sharing problem solving year 1

• August 11, 2017

Helping Young Children With Sharing

Learning to share with grace is a long process. here’s how to turn moments of struggle into rich opportunities to help children learn critical skills..

Imagine the scene: a 3-year-old and a 2-year-old happen upon a pile of toy trains. The younger child picks up two of the trains. Instead of picking up any of the remaining trains, the older child reaches over to grab the trains the younger child is holding. The 2-year-old grabs them back—knocking the other child off balance—and both children start crying.

Why is learning to share so hard?

For one, children this age haven’t developed the ability to put themselves in another’s shoes yet. This doesn’t mean your child is a bad person, or that you’ve failed as a parent. Children this age are focused on their own feelings and thoughts, and they’re thinking,  “I want those trains, and I want them now!”

This behavior may embarrass and frustrate parents, but an unwillingness to share is perfectly normal at this age! In  Tuning In,  ZERO TO THREE’s national parent survey, 43% of parents surveyed thought that children should be able to master sharing by age 2. In fact, these skills develop between 3.5 to 4 years old.  Knowing what to expect  can help parents manage their expectations  and  their frustration when they see children having difficulty with turn-taking.

What You Can Do

There are  many ways to support young children  in learning to share. Here are a few suggestions to try. Some approaches may work better than others, depending on the situation and your child:

Ensure safety.  When young children feel threatened (like when a friend tries to snatch their toy!), they often respond in an aggressive way. That means grabbing, hitting, and throwing things. When this behavior occurs, move in close and stop the aggression. A simple statement in a low voice such as,  “I can’t let you hit,”  or  “No grabbing,”  shows your calm authority.

Narrate or “sportscast” the situation.   “Two children who both want the same trains! Sam, you picked them up and then Jade grabbed them. Sam, you tried to get them back and now you’re both crying.”  Sometimes slowing things down and creating a space for calm problem-solving is a great beginning.

Offer a “long turn.”  In some instances, a child can be given a long turn with a toy.  “Take as long as you like with those trains, Sam, and Jade will wait for you to be done. Jade, would you like to play with these trains over here until Sam is done?”  Sometimes it can feel to children that as soon as they start to play, a peer demands to “take a turn.” It is okay to let children have a “long turn”—a chance to play with the toy—before they share. Help the other child wait by offering a different activity.

Use a timer or clock.  In some cases, letting a child decide when their turn will be over just isn’t practical. At those times, a timer or clock can be a helpful rule-keeper and visual aid. The great thing about the timer is that it’s not the adult telling the children when to share, it’s the “bell.”

Reflect the feelings.  When struggles happen, it’s important to acknowledge how both children feel. “You took that train because it looked like so much fun to play with.” Then, help the other child with his feelings by showing empathy:  “He picked those trains up first so he gets to play with them for now. You can have a turn later. It’s OK to be upset when you have to wait. Waiting is hard!”

Provide “emotion-coaching.”  It’s usually the child who is waiting for a turn who is having big feelings. Sometimes this means listening to a child’s temporary emotional meltdown. Her disappointment, though out-of-proportion to an adult’s eyes, feels very real! When a child’s emotions are understood and validated, it helps her learn to put herself in others’ shoes and move on to the next step—finding solutions.

Guide children to come up with solutions.  Help them brainstorm ways to work it out—but also ask their opinions. Don’t underestimate children’s ability to come up with great ideas and strategies. For example, you can ask:  “We need to stir the batter for our cookies, but I only have one spoon. What should we do?”  The more we empower children to be kind, compassionate, problem-solvers, the more likely they will be just that.

Offer social information and a vote of confidence.  In the heat of the moment, children under 3 won’t be able to hear corrective feedback about their behavior. Once everyone is calm, a short statement about expectations will help children learn new behaviors. You could say,  “Next time you want something, you can say, ‘Can I have a turn?’ Grabbing and pushing aren’t safe. Next time, you can ask first. Keep practicing.”

Learning to share with grace is a long process. Even some adults are still working on it! Rather than dreading moments of struggle between children, consider them to be rich opportunities to help children learn critical skills—in this case, self-regulation, empathy, and conflict resolution—all of which will help them become better at sharing.

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Problem Solving Grade 1 Grouping And Sharing

Displaying top 8 worksheets found for - Problem Solving Grade 1 Grouping And Sharing .

Some of the worksheets for this concept are Puzzles and problems for year 1 and year 2, Unit three teaching through problem solving, Division by sharing word problems 2, Lesson plan halving, Division by sharing word problems 1, Factoring by grouping, Lesson plan fractions, Fifth grade unit 1 order of operations and whole numbers.

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1. Puzzles and Problems for Year 1 and Year 2

2. unit three: teaching through problem solving, 3. division by sharing (word problems 2), 4. lesson plan: halving, 5. division by sharing (word problems 1), 6. factoring by grouping, 7. lesson plan: fractions, 8. fifth grade unit 1: order of operations and whole numbers.

