Teaching Math to Young Children for Families and Caregivers

Early childhood, between the ages of 2-8, is an important period for developing math skills. From the first years of life, your child is learning math and developing interest in the subject through everyday routines and play. Your support for the development of math knowledge and skills will help prepare your child for future success in school and life. Check out this infographic title, Supporting Your Child in Developing Math Skills for Future Success, to learn more about how early math success opens doors for future success in college and careers.

These family and caregiver resources and activities, organized by math topics such as counting or shapes, include research-based and easy-to-follow steps to help you support your child’s math skills during a typical day.

The activities and resources are organized under five different sections. The first two sections cover number, shape, pattern, measurement, and data analysis. In these sections the activities and resources support the development of specific math skills. The next three sections provide activities and resources that can be used to support the development of all math skills more broadly, such as suggestions for ways to include math learning during a typical day or trip to the grocery store (section three). Check out the At A Glance table below for a quick overview of the sections and what you will find in each one. To get started you might review each section and think about what areas your child needs more support in. Alternately, you might start in an area that your child is most interested in and build on their engagement with math!

Using the activities will be a fun way to spend time together!

Resources at a Glance

Additional Resources:

The family and caregiver activities were excerpted from the following resources:
(all free online)

• Teaching Math to Young Children Practice Guide: https://ies.ed.gov/ncee/wwc/PracticeGuide/18
• Community Math Night Facilitator Guide: https://ies.ed.gov/ncee/rel/regions/appalachia/pdf/4_10_19_MathNights-REL-AP_FacilitatorsGuide_508.pdf
• You can also access all videos here:
  https://www.youtube.com/playlist?list=PLVHqsnePfULoxiBmLn3bw_GqOS1qj5piw

Children are naturally interested in numbers and finding out “how much” and “how many.” They learn to use their developing number skills to compare who has more blocks or to find out how many crackers are in their lunch boxes. Children then begin to learn that number symbols can represent many different quantities, such as how many blocks they have, how old they are, or what day of the month it is. With concrete objects and in everyday contexts, they will start to build the skills they need to answer “plus one” and “minus one” number problems.

Quick Tips, Resources and Activities

Recognizing small numbers or subitizing means to practice recognizing the total number of objects in small collections (one to three items) and labeling them with a number word without needing to count them. Subitizing is an important strategy that your child will use one day to support more complex problem-solving.

Quick Tips:

• Instead of asking your child to put on shoes to go outside, say “Put on your two shoes.”
• Gather any small collection of objects (one to three blocks or crayons) and ask “How many (objects) do I have? Without counting.”
• During mealtime, ask your child to quickly name–without counting–how many pieces of fruit are on their plate at snack, or how many cups or napkins are on the table.

At young ages, you may hear your child say numbers that they have heard you or a sibling say, but out of order. Eventually, verbal counting develops into one-to-one counting–saying the correct number for each object, then identifying the last number counted as the total number of objects in a set (cardinality), and then counting out a collection of objects correctly. Mastering each of these steps in the development of counting can be challenging for your child, but there are ways you can help.

Quick Tips:

• Help your child learn that counting is a way to answer the question “how many?” Ask them to tell you “how many” there are of something when you read together, at mealtimes, or while playing.
• To support your child’s understanding of the total number in a set of objects (cardinality), adults can model counting. Start with a small number of objects, point to each object as you count, circle all the objects in the group with your finger, and repeat the last number in the counting sequence. Eventually, children will count larger collections accurately, and, with practice and support, they will figure out that the last number in a set is the same as the total number without having to recount.

Once children can accurately recognize number (subitizing) or count to answer how many objects are in a collection, they are ready to compare numbers. Keep in mind that children develop counting and number recognition at different rates. It is OK if your child is still working on these foundational skills for a while. Repeating activities is OK too if you and your child are having fun and want to spend more time mastering foundational skills before moving onto comparing.

Quick Tips:

• At mealtime, ask “Which plate has more or fewer grapes?” After your child responds, it’s a great opportunity to discuss what “more” and “fewer” mean.
• Provide examples for your child to compare when amounts are “equal” and explain what it means to have the same amount of something.
• Once your child is comfortable making verbal comparisons, encourage him or her to use counting to compare the size of two groups of objects.

