Each fall teachers struggle with how to support parents who are helping their children with math homework. When conducting backtoschool meetings with parents, teachers typically summarize the math curriculum by course content. Sometimes, teachers will hand out a list of resources, study aids, and games that parents can share with their children to develop number sense and reasoning. Some schools offer parent education nights that provide parents with detailed information about academic standards. Other schools host family math nights where parents can participate with their children and play various math games that support the curricular content. At these events, parents can make math game kits to use at home with their children. Other schools provide afterschool math tutoring for parents and children through afterschool literacy program funding or through federally funded school improvement funding.
When guiding parents on how they can help their children with mathematic reasoning at home, consider the following examples and activities that align to the math standards:

Define problems and persevere in solving them.
Students should first describe a math problem and identify what they are being asked in order to help them determine the solution and show their work. Word problems are best solved by this approach. For example, if a student has $50 to spend on school clothes where pants cost $20 and shirts cost $10, how many shirts and pants can be purchased? A primary grade student could subtract $20 from $50 and find that they have $30 left for three shirts or one more pair of pants and one shirt. A middle school student might set up the algebraic equation $20x + $10y = $50 and create a table of values for x and y that satisfy the equation. Content specific math games can help students learn concepts and properties of math.

Reason abstractly and quantitatively.
Students need the ability to justify how they solve a particular math problem. One application might be to set up a budget for school supplies. The student must research the best prices for school paper, writing tools, a binder, a pencil holder, and art supplies. By identifying what the student needs to purchase to supplement what the student already has at home, the student must problem solve abstractly by prioritizing needs and quantitatively by using the budget for needed supplies.

Construct viable arguments and critique the reasoning of others.
When working with a classroom of students, teachers often facilitate a discussion on how or why a student approached a particular math problem with a specific solution. At home, parents can have a discussion with their child about options to consider when planning a budget or deciding on a specific purchase. For example, a parent can ask their child “what if” questions or ask if there are other means to obtain the solution. If buying a Lego set with an allowance, the child might want to consider what set might be interchangeable with other sets that the child already owns. When shopping for a cell phone, the child should be asked to consider which plan and type of phone best supports individual needs and overall family cost.

Group and sort with math.
At the elementary levels of mathematic reasoning, parents can apply mathematics in a variety of ways. For example, at the primary level, parents can help their children count and sort collections of leaves, coins, stamps, buttons, or other collections. The children can chart groups of leaves, coins, stamps, or buttons. At a higher level of math, children can calculate the fractional quantities of different groups, convert to percentages, graph on a computer, or create a chart on graph paper. Food recipes can be increased or reduced for different numbers of servings. Children can calculate unit costs of various food selections when they shop and show their work to parents.

Use measuring tools.
Teachers can guide parents in helping their children consider the use of tools when solving a math problem. Young children love using tape measures, yard sticks, and rulers. Favorite home projects include designing container gardens by using graph paper and a pencil to create scale drawings. Parents can help their children calculate the area required when planting different types of plants and vegetables. Children can also compute the area of home features with measurements for carpeting, window covers, surface painting, and landscaping.

Use family activities to give context to problem solving.
Parents can encourage children to apply their math skills when planning for the family vacation to a national park, a local campsite, or a nearby beach. Children can accurately calculate the driving distance to each stopping point during the trip and predict the amount of gas that must be purchased during the trip. Children can help parents plan the vacation’s budget by determining where they will stay and if they qualify for travel discounts. Research can be conducted on statistical information on points of interest, anticipated weather forecasts, and costs for supplies required for the trip.

Look for and make use of structure.
Teachers can encourage parents to talk to their children about observable patterns in solving problems. When teaching children about money conversions, such as how many nickels are in a dollar, the parent can reinforce the discussion by helping the child count by five, ten, or twentyfive to identify the patterns of conversion options in a dollar.

Look for and express regularity in repeated reasoning.
As parents become proficient working with their children in mathematical problemsolving, they can help their children notice that calculations are repeated. When multiplying a twodigit number by a single digit number, the child can be shown how to deconstruct the twodigit number into the sum of easy to multiply numbers. Then the child can multiply each of the easy to multiply numbers by the single digit number creating two products. The two products can be added to give the answer to the original multiplication problem. For instance, the product of 5 times 27 can be found by multiplying 5 times 20 and adding the product to the product of 5 times 7. Thus, 5 times 27 will equal the sum of 100 + 35 = 135. In this example, the ability to deconstruct and multiply also provides practice in applying the distributive property; 5(20 + 7) = 100 + 35 = 135.
Teachers can feel overwhelmed with the added job of helping parents use mathematical reasoning with their children at home. The benefits of this guidance is bittersweet. When parents understand that the mathematical standards are internationally benchmarked, they are assured that all students have access to quality content when transferring between schools and applying for colleges out of state. In next month’s blog we will discuss how to expand on the use of these standards when helping parents integrate technology into mathematical reasoning with their children at home.
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