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Problem Solving Grade 1 Grouping And Sharing

Problem Solving Grade 1 Grouping And Sharing - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Puzzles and problems for year 1 and year 2, Unit three teaching through problem solving, Division by sharing word problems 2, Lesson plan halving, Division by sharing word problems 1, Factoring by grouping, Lesson plan fractions, Fifth grade unit 1 order of operations and whole numbers.

Found worksheet you are looking for? To download/print, click on pop-out icon or print icon to worksheet to print or download. Worksheet will open in a new window. You can & download or print using the browser document reader options.

1. Puzzles and Problems for Year 1 and Year 2

2. unit three: teaching through problem solving, 3. division by sharing (word problems 2), 4. lesson plan: halving, 5. division by sharing (word problems 1), 6. factoring by grouping, 7. lesson plan: fractions, 8. fifth grade unit 1: order of operations and whole numbers.

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Sharing Equally Year 1 Multiplication and Division Resource Pack

Step 7: Sharing Equally Year 1 Summer Block 1 Resources

This Sharing Equally Year 1 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Summer Block 1.

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What's included in the pack?

This pack includes:

• Sharing Equally Year 1 Teaching PowerPoint.
• Sharing Equally Year 1 Varied Fluency with answers.
• Sharing Equally Year 1 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 1: (1N1b) Count in multiples of twos, fives and tens

Mathematics Year 1: (1C8) Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher

Differentiation:

Varied Fluency Developing  Questions to support sharing up to 20 items equally between 2 groups. All questions have 1-to-1 pictorial support. Expected  Questions to support sharing up to 30 items equally between 2, 5 or 10 groups. All questions have 1-to-1 pictorial support. Greater Depth  Questions to support sharing up to 30 items equally between 2, 3, 4, 5 or 10 groups with minimal pictorial support.

Reasoning and Problem Solving Questions 1, 4 and 7 (Problem Solving) Developing  Working out the mystery number from a set of 2 clues. Numbers up to 20 used, shared into 2 groups. Expected  Working out the mystery number from a set of 3 clues. Numbers up to 30 used, shared into 2, 5 or 10 groups. Greater Depth  Working out the mystery number from a set of 3 clues. Numbers up to 30 used, shared into 2, 3, 4, 5 or 10 group.

Questions 2, 5 and 8 (Reasoning) Developing  Choosing how many groups (2 options) to share a number of items between. Numbers up to 20 used, split into 2 groups. Expected  Choosing how many groups (3 options) to share a number of items between. Numbers up to 30 used, split into 2, 5 or 10 groups. Greater Depth  Choosing how many groups (3 options) to share a number of items between. Numbers up to 30 used, split into 2, 3, 4, 5 or 10 groups.

Questions 3, 6 and 9 (Problem Solving) Developing  Working out how many items to take away to be left with a number that can be shared equally. Numbers up to 20 used, shared into 2 groups. Expected  Working out how many items to take away to be left with a number that can be shared equally. Numbers up to 30 used, shared into 2, 5 or 10 groups. Greater Depth  Working out how many items to take away to be left with a number that can be shared equally. Numbers up to 30 used, shared into 2, 3, 4, 5 or 10 groups.

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Exploring the difference between equal sharing and equal grouping in division

How can you make sure your pupils develop the conceptual understanding they need to solve problems using division? And what’s the difference between equal sharing and equal grouping? MNP founder Andy Psarianos breaks it down for us.

When you’re busy managing a class of boisterous six-year-olds, it’s tempting to let them fall back on one understanding of division and stick to it. Just remember that encouraging your pupils to use multiple division strategies now will benefit their understanding in the long run.

There are two ways you can approach teaching division: equal sharing and equal grouping.

Children should experience both concepts, but here’s the interesting bit, research suggests that teaching equal grouping before equal sharing will help your pupils develop a deeper understanding of division.

First up, what are equal sharing problems?

Sharing is probably the most common way of thinking about division. In equal sharing problems, you start with the number of groups and the total number of objects you want to share between them. Your goal is to find out how many objects each (equal) group can receive. A problem based on equal sharing can be written as follows:

We have 12 cookies and we want to share them among three friends, how many cookies does everyone get?

You can also write the following expression to represent the situation: 12 ÷ 3 = 4

So, what’s equal grouping?

Sharing may be the most common way of thinking of division, but it’s not the only way. A more conceptually complicated method is the notion of grouping. In an equal group problem, you know the number of objects each group should receive as well as the total number of objects you can distribute. The objective here is to find out how many (equal) groups can be created. The next example uses the same total amount of cookies as the equal sharing problem, but doesn’t give us the number of groups involved. We want to make boxes of cookies for our friends. Each box will have 4 cookies. We have 12 cookies in total. How many boxes can we make? This situation requires a different expression to represent the situation: 12 ÷ 4 = 3 The answer to this equation reflects how many groups can be made which is why we call this concept grouping.