Sometimes, children may already recognize numerals (number symbols, e.g., 1, 5, 8) in the world around them–such as numbers on a street sign or poster–before they are able to count. However, once children have a basic understanding of numbers and counting, it may become easier for them to learn about numerals and how they can represent amounts of something.

Quick Tips:

• When your child counts a group of objects, such as their stuffed animal collection, try writing the number for how many they counted so that the child starts to learn that the numeral, objects, and spoken word represent the same thing.
• For children who do not yet recognize numerals, you can also use dots next to the numeral for them to count and figure out what the numeral indicates.

Once your child develops basic number skills, they can begin using their subitizing, counting, and comparing strategies to perform simple adding and subtracting problems.

Quick Tips:

• Provide your child with opportunities to practice adding and subtracting or to solve problems with “more” and “fewer”. For example, as your child eats his or her snack, ask them to count how many items they have. Next, introduce a problem-solving opportunity by asking “How many will you have after you eat one?” or “How many will you have after your friend gives you one?” Because the number will change, this activity provides good practice for understanding comparisons of more and fewer and combining or removing objects.

Handouts:

• Flip the Cards Game

Although numbers may be the first things that come to mind when you think about math, many other skills are equally important. For example, young children can begin to recognize shapes in the world around them and become increasingly aware of the similarities and differences between shapes as they create and use them with building blocks and in drawings, and by completing puzzles. The patterns children begin to observe in these activities and their environments set the foundation for algebraic reasoning. Measurement and data analysis are also developing in young children. You can support your child in these skills by offering him or her a wide variety of experiences and materials.

Quick Tips, Resources and Activities

Your child is quickly learning to recognize and name many common shapes such as circles, triangles, and squares. They learn about the attributes of shapes and begin to describe shapes based on these attributes–“It has three sides, so I know it’s a triangle.” Young children use their developing knowledge about shapes and their attributes when they build with blocks, draw, and work puzzles. These types of experiences require children to compare and match shapes; reorient shapes by rotating, flipping, or sliding them; and put shapes together to make new shapes. For example, two triangles can be flipped and rotated to form a square, a parallelogram, a larger triangle, and other irregular shapes.

Quick Tips:

• Go on a walk and ask your child to point out the shapes they see around them.
• Encourage your child to name and describe the shapes, counting the number of sides or angles they have.
• Look for different examples of a shape to expand your child’s understanding. For example, different triangles can vary in appearance and children need to see lots of examples.
• Grow understanding of shapes and spatial relations to use shapes more efficiently and accurately. For example, children can think about where a puzzle piece might go and how it should be oriented before placing it. Use words like “on,” “under,” and “next to” to describe the location of objects.

Handouts:

• Everyday Math: Shapes and Patterns
• Fill in the Shapes

Patterns are regular, predictable arrangements of things. Anything–objects, numbers, shapes, sounds, actions, or events–can make a pattern. Patterns are important in young children’s lives because they provide order and predictability. They help children learn, remember, and anticipate what comes next. Additionally, learning about patterns in the early years sets the stage for a future understanding of algebraic concepts. Preschoolers need opportunities to engage in a variety of experiences with patterns; for example, in music and movement, art, playing with blocks, and stories. Through these experiences, they learn to recognize and reproduce patterns that they hear or see and even create their own patterns.

Quick Tips:

• Help your child to find patterns in their environment. They may point out stripes on their clothes, designs in rugs, or bricks on the sides of buildings.
• Ask your child what patterns they notice in their day. You might point out the predictability of a bedtime routine or mealtime. Talk about what parts of their day repeat.
• Sing songs with your child and retell stories that have repetitive rhythms and words.
• Encourage your child to determine their own rules for sorting and organizing objects.

Handouts:

• Everyday Math: Shapes and Patterns

For young children, measurement is about exploring and comparing measurable dimensions–such as length or weight–in the world around them using standard (inches and pounds) or nonstandard units (length of their arm or blocks). Your child’s interest in measurement is reflected when they ask questions such as “Am I older than my brother?” or “Who is taller, me or Beth?”

Quick Tips:

• Provide opportunities to make direct comparisons, such as invite your child to stand back-to-back with a friend, parent, or sibling to see who is taller. Or try holding two different objects in each hand and talk about which is heavier.
• When you are comparing, use language to describe objects, people, and events; for example, taller/tallest, faster/fastest, heavier/heaviest.
• Explore nonstandard measurement tools; for example, hands, paper clips, blocks, and paper cups.
• Explore standard measurement tools; for example, measuring cups, balance scales, and measuring tapes.

Handouts:

• How Many Of Me?
• Making Playdough

Graphs and charts show numbers and quantities represented in a variety of ways. Graphs are a great way for children to practice organizing the information they might have counted or sorted in a visual way. Graphs will help your child to associate number concepts, vocabulary, quantities, and written numerals in meaningful ways.

Quick Tips:

• Introduce how to graph with simple tally marks or pictures to show how long different objects are.
• Try creating graphs that describe different characteristics of people in the family, such as hair color or favorite foods.

Overview

You can make math more meaningful to your child by connecting it to everyday experiences. For example, games can provide an enjoyable and meaningful way to learn a range of math ideas and practice a wide variety of basic skills. Additionally, everyday materials such as cups, boxes, and blocks can be found in the environment to use math purposefully.

Below the video you will find three ways to support math throughout the day.

Overview

You can encourage your child to look for opportunities to describe math ideas in the world around them. By exploring their environment and interacting with objects, children can begin to apply their math knowledge. For example, using physical objects can support children’s progression from verbalizing numerical representations with words such as “a lot” or “more” to counting. At first, counting of objects may not be exact, but over time children begin to count accurately–and then recognize “how many.” You can support development in these areas by offering a wide variety of experiences and materials for your child.

These videos introduce ways you can help your child view and describe the world mathematically. Following the video you will find more information and resources on three ways to view and describe the world mathematically.

Children as young as preschoolers can learn to talk about the many strategies they invent. Modeling your approaches to problem-solving will help them to talk about their own strategies when opportunities arise.

Quick Tips:

• Give children time to think about how to solve problems.
• Narrate your own problem solving and ask your child for help with problems that arise throughout the day. For example, you might say “I have to figure out how many cups we are going to need for the birthday party. Can you help me? How should we do that?”

Handouts:

• Finding Math Around You

It is important to teach children math words so that they have the words needed to connect their experiences to formal terms. Math language can be used throughout the day. For example, you can make a comment about which friend is standing “first” in line or which child has “more” or “fewer” objects than another child.

Another important part of using math language is being aware of how we as parents talk about math. Many adults and children feel tension, apprehension, and fear in situations involving math–this is called math anxiety. Math anxiety is different from just not liking math. It’s a physical and mental response that can be crippling and keep you from performing at your best because your brain is spending too much energy on being anxious. Children start developing math anxiety in the early grades, and when parents and teachers have anxiety about math themselves, they can pass it on.

Quick Tips:

• While your child is drawing pictures of his or her family, they can talk about the “number” of family members and who is “older” or “younger”.
• Talk about your own math skills positively. Instead of saying “I’m just not a math person” or similar phrases, try “I work hard to solve math problems”.
• If your child is struggling, say “Yes, this is challenging, but I’m confident you could work through it if you stick with it.” Avoid saying things like “It’s okay, not everyone is good at math” or “Not everyone can do these types of problems.” That kind of language can make your child think that math is too hard for them.

Handouts:

• Math Throughout the Day: Math Talk

You can use open-ended questions to prompt your child to apply their math knowledge. Ask questions that require your child to use math-related terms to describe something. For example, asking “How can we find out [how many cups we need for dinner]?” will give your child the opportunity to communicate about a math strategy and then to practice that strategy.

Quick Tips:

• When you ask an open-ended question, be sure to allow enough time for your child to think of an answer. If you child simply says “yes” or “no” quickly, try asking “How do you know?” to encourage further discussion and reflection on math strategies.

Children develop knowledge at different times and at different paces. Progress monitoring is a practice that teachers use to understand what a child knows and can do. Progress monitoring helps teachers tailor instruction to the child’s needs and identify activities that help children learn math concepts and skills that are appropriately challenging.

Progress monitoring relies on regularly observing children’s developing skills. Family members and caregivers can make these observations throughout the day while children are eating, playing, and following their regular routines.

Quick Tips:

• Just asking simple questions like “How did you know that? How did you figure that out?” or asking children to help with counting or sorting provides information about children’s developing math skills. Understanding what your child knows and building on that knowledge helps to ensure that the activities you do are meaningful and engaging and keep your child learning.

Handouts:

• Observing and Building on What Your Child Knows