right answers.
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