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What is the difference between equal sharing and equal grouping and why is it important?

The difference between equal sharing and equal grouping boils down to what the quotient represents. When sharing, the quotient represents the quantity of shared objects in each group. When grouping, the quotient represents the amount of groups within the shared quantity. At the start of teaching division, teachers often focus on sharing, but not always on grouping. At this stage, it’s important to give equal, or more, emphasis on grouping when pupils are first getting their heads around multiplicative structures. One rationale for this belief is that sharing is more intuitive and it’s likely that pupils already have a notion of sharing — although not necessarily a very deep one. Grouping is conceptually more difficult and it’s less likely that pupils will have a strong notion of it. Letting them struggle early on with grouping before moving on to the simpler notion of sharing is more likely to create the necessary relational depth. Encouraging them to think of the less-intuitive representation of division as grouping helps them stretch to accommodate this less-familiar concept alongside their pre-existing and more child-like understanding of division. If you do the opposite and let children spend time playing with, structuring and later practicing the notion of sharing before they spend any time thinking about grouping, their understanding of division may become fixated on the sharing model. This can make it harder to relate the notion of grouping with division, causing difficulty later on.

As long as they get the correct answer, why care?

A cynic might take the point of view that these semantics aren’t really necessary and are a form of intellectual nonsense that has no place in teaching children how to add, subtract, multiply and divide. As long as someone can produce the correct quotient, why care? This is quite a common point of view and is sometimes the fuel for ‘back to basics’ movements we hear about.

How does this help pupils?

All pupils should be able to do efficient calculations, but that in itself isn’t enough. They have to know how and why they should do calculations, and when to apply what calculation. This can only be achieved through an emphasis on relational understanding. More to the point, when pupils progress and need to wrap their heads around concepts like dividing fractions by fractions, if they don’t have a secure understanding of grouping and know the difference between equal sharing and equal grouping, it’s unlikely they will know what to do in a situation like this one: In a controlled laboratory experiment, a flask contains 8/9 l of water. Each hour exactly 6/135 l of water evaporates from the container. How long will it take for all the water to evaporate from the flask? If pupils don’t know what to do with this problem, even with a calculator in hand, it’s because they don’t understand the notion of grouping. Grouping is necessary for dividing fractions by fractions, sharing doesn’t make any sense in this context. Once you know that the solution lies in dividing the two fractions, the calculation part is easy — although it might be a bit tedious without a calculator.

Andy Psarianos

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NA1-1: Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.

This means students will use counting strategies including counting on and back, double counting, and skip counting. This corresponds to the counting stages of the number framework so achieving level one means that a student is at the Advanced Counting Stage. Examples of their strategies might be: to calculate 6 + 5 count 7, 8, 9, 10, 11, to calculate 12 – 3 count 11, 10, 9, or to calculate three groups of three double counting 1, 2, 3,...4, 5, 6,...7, 8, 9. Grouping and equal sharing strategies are simple ways to solve addition, subtraction, multiplication and division, and fractions of sets problems without counting every object. Examples of these strategies might be: knowing 4 + 4 equals 8, skip counting 5, 10, 15, 20 to count four groups of five, or sharing objects in ones, twos or threes to find one quarter of a set of 12 items.

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Solve addition problems to 20 by joining sets and counting all the objects.

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Building with tens.

• Describe representations of numbers to 100.
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• Partition (decompose300

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Students will be able to identify pairs of features for counting by 2s.

Students will be able to create equal sized groups and count the total set either by counting all or by skip counting.

Students will be able to create models of equal sized groups using materials to represent features in a book300

Games on all fields

• Continue a skip-counting pattern.
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How Many Cubes?

Count a set of objects in the range 1–10.

• Equally partition a length into two, four, or eight parts using symmetry.
• Equally partition a length into three or five parts using estimation and iteration (copying of a unit).
• Name the result of equally sharing a number of objects among two, or four parties, extended to three, five and eight parties300

Learning to count: Counting one-to-one

• Understand that the number of objects in a set stays the same as changes are made to spatial layout, size, or colour.
• Understand that the count of a collection of objects can be trusted and worked from as objects are added or taken away, or the set is rearranged into parts.

Learning to count: Exploring collections

• Use counting to find the number when two different collections are compared (difference).
• Use counting to find the number when two or more collections are joined (addition).
• Use counting to find the number when objects are removed from a collection (subtraction).

Learning to count: Five-based grouping

• Identify five-based groupings.
• Represent five-based groupings in a variety of ways.

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Year 1 Making Equal Groups

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

17 April 2018

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Here are some resources for making equal groups following the WRMaths planning.

UPDATE: now added some reasoning and problem solving questions

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How Students Can Rethink Problem Solving

Finding, shaping, and solving problems puts high school students in charge of their learning and bolsters critical-thinking skills.

As an educator for over 20 years, I’ve heard a lot about critical thinking , problem-solving , and inquiry and how they foster student engagement. However, I’ve also seen students draw a blank when they’re given a problem to solve. This happens when the problem is too vast for them to develop a solution or they don’t think the situation is problematic. 

As I’ve tried, failed, and tried again to engage my students in critical thinking, problem-solving, and inquiry, I’ve experienced greater engagement when I allow them to problem-find, problem-shape, and problem-solve. This shift in perspective has helped my students take direct ownership over their learning.

Encourage Students to Find the Problem 

When students ask a question that prompts their curiosity, it motivates them to seek out an answer. This answer often highlights a problem. 

For example, I gave my grade 11 students a list of topics to explore, and they signed up for a topic that they were interested in. From that, they had to develop a research question. This allowed them to narrow the topic down to what they were specifically curious about. 

Developing a research question initiated the research process. Students launched into reading information from reliable sources including Britannica , Newsela , and EBSCOhost . Through the reading process, they were able to access information so that they could attempt to find an answer to their question.

The nature of a good question is that there isn’t an “answer.” Instead, there are a variety of answers. This allowed students to feel safe in sharing their answers because they couldn’t be “wrong.” If they had reliable, peer-reviewed academic research to support their answer, they were “right.”

Shaping a Problem Makes Overcoming It More Feasible 

When students identify a problem, they’re compelled to do something about it; however, if the problem is too large, it can be overwhelming for them. When they’re overwhelmed, they might shut down and stop learning. For that reason, it’s important for them to shape the problem by taking on a piece they can handle.

To help guide students, provide a list of topics and allow them to choose one. In my experience, choosing their own topic prompts students’ curiosity—which drives them to persevere through a challenging task. Additionally, I have students maintain their scope at a school, regional, or national level. Keeping the focus away from an international scope allows them to filter down the number of results when they begin researching. Shaping the problem this way allowed students to address it in a manageable way.

Students Can Problem-Solve with Purpose

Once students identified a slice of a larger problem that they could manage, they started to read and think about it, collaborate together, and figure out how to solve it. To further support them in taking on a manageable piece of the problem, the parameters of the solution were that it had to be something they could implement immediately. For example, raising $3 million to build a shelter for those experiencing homelessness in the community isn’t something that students can do tomorrow. Focusing on a solution that could be implemented immediately made it easier for them to come up with viable options. 

With the problem shaped down to a manageable piece, students were better able to come up with a solution that would have a big impact. This problem-solving process also invites ingenuity and innovation because it allows teens to critically look at their day-to-day lives and experiences to consider what actions they could take to make a difference in the world. It prompts them to look at their world through a different lens.

When the conditions for inquiry are created by allowing students to problem-find, problem-shape and problem-solve, it allows students to do the following:

• Critically examine their world to identify problems that exist
• Feel empowered because they realize that they can be part of a solution
• Innovate by developing new solutions to old problems

Put it All Together to Promote Change

Here are two examples of what my grade 11 students came up with when tasked with examining the national news to problem-find, problem-shape, and problem-solve.

Topic: Indigenous Issues in Canada

Question: How are Indigenous peoples impacted by racism?

Problem-find: The continued racism against Indigenous peoples has led to the families of murdered women not attaining justice, Indigenous peoples not being able to gain employment, and Indigenous communities not being able to access basic necessities like healthcare and clean water.

Problem-shape: A lot of the issues that Indigenous peoples face require government intervention. What can high school teens do to combat these issues?

Problem-solve: Teens need to stop supporting professional sports teams that tokenize Indigenous peoples, and if they see a peer wearing something from such a sports team, we need to educate them about how the team’s logo perpetuates racism.

Topic: People With Disabilities in Canada

Question: What leads students with a hearing impairment to feel excluded?

Problem-find: Students with a hearing impairment struggle to engage with course texts like films and videos.

Problem-shape: A lot of the issues that students with a hearing impairment face in schools require teachers to take action. What can high school teens do to help their hearing-impaired peers feel included?

Problem-solve: When teens share a video on social media, they should turn the closed-captioning on, so that all students can consume the media being shared.

Once my students came up with solutions, they wanted to do something about it and use their voices to engage in global citizenship. This led them to create TikTok and Snapchat videos and Instagram posts that they shared and re-shared among their peer group. 

The learning that students engaged in led to their wanting to teach others—which allowed a greater number of students to learn. This whole process engendered conversations about our world and helped them realize that they aren’t powerless; they can do things to initiate change in areas that they’re interested in and passionate about. It allowed them to use their voices to educate others and promote